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Transcript of The Works of Aristotle - Vol 8 - Editor William Ross
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JOHN M. KELLY LIBDAEY
University of
St. Michael s College, Toronto
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OXFORD UNIVERSITYPRESS
LONDON: AMEN HOUSE, E.G. 4
EDINBURGH GLASGOW LEIPZIG
COPENHAGEN NEW YORK TORONTO
MELBOURNE CAPETOWN BOMBAY
CALCUTTA MADRAS SHANGHAI
HUMPHREY MILFORDPUBLISHER TO THE
UNIVERSITY
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THE
WORKS OF ARISTOTLETRANSLATED INTO ENGLISH
UNDER THE EDITORSHIP
OF
W. D. ROSS, M.A., HON. LL.D. (EDIN.)
FELLOW OF ORIEL COLLEGE
FELLOW OF THE BRITISH ACADEMY
VOLUME VIII
METAPHYSICA
SECOND EDITION
OXFORD
AT THE CLARENDON PRESS
1928
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TO
INGRAM BYWATER
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PREFACE TO FIRST EDITION
WITH the permission of Messrs. Teubner I have followed in
this translation the text of W. Christ (Leipzig, 1895). All
divergences from his readings have been mentioned in the
notes, except that I have frequently left it to the rendering
itself to show that I have not followed his punctuation or his
excisions. The commentaries of Alexander and Bonitz havebeen my greatest help ;
but I owe much also to Bullinger s
notes, and to the translation of Book Z, chaps, i-xi, by
the late Mr. Richard Shute.
I wish to acknowledge my deep obligations to Mr. Bywater
and Prof. Cook Wilson, whose opinions on several difficult pas
sages
have been mostkindly placed
at
my disposal;to the mem
bers of the Oxford Aristotelian Society, for what I learnt from
them during our reading of Books M and N;to Mr. H. H.
Joachim, Fellow of Merton College, for the loan of his valuable
notes on Books Z, H, and;to Mr. C. Cannan, Secretary to
the Delegates of the University Press, and Mr. R. P. Hardie, of
Edinburgh University, whose comments on various parts of
the work have been of the greatest assistance to me;to my
co-editor Mr.J.
A. Smith, and to Dr. G. R. T. Ross, who have
read the whole book both in manuscript and in proof, and
whose suggestions I have adopted in countless passages ;and
to my wife, who has read the whole book in proof, and has
aided me very greatly in points of style.
W. D. R.
1908
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PREFACE TO SECOND EDITION
THE present edition of this translation is based on the text
published with my commentary on the Metaphysics (Oxford,
1924). The translation has been carefully revised throughout,
and brought into agreement with the commentary, except in
a very few places where later reflection has led me to revive
an old or to propose a new interpretation.
My thanks are due to the officials and staff of the Clarendon
Press for the care and skill shown in the production of the
work.
W. D. R.
1928
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CONTENTSCH. A.
1. The advance from sensation through memory, experience, and art, to
theoretical knowledge.
2. Characteristics of wisdom (philosophy).
3. The successive recognition by earlier philosophers of the material,
efficient, and final causes.
4. Inadequacy of the treatment of these causes.
5. The Pythagorean and Eleatic schools;the former recognizes vaguely
the formal cause.
6. The Platonic philosophy ;it uses only the material and formal causes.
7. The relation of the various systems to the four causes.
8. Criticism of the pre-Platonic philosophers.
9. Criticism of the doctrine of Ideas.
10. The history of philosophy reveals no causes other than the four.
a.
1. General considerations about the study of philosophy.
2. There cannot be an infinite series, nor an infinite variety of kinds, of
causes.
3. Different methods are appropriate to different studies.
B.
1. Sketch of the main problems of philosophy.
2. Fuller statement of the problems :
(i) Can one science treat of all the four causes ?
(ii) Are the primary axioms treated of by the science of substance,
and if not, by what science ?
(iii) Can one science treat of all substances?
(iv) Does the science of substance treat also of its attributes?
(v) Are there any non-sensible substances, and if so, of how manykinds ?
3. (vi) Are the genera, or the constituent paits, of things their first
principles ?
(vii) If the genera, is it the highest genera or the lowest ?
4. (viii) Is there anything apart from individual things?
(ix) Is each of the first principles one in kind, or in number ?
(x) Are the principles of perishable and of imperishable things the
same ?
(xi) Are being and unity substances or attributes?
5. (xii) Are the objects of mathematics substances ?
ix
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CONTENTSCH.
6. (xiii) Do Ideas exist, as well as sensible things and the objects of
mathematics ?
(xiv) Do the first principles exist potentially or actually ?
(xv) Are the first principles universal or individual ?
r.
1. Our object is the study of being as such.
2. We must therefore study primary being (viz. substance), unity and
plurality, and the derivative contraries, and the attributes of being
and of substance.
3. We must study also the primary axioms, and especially the law of
contradiction.
4. Fatal difficulties involved in the denial of this law.
5. The connexion of such denial with Protagoras doctrine of relativity ;
the doctrine refuted.
6. Further refutation of Protagoras.
7. The law of excluded middle defended.
8. All judgements are not true, nor are all false;
all things are not at
rest, nor are all in motion.
A.
Philosophical Lexicon.
1. Beginning.
2. Cause.
3. Element.
4. Nature.
5. Necessary.
6. One. Many.
7. Being.
8. Substance.
9. The same. Other. Different. Like. Unlike.
10. Opposite. Contrary. Other in species. The same in species.
11. Prior. Posterior.
12. Potency. Capable. Incapacity. Possible. Impossible.
13. Quantum.
14. Quality.
15. Relative.
16. Complete.
17. Limit.
18. That in virtue of which. In virtue of itself.
19. Disposition.
20. Having or habit (eis~).
21. Affection.
22. Privation.
23. Have or hold(ex*")-
Be in -
24. From.
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CONTENTSCH.
25. Part.
26. Whole. Total. All.
27. Mutilated.
28. Race or genus (yevos). Other in genus.
29. False.
30. Accident.
E.
1. Distinction of theology ,the science of being as such, from the other
theoretical sciences, mathematics and physics.
2. Four senses of being . Of these(i)
accidental being is the object
of no science.
3. The nature and origin of accident.
4. (ii) Being as truth is not primary being.
Z.
1. The study of being is primarily the study 01 substance.
2. Various opinions on the question, what things are substances ?
3. Four things are commonly held to be substantial the essence, the
universal, the genus, the substratum. The last may be conceived
as matter, form, or the concrete individual. Reasons why matter
and the concrete individual cannot be primary substance. Form
to be studied first in sensible things.
4. What is essence and to what does it belong, i. e. what things can be
defined ? Primarily substance.
5. Combinations of a subject with one of its proper attributes have no
definition nor essence.
6. Is a thing the same as its essence ? Yes, if it is a substance.
(7. Analysis of generation, whether by nature, art, or spontaneity.
8. Form is not generated, but put into matter; yet it did not previously
exist apart the agent in generation is form embodied in another
individual of the same species.
9. Why spontaneous generation sometimes takes place. The conditions
of generation in the categories other than substance.)
10. When are definitions of the parts included in the definition of the
whole ? When the parts are parts of the form.
1 1. Which parts are parts of the form, which of the concrete individual ?
12. Wherein consists the unity of an object of definition ? In the appro
priateness of the differentia to the genus.
13. A universal cannot be either the substance or an element in the sub
stance of anything (yet how else can a thing be defined ?).
14. Hence it is fatal to make Ideas substances and yet hold that they are
composed of other Ideas.
15. No individual can be defined, whether sensible or, like the Ideas,
intelligible.
xi
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CONTENTSCH.
16. The parts of sensible things are only potencies. Unity and being
are not the substance of things.
17. Substance is the cause or form which puts matter into a determinate
state;
it is that in a thing which is distinct from its material
elements.
H.
1. The discussion of sensible substances continued. Their matter is
itself substance.
2. The main types of form or actuality. Definitions of matter, of form,
and of the concrete individual distinguished.
3. Form distinguished from the material elements;Antisthenes attack
on definition;definition analogous to number.
4. Remote and proximate matter;the substratum of attributes not matter
but the concrete individual.
5. The relation of matter to its contrary states.
6. What gives unity to a definition ? The fact that the genus is simply the
potency of the differentia, the differentia the actuality of the genus.
0.
1. Being as potency and actuality. Potency in the strict sense, as
potency of motion, active or passive.
2. Non- rational potencies are single, rational potencies twofold.
3. Potency defended against the attack of the Megaric school.
4. Potency as possibility.
5. How potency is acquired, and the conditions of its actualization.
6. Actuality distinguished from potency ;a special type of potency
described;
actuality distinguishedfrom movement.
7. When one thing may be called the potency or matter of another;
how things are described by names derived from their matter
or their accidents.
8. Actuality prior to potency in definition, time, and substantiality ;
nothing eternal or necessary is a mere potency.
9. Good actuality better than potency, and bad actuality worse;therefore
no separate evil principle in the universe. Geometrical truths
found by actualization of potencies.10. Being as truth, with regard to both composite and simple objects.
I.
1. Four kinds of unit;theessenceof a unit is to be a measure of quantity
or of quality ;various types of measure.
2. Unity not a substance but a universal predicate ;its denotation the
same as that of being.
3. Unity and plurality ; identity ;
likeness;
otherness; difference.
4. Contrariety is complete difference;how related to privation and
contradiction.
xii
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CONTENTSCH.
5. The opposition ofJhe equal to the great and the small.
6. The opposition of the one to the many.
7. Intermediates are homogeneous with each other and with the
extremes, stand between contraries, and are compounded out of
these contraries.
8. Otherness in species is otherness 0/"the genus and is contrariety ;
its nature further described.
9. What contrarieties constitute otherness in species.
lo. The perishable and the imperishable differ in kind.
K.
1. Shorter form of B. 2, 3,
2. B. 4-6.
3. r. i, 2.
4, 5- r. 3j 4.
6. r. 5-8.
7. E. i.
8. E. 2-4.
Extracts fromPhysics
:
8. II. 5, 6, on luck.
9. III. 1-3, on potency, actuality, and movement,
10. III. 4, 5, 7, on the infinite; there is no actual infinite, and
especially no infinite body.
11. V. i, on change and movement.
12. V. 2, on the three kinds of movement.
V. 3, definitions of together in place , apart *,touch
,be
tween , contrary in place , successive ,
*
contiguous ,
continuous .
1. Substance the primary subject of inquiry. Three kinds of substance
perishable sensible, eternal sensible, and unmovable (non-
sensible).
2. Change implies not only form and privation but matter.
3. Neither matter nor form comes into being. Whatever comes into
being comes from a substance of the same kind. If form ever
exists apart from the concrete individual, it is in the case of
natural objects.
4. Different things have elements numerically different but the same
in kind; they all have form, privation, and matter. They also
have a proximate and an ultimate moving cause.
5. Again actuality and potency are principles common to all things,
though they apply differently in different cases. The principles of
all things are only analogous, not identical,
xiii
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CONTENTSCH.
6. Since movement must be eternal, there must be an eternal mover,
and one whose essence is actuality (actuality being prior to
potency). To account for the uniform change in the universe,
there must be one principle which acts always alike, and onewhose action varies.
7. The eternal mover originates motion by being the primary object of
desire (as it is of thought) ; being thoroughly actual, it cannot
change or move;
it is a living being, perfect, separate from
sensible things, and without parts.
8. Besides the first mover there must be as many unmoved movers
as there are simple motions involved in the motions of the planets.
The number is probably either 55 or 47. As there is but one
prime mover, there must be but one heaven.
9. The divine thought must be concerned with the most divine object,
which is itself. Thought and the object of thought are never
different when the ooject is immaterial.
10. How the good is present in the universe both as the order of the parts
and (more primarily) as their ruler. Difficulties which attend the
views of other philosophers.
M.
1. We pass to immaterial substance. Two kinds of immaterial
substances have been believed in, mathematical objects and
Ideas. We shall discuss first the former, then the latter, then
the view that numbers and Ideas are the substance of sensible
things.
2.(i) Mathematical objects cannot exist as distinct substances either in
or apart from sensible things.
3. They can be separated only in thought. Mathematics is not entirely
divorced from consideration of the beautiful, as is sometimes
alleged.
4. (ii) Arguments which led to the belief in Ideas. Some prove too
little, others too much.
5. Even if there were Ideas, they would not explain the changes in the
sensible world.
6. (iii) Various ways in which numbers may be conceived as the substanceof things.
7. (a) If all units are associable, this gives only mathematical, not ideal
number,(b) If all units are inassociable, this gives neither mathe
matical nor ideal number, (c) If only the units in the same
number are associable, this leads to equal difficulties;units must
have no difference of kind.
8. The views of Platonists who disagree with Plato, and those of the
Pythagoreans, lead to equal difficulties. Further objections to
ideal numbers : (a) How are the units derived from the indefinite
xiv
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CONTENTSCH.
dyad ? (b] Is the series of numbers infinite or finite;and if finite,
what is its limit ?(c) What sort of principle is the One ?
9. Discussion of the principles of geometrical objects. Criticism of the
generation of numbers from unity and plurality, and of spatial
magnitudes from similar principles. The criticism of ideal
numbers summed up. The upholders of Ideas make them at once
universal and individual.
10. Are the first principles of substances individual or universal ?
N.
1. The principles cannot be contraries. The Platonists in making them
contraries treated one of the contraries as matter. Various forms
of this theory. The nature of unity and plurality expounded.
2. Eternal substances cannot be compounded out of elements. The
object of the Platonists is to explain the presence of plurality in
the world, but in this they do not succeed. What justifies the
belief in the separate existence of numbers ?
3. Difficulties in the various theories of number. The Pythagoreans
ascribe generation to numbers, which are eternal.
4. The relation between the first principles and the good.
5. How is number supposed to be derived from its elements ? How is it
the cause of substances ?
6. The causal agency ascribed to numbers is purely fanciful.
xv
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BOOK A
I ALL men by nature desire to know. An indication of g8oa
this is the delight we take in our senses;for even apart
from their usefulness they are loved for themselves;and
above all others the sense of sight. For not only with a
view to action, but even when we are not going to do any- 25
thing, we prefer seeing (one might say) to everything else.
The reason is that this, most of all the senses, makes us
know and brings to light many differences between things.
By nature animals are born with the faculty of sensation,
and from sensation memory is produced in some of them,
though not in others. And therefore the former are more 98
intelligent and apt at learning than those which cannot
remember;
those which are incapable of hearing sounds
are intelligent though they cannot be taught, e. g. the bee,
and any other race of animals that may be like it;and those
which besides memory have this sense of hearing can be
taught.
The animals other than man live by appearances and 25
memories, and have but little of connected
experience;but
the human race lives also by art and reasonings. Now
from memory experience is produced in men;
for the
several memories of the same thing produce finally the
capacity for a single experience. And experience seems 98ia
pretty much like science and art, but really science and art
come to men throiigh experience ;for experience made
art , as Polus says,
1
but inexperience luck.
Now art 5
arises when from many notions gained by experience one
universal judgement about a class of objects is produced.
For to have a judgement that when Callias was ill of this
disease this did him good, and similarly in the case of
Socrates and in many individual cases, is a matter of experi
ence;but to judge that it has done good to all persons of 10
1Cf. PI. Gorg. 448 c, 462 BC.
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9 8ia METAPHYSICA
a certain constitution, marked off in one class, when they
were ill of this disease, e. g. to phlegmatic or bilious people
when burning with fever, this is a matter of art.
With a view to action experience seems in no respectin
ferior to art, and men of experience succeed even better
15 than those who have theory without experience. (The
reason is that experience is knowledge of individuals, art of
universals, and actions and productions are all concerned
with the individual;for the physician does not cure man,
except in an incidental way, but Callias or Socrates or
some other called by some such individual name, who20 happens to be a man. If, then, a man has the theory with
out the experience, and recognizes the universal but does not
know the individual included in this, he will often fail to
cure;for it is the individual that is to be cured.) But yet we
think that knowledge and understanding belong to art
25 rather than to experience, and we suppose artists to be
wiser than men of experience (which implies that Wisdom
depends in all cases rather on knowledge) ;and this because
the former know the cause, but the latter do not. For men
of experience know that the thing is so, but do not know
3o why, while the others know the 4
why and the cause. Hence
we think also that the master-workers in each craft are
more honourableand know in a truer sense and are wiser
98ib than the manual workers, because they know the causes of
the things that are done (we think the manual workers are
like certain lifeless things which act indeed, but act without
knowing what they do, as fire burns, but while the lifeless
things perform each of their functions by a natural tendency,
5 the labourers perform them through habit) ;
1 thus we view
them as being wiser not in virtue of being able to act, but
of having the theory for themselves and knowing the causes.
And in general it is a sign of the man who knows and of
the man who does not know, that the former can teach, and
therefore we think art more truly knowledge than experi
ence is;for artists can teach, and men of mere experience
cannot.
10 Again, we do not regard any of the senses as Wisdom;
1
98ib 2 TOVS ...
5 etfoy may be a later addition.
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BOOK A. I 981*
yet surely these give the most authoritative knowledge of
particulars. But they do not tell us the why ofanything
e. g. why fire is hot; they only say that it is hot.
At first he who invented any art whatever that went
beyond the common perceptions of man was naturally
admired by men, not only because there was something I5
useful in the inventions, but because he was thought wise
and superior to the rest. But as more arts were invented,
and some were directed to the necessities of life, others
to recreation, the inventors of the latter were naturally
always regardedas wiser than the inventors of the
former,because their branches of knowledge did not aim at utility.
Hence when all such inventions were already established, ao
the sciences which do not aim at giving pleasure or at the
necessities of life were discovered, and first in the places
where men first began to have leisure.1 This is why the
mathematical arts were founded in Egypt ;for there the
priestly caste was allowed to be at leisure.
We have said in the Ethics 2 what the difference is 25
between art and science and the other kindred faculties;
but the point of our present discussion is this, that all men
suppose what is called Wisdom to deal with the first causes
and the principles of things ;so that, as has been said
before, the man of experience is thought to be wiser than 30
the possessors of any sense-perception whatever, the artist
wiser than the men of experience, the master-worker than
the mechanic, and the theoretical kinds of knowledge to
be more of the nature of Wisdom than the productive.
Clearly then Wisdom is knowledge about certain principles 982*
and causes.
2 Since we are seeking this knowledge, we must inquire of 5
what kind are the causes and the principles, the knowledgeof which is Wisdom. If one were to take the notions we
have about the wise man, this might perhaps make the
answer more evident. We suppose first, then, that the wise
man knows all things, as far as possible, although he has not
1
Reading in 98 l b 23 ov Trpurov e
2
Ii39bi4-ii4i
b8.
B 2
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982a METAPHYSICA
10 knowledge of each of them in detail; secondly, that he who
can learn things that are difficult, and not easy for man to
know, is wise (sense-perception is common to all, and
therefore easy and no mark of Wisdom) ; again, that hewho is more exact and more capable of teaching the causes
is wiser, in every branch of knowledge ;and that of the
1 5 sciences, also, that which is desirable on its own account
and for the sake of knowing it is more of the nature of
Wisdom than that which is desirable on account of its
results, and the superior science is more of the nature of
Wisdom than the ancillary ;for the wise man must not be
ordered but must order, and he must not obey another, but
the less wise must obey hint.
20 Such and so many are the notions, then, which we have
about Wisdom and the wise. Now of these characteristics
that of knowing all things must belong to him wrho has in
the
highest degree
universal
knowledge;for he knows in
a sense all the instances that fall under the universal. And
these things, the most universal, are on the whole the
hardest for men to know;for they are farthest from the
25 senses. And the most exact of the sciences are those which
deal most with first principles ;for those which involve
fewer principles are more exact than those which involve
additional principles, e. g. arithmetic than geometry. Butthe science which investigates causes is also instritctive, in
a higher degree, for the people who instruct us are those
30 who tell the causes of each thing. And understanding and
knowledge pursued for their own sake are found most in
the knowledge of that which is most knowable (for he who
chooses to know for the sake of knowing will choose most
g82breadily that \vhich is most truly knowledge, and such is
the knowledge of that which is most knowable) ;and the
first principles and the causes are most knowable;for by
reason of these, and from these, all other things come to be
known, and not these by means of the things subordinate
to them. And the science which knows to what end each
5
thing
must be done is the most authoritative of the sciences,
and more authoritative than any ancillary science;and this
end is the good of that thing, and in general the supreme
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BOOK A. 2 g82b
good in the whole of nature. Judged by all the tests we
have mentioned, then, the name in question falls to the same
science;this must be a science that investigates the first
principles and causes; for the good, i. e. the end, is one of
i
the causes.
That it is not a science of production is clear even from
the history of the earliest philosophers. For it is owing to
their wonder that men both now begin and at first began to
philosophize ; they wondered originally at the obvious
difficulties, then advanced little by little and stated diffi
culties about the greater matters, e.g. about the phenomena J 5
ofthe moon and those of the sun and of the stars, and about
the genesis of the universe. And a man who is puzzled
and wonders thinks himself ignorant (whence even the lover
of myth is in a sense a lover of Wisdom, for the myth is
composed of wonders) ;therefore since they philosophized
in order to escape from ignorance, evidently they were 20
pursuing science in order to know, and not for any utili
tarian end. And this is confirmed by the facts;
for it was
when almost all the necessities of life and the things that
make for comfort and recreation had been secured, that
such knowledge began to be sought. Evidently then we do
not seek it for the sake of any other advantage ;but as the 25
man isfree, we say, who
exists for his
ownsake and not for
another s, so we pursue this as the only free science, for it
alone exists for its own sake.
Hence also the possession of it might be justly regarded
as beyond human power ;for in many ways human nature
is in bondage, so that according to Simonides l God alone 30
can have this privilege ,and it is unfitting that man should
not be content to seek the knowledge that is suited to him.
If, then, there is something in what the poets say, and
jealousy is natural to the divine power, it would probably 983**
occur in this case above all, and all who excelled in this
knowledge would be unfortunate. But the divine power
cannot be jealous (nay, according to the proverb,2 l bards
tell many a lie),nor should any other science be thought
more honourable than one of this sort. For the most 5
1Fr. 3 Hiller.
2Cf. Solon, fr. 26 Killer.
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983a METAPHYSICA
divine science is also most honourable; and this science
alone must be, in two ways, most divine. For the science
which it would be most meet for God to have is a divine
science, and so is any science that deals with divine objects;
and this science alone has both these qualities ;for
(i)God is
thought to be among the causes of all things and to be a
first principle, and (2) such a science either God alone can
10 have, or God above all others. All the sciences, indeed,
are more necessary than this, but none is better.
Yet the acquisition of it must in a sense end in something
which is the opposite of our original inquiries. For all
men begin, as we said, by wondering that things are as
15 they are, as they do about self-moving marionettes, or
about the solstices or the incommensurability of the diagonal
of a square with the side;for it seems wonderful to all who
have not yet seen the reason, that there is a thing which
cannot be measured even by the smallest unit. But we
must end in the contrary and, according to the proverb,1
the better state, as is the case in these instances too when
men learn the cause;
for there is nothing which would
ao surprise a geometer so much as if the diagonal turned out
to be commensurable.
We have stated, then, what is the nature of the science
we are searching for, and what is the mark which oursearch and our whole investigation must reach.
Evidently we have to acquire knowledge of the original 3
25 causes (for we say we know each thing only when we think
we recognize its first cause), and causes are spoken of in
four senses. In one of these we mean the substance, i. e.
the essence(for
the*
whyis reducible
finally
to the defini
tion, and the ultimate why is a cause and principle) ;in
30 another the matter or substratum, in a third the source of
the change, and in a fourth the cause opposed to this, the
purpose and the good (for this is the end of all generation
and change). We have studied these causes sufficiently in
our work on nature,2 but yet let us call to our aid those who
1 Cf. Leutsch and Schneidewin, Paroemiographi Graeci, i. 62, 234,
ii. 357-2
Phys. ii. 3, 7-
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BOOK A. 3 98ab
have attacked the investigation of being and philosophized
about reality before us. For obviously they too speak of
certain principles and causes;to go over their views, then,
will be ofprofit
to the
present inquiry,
for we shall either 5
find another kind of cause, or be more convinced of the
correctness of those which we now maintain.
Of the first philosophers, then, most thought the prin
ciples which were of the nature of matter were the only
principles of all things. That of which all things that are
consist, the first from which they come to be, the last into
which they are resolved (the substance remaining, but
changing in its modifications), this they say is the element 10
and this the principle of things, and therefore they think
nothing is either generated or destroyed, since this sort of
entity is always conserved, as we say Socrates neither comes
to be absolutely when he comes to be beautiful or musical,
nor ceases to be when he loses these characteristics, because 15
the substratum, Socrates himself, remains. Just so they say
nothing else comes to be or ceases to be;for there must be
some entity either one or more than one from which all
other things come to be, it being conserved.
Yet they do not all agree as to the number and the
nature of these principles. Thales, the founder of this type 20
of philosophy, says the principle is water (for which reason
he declared that the earth rests on water), getting the
notion perhaps from seeing that the nutriment of all things
is moist, and that heat itself is generated from the moist and
kept alive by it (and that from which they come to be is
a principle of all things). He got his notion from this fact, 25
and from the fact that the seeds of all things have a moist
nature,and that water is the
originof the nature of moist
things.
Some l think that even the ancients who lived long before
the present generation, and first framed accounts of the
gods, had a similar view of nature;for they made Ocean 3
and Tethys the parents of creation,2 and described the oath
1
The reference is probably to Plato (Crat. 4026, Theaet. 152 E,162 D, i8oc).
2Horn. //. xiv. 201, 246.
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g8ab METAPHYSICA
of the gods as being by water,1to which they give the
name of Styx ;for what is oldest is most honourable, and
the most honourable thing is that by which one swears. It
984** may perhaps be uncertain whether this opinion aboutnature is primitive and ancient, but Thales at any rate is
said to have declared himself thus about the first cause.
Hippo no one would think fit to include among these
thinkers, because of the paltriness of his thought.
5Anaximenes and Diogenes make air prior to water, and
the most primary of the simple bodies, while Hippasus of
Metapontium and Heraclitus of Ephesus say this of fire, and
Empedocles says it of the four elements (adding a fourth
earth to those which have been named) ;for these, he
says, always remain and do not come to be, except that
TOthey come to be more or fewer, being aggregated into one
and segregated out of one.
Anaxagorasof Clazomenae, who,
thougholder than
Empedocles, was later in his philosophical activity, says the
principles are infinite in number;for he says almost all the
things that are made of parts like themselves, in the manner
of water or fire, are generated and destroyed in this
i 5 way, only by aggregation and segregation, and are not
in any other sense generated or destroyed, but remain
eternally.
From these facts one might think that the only cause is
the so-called material cause;but as men thus advanced, the
very facts opened the way for them and joined in forcing
them to investigate the subject. However true it may be
20 that all generation and destruction proceed from some one
or (for that matter) from more elements, why does this
happen and what is the cause ? For at least the substratum
itself does not make itself change ;e. g. neither the wood
nor the bronze causes the change ofeither of them, nor does
the wood manufacture a bed and the bronze a statue, but
25 something else is the cause of the change. And to seek
this is to seek the second cause, as we should say, that
from which comes the
beginning
of the movement. Nowthose who at the very beginning set themselves to this kind
1Ibid. ii. 755, xiv. 271, xv. 37.
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BOOK A. 3 g84a
of inquiry, and said the substratum was one,1 were not at
all dissatisfied with themselves;but some at least of those
who maintain it to be one 2 as though defeated by this 30
searchfor
thesecond
causesay
the one and nature as
a whole is unchangeable not only in respect of generation
and destruction (for this is a primitive belief, and all agreed
init), but also of all other change ;
and this view is peculiar
to them. Of those who said the universe was one, then,
none succeeded in discovering a cause of this sort, except
perhaps Parmenides, and he only inasmuch as he supposes
that there is not only one but also in some sense two causes.
But for those who make more elements 3it is more possible 5
to state the second cause, e. g. for those who make hot and
cold, or fire and earth, the elements;for they treat fire as
having a nature which fits it to move things, and water and
earth and such things they treat in the contrary way.
When these men and the principles of this kind had had
their day, as the latter were found inadequate to generate
the nature of things men were again forced by the truth 10
itself, as we said,4to inquire into the next kind of cause.
For it is not likely either that fire or earth or any such
element should be the reason why things manifest goodness
and beauty both in their being and in their coming to be,
or that those thinkers should havesupposed
it was;nor
again could it be right to entrust so great a matter to
spontaneity and chance. When one man 5said, then, that 15
reason was present as in animals, so throughout nature
as the cause of order and of all arrangement, he seemed
like a sober man in contrast with the random talk of his
predecessors. We know that Anaxagoras certainly adopted
these views, but Hermotimus ofClazomenae is credited with
expressing them earlier. Those who thought thus stated 20
that there is a principle of things which is at the same time
the cause of beauty, and that sort of cause from which
things acquire movement.
4 One might suspect that Hesiod was the first to look for
1
Thales, Anaximenes, and Heraclitus.
2
The Eleatics.3 The reference is probably to Empedocles4 a
i8.5
Anaxagoras ;cf. esp. fr. 12.
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984b METAPHYSICA
such a thing or some one else who put love or desire
among existing things as a principle, as Parmenides, too,
25 does; for he, in constructing the genesis of the universe,
saysl
:
Love first of all the Gods she planned.
And Hesiod says2
:
First of all things was chaos made, and then
Broad-breasted earth, . . .
And love, mid all the gods pre-eminent,
30 which implies that
amongexisting things there must be
from the first a cause which will move things and bring
them together. How these thinkers should be arranged
with regard to priority of discovery let us be allowed to
decide later;
* but since the contraries of the various forms
of good were also perceived to be present in nature not
only order and the beautiful, but also disorder and the ugly,
985 and bad things in greater number than good, and ignoble
things than beautiful therefore another thinker introduced
friendship and strife, each of the two the cause of one of
these two sets of qualities. For if we were to follow out
the view of Empedocles, and interpret it according to its
5 meaning and not to its lisping expression, we should find
that friendship is the cause of good things, and strife ofbad.
Therefore, ifwe said that Empedocles in a sense both men
tions, and is the first to mention, the bad and the good as
principles, we should perhaps be right, since the cause of
all goods is the good itself.
10 These thinkers, as we say, evidently grasped, and to this
extent, two of the causes which we distinguished in our
work on nature4
the matter and the source of the move
ment vaguely, however, and with no clearness, but as
untrained men behave in fights ;for they go round their
15 opponents and often strike fine blows, but they do not fight
on scientific principles, and so too these thinkers do not
seem to know what they say ;for it is evident that, as a
rule, they make no use of their causes except to a small
1Fr. 13.
2
Theog. 116-120.3 The promise is not fulfilled.
*
Phys. ii. 3, 7.
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BOOK A. 4 985
extent. For Anaxagoras uses reason as a deus ex machina
for the making- of the world, and when he is at a loss to tell
from what cause something necessarily is, then he drags20
reasonin,
but in all other cases ascribes events to
anything rather than to reason.
1 And Empedocles, though
he uses the causes to a greater extent than this, neither
does so sufficiently nor attains consistency in their use. At
least, in many cases he makes love segregate things, and
strife aggregate them. For whenever the universe is dis- 25
solved into its elements by strife, fire is aggregated into
one, and so is each of the other elements ; but whenever
again under the influence of love they come together
into one, the parts must again be segregated out of each
element.
Empedocles, then, in contrast with his predecessors, was
the first to introduce the dividing of this cause, not positing 30
one source ofmovement, but different and contrary sources.
Again, he was the first to speak of four material elements;
yet he does not use four, but treats them as two only ;he
treats fire by itself, and its opposites -earth, air, and water
as one kind of thing. We may learn this by study of his
verses.2
This philosopher then, as we say, has spoken of the
principles in this way, and made them of this number.
Leucippus and his associate Democritus say that the full 5
and the empty are the elements, calling the one being and
the other non-being the full and solid being being, the
empty non-being (whence they say being no more is than
non-being, because the solid no more is than the empty) ;
and they make these the material causes of things. And as 10
those who make the underlying substance one generate all
other things by its modifications, supposing the rare and
the dense to be the sources of the modifications, in the same
way these philosophers say the differences in the elements
are the causes of all other qualities. These differences, they
say, are three shape and order and position. For they 15
say the real is differentiated only by rhythm and inter-
1Cf. PI. PhaedO) 98 BC, Laws, 967 B-D.
2Cf. fr. 62.
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985b METAPHYSICA
contact and turning ;and of these rhythm is shape,
inter-contact is order, and turning is position ;for A differs
from N in shape, AN from NA in order, HJ from H in
position.The
questionof
movementwhence or
howit is
to belong to things these thinkers, like the others, lazily
neglected.
20 Regarding the two causes, then, as we say, the inquiry
seems to have been pushed thus far by the early philo
sophers.
Contemporaneously with these philosophers and before 5
them, the so-called Pythagoreans, who were the first to take
up mathematics, not only advanced this study, but also
25 having been brought up in it they thought its principles
were the principles of all things. Since of these principles
numbers are by nature the first, and in numbers they
seemed to see
manyresemblances to the
thingsthat exist
and come into being more than in fire and earth and
water (such and such a modification of numbers being
30 justice, another being soul and reason, another being oppor
tunity and similarly almost all other things being numeri
cally expressiblel
) ; since, again, they saw that the
modifications and the ratios of the musical scales were
expressible in numbers ; since, then, all other things
seemed in their whole nature to be modelled on numbers,
and numbers seemed to be the first things in the whole of
g86anature, they supposed the elements of numbers to be the
elements of all things, and the whole heaven to be a musical
scale and a number. And all the properties of numbers
and scales which they could show to agree with the attri-
5 butes and parts and the whole arrangement of the heavens,
they collected and fitted into their scheme;and if there
was a gap anywhere, they readily made additions so as to
make their whole theory coherent. E.g. as the number 10
is thought to be perfect and to comprise the whole nature
ic of numbers, they say that the bodies which move throughthe heavens are
ten,but as
the visible bodiesare
only nine,
1Cf. Diels, Vorsokratiker, ed. 3, i. 303. 15-19.
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BOOK A. 5 g86a
to meet this they invent a tenth the*
counter-earth . Wehave discussed these matters more exactly elsewhere.
1
But the object of our review is that we may learn from
these philosophers also what they suppose to bethe
prin
ciples and how these fall under the causes we have named. 15
Evidently, then, these thinkers also consider that number is
the principle both as matter for things and as forming both
their modifications and their permanent states, and hold
that the elements of number are the even and the odd, and
that of these the latter is limited, and the former unlimited;
and that the One proceeds from both of these (for it is both
even and odd), and number from the One;and that the 20
whole heaven, as has been said, is numbers.
Other members of this same school say there are ten
principles, which they arrange in two columns ofcognates2
limit and unlimited, odd and even, one and plurality,
right and left, male and female, resting and moving, straight 25
1 De Caelo, ii. 13; Fr. de Pythagoreis, ii. I5i3a4.o-
b 20. Cf. Diels,
ibid. 347. 3-11.2
arvo-Toi\in and o-to-roi^o? are used in a great variety ofconnexions byAristotle, but the common notion is that of things which from some point
of view may be treated as forming one line or column. The meaningsin the Metaphysics may be summarized thus :
In A. g86a23, N. ic93
b 12 the reference is to a Pythagorean classifica
tion of important general notions. The first column is the line of good
(f) (Tvoroi^ta TI TOV KaXoO, N. io93
b
12), the second the line of evil. Tothe line of good N. io93b13 adds the equal and the potencies of
certain numbers .
In r. ioo4b27, K. io66a 15, A. io72
a31 there is no explicit reference
to the Pythagorean doctrine, but Aristotle speaks of two lines,one
of which is knowable in itself, while the other is privative ,and its
*
principles are indefinite because they are privative .
In I. I054b35, 1058*13 we have a different sort of line. Terms
which in the strict sense differ are said to be either different in genusor in the same line of predication, and therefore in the same genus ;
and contraries which differ in species and not in genus are said to bein the same line of predication, o-uorot^ia rfjs Karr^yopias seems to
correspond to V\THJM rr}? Karrjyopins (lo54b29), which is said in A.
Ioi6b 33 to be coextensive with a ycvos. It is at first sight surprisingto find genus identified with category, and one is tempted to suggestthat orvtTTotxia (or o-^/ua) TTJS KaTr)yopis means one of the main divisions
of a category, within which the same sort of predicate is found. Thusnumber would be the genus within which the predicates odd and even,and various subordinate predicates, are found. Then the subordinate
predicates might be thought of as forming a column under odd and
even.
But A. io24b 12-16 shows that genus in one sense can beidentified with category. The categories are the only genera proper,since they are the only genera which are not species.
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986a METAPHYSICA
and curved, light and darkness, good and bad, square and
oblong. In this way Alcmaeon of Croton seems also to
have conceived the matter, and either he got this view from
30 them or they gotit
from him; for he expressed himself
similarly to them. For he says most human affairs go in
pairs, meaning not definite contrarieties such as the Pytha
goreans speak of, but any chance contrarieties, e. g. white
and black, sweet and bitter, good and bad, great and small.
He threw out indefinite suggestions about the other con-
g86btrarieties, but the Pythagoreans declared both how many
and which their contrarieties are.
From both these schools, then, we can learn this much,
that the contraries are the principles of things ;and how
many these principles are and which they are, we can learn
from one of the two schools. But how these principles can
5 be brought together under the causes we have named has
not been clearly and articulately stated by them; they
seem, however, to range the elements under the head of
matter;for out of these as immanent parts they say sub
stance is composed and moulded.
From these facts we may sufficiently perceive the mean
ing of the ancients who said the elements of nature were
10 more than one;
but there are some who spoke of the
universe asif it
were one entity, though they were not all
alike either in the excellence of their statement or in its
conformity to the facts of nature. The discussion of them
is in no way appropriate to our present investigation of
causes, for they do not, like some of the natural philo
sophers, assume being to be one and yet generate it out of
15 the one as out of matter, but they speak in another way ;
those others add change, since they generate the universe,
but these thinkers say the universe is unchangeable. Yet
this much is germane to the present inquiry : Parmenides
seems to fasten on that which is one in definition,
a Melissus on that which is one in matter, for which reason
the former says that it is limited, the latter that it is
unlimited;
:while Xenophanes, the first of these partisans
of the One (for Parmenides is said to have been his pupil),
1Cf. Phys. 185* 32-
b3, 2o;
a15-17.
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BOOK A. 5 g86b
gave no clear statement, nor does he seem to have grasped
the nature of either of these causes, but with reference to
the whole material universe he says the One is God. Now 25
these thinkers, as we said, must be neglected for the pur
poses of the present inquiry two of them entirely, as being
a little too naive, viz. Xenophanes and Melissus;but Par-
menides seems in places to speak with more insight. For,
claiming that, besides the existent, nothing non-existent
exists, he thinks that of necessity one thing exists, viz. the
existent and nothing else (on this we have spoken more 30
clearly in our work on nature),1 but being forced to follow
the observed facts, and supposing the existence of that
which is one in definition, but more than one according to
our sensations, he now posits two causes and two principles,
calling them hot and cold, i. e. fire and earth;and of these
he ranges the hot with the existent, and the other with the 987**
non-existent.
From what has been said, then, and from the wise men
who have now sat in council with us, we have got thus
much on the one hand from the earliest philosophers, who
regard the first principle as corporeal (for water and fire
and such things are bodies), and of whom some supposes
that there is one corporeal principle, others that there are
more than one, but both put these under the head of matter;
and on the other hand from some who posit both this cause
and besides this the source of movement, which we have got
from some as single and from others as twofold.
Down to the Italian school, then, and apart from it,
philosophers have treated these subjects rather obscurely, 10
except that, as we said, they have in fact used two kinds of
cause, and one of these the source of movement sometreat as one and others as two. But the Pythagoreans have
said in the same way that there are two principles, but
added this much, which is peculiar to them, that they 15
thought that finitude andinfinity were not attributes of
certain other things, e. g. of fire or earth or anything else
of this kind, but that infinity itself and unity itself were the
1
Phys. i. 3.
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987a METAPHYSICA
substance of the things of which they are predicated. This
is why number was the substance of all things. On this
20 subject, then, they expressed themselves thus;and regarding
the question of essence they began to make statements anddefinitions, but treated the matter too simply. For they
both defined superficially and thought that the first subject
of which a given definition was predicable was the sub
stance of the thing defined, as if one supposed thatl
double
and 2 were the same, because 2 is the first thing of which
25 double is predicable. But surely to be double and to be
2 are not the same ;if they are, one thing will be many l
a consequence which they actually drew.2 From the earlier
philosophers, then, and from their successors we can learn
thus much.
After the systems we have named came the philosophy 6
30 of Plato, which in most respects followed these thinkers,
but had peculiarities that distinguished it from the philo
sophy of the Italians. For, having in his youth first become
familiar with Cratylus and with the Heraclitean doctrines
(that all sensible things are ever in a state of flux and there
is no knowledge about them), these views he held even in
later years. Socrates, however, was busying himself about
ethical matters and neglecting the world of nature as a whole
but seeking the universal in these ethical matters, and fixed
thought for the first time on definitions;Plato accepted his
5 teaching, but held that the problem applied not to sensible
things but to entities of another kind for this reason, that
the common definition could not be a definition of any
sensible thing, as they were always changing. Things of
this othersort, then,
he calledIdeas,
and sensiblethings,
he
said, were all named after these, and in virtue of a relation
to these;for the many existed by participation in the
10 Ideas that have the same name as they. Only the name
participation was new;for the Pythagoreans say that
things exist by*
imitation of numbers, and Plato says they
exist by participation, changing the name. But what the
1i. e. 2 will be each of several things whose definition is predicable
of it.
2
e.g. 2 was identified both with opinion and with daring.
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BOOK A. 6 g87b
participation or the imitation of the Forms could be they
left an open question.
Further, besides sensible things and Forms he says there
are the objects of mathematics, which occupy an inter- 15
mediate position, differing1
from sensible things in being
eternal and unchangeable, from Forms in that there are
many alike, while the Form itself is in each case unique.
Since the Forms were the causes of all other things, he
thought their elements were the elements of all things. As 20
matter, the great and the small were principles ;as essen
tial reality, the One ; for from the great and the small, by
participation in the One, come the Numbers.
But he agreed with the Pythagoreans in saying that the
One is substance and not a predicate of something else;
and in saying that the Numbers are the causes of the
reality of other things he agreed with them;but positing 25
a dyad and constructing the infinite out of great and small,
instead of treating the infinite as one, is peculiar to him;
and so is his view that the Numbers exist apart from sensible
things, while they say that the things themselves are Num
bers, and do not place the objects of mathematics between
Forms and sensible things. His divergence from the 30
Pythagoreans in making the One and the Numbers separate
fromthings,
and his introduction of the
Forms,were due to
his inquiries in the region of definitions(for the earlier
thinkers had no tincture of dialectic), and his making the
other entity besides the One a dyad was due to the belief
that the numbers, except those which were prime,1could be
neatly produced out of the dyad as out of some plastic
material.
Yet what happens is the contrary ; the theory is not a 988*
reasonable one. For they make many things out of the
matter, and the form generates only once, but what we
1This is not quite accurate. Really it is only 2 and its powers that
could be neatly produced out of the I and the indefinite dyad ;cf.
N. 109^9-12. In Parmenides 143 C-I44A, 3 is derived from I and 2
(the number 2, not, as Aristotle says, the indefinite 2) by addition, andthe numbers higher than 3 are derived from 2 and 3 by multiplication.
Primes are not there excepted ; Plato speaks as if all the highernumbers could be got by multiplication. Nothing in the works of
Plato corresponds exactly to what Aristotle says here.
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988a METAPHYSICA
observe is that one table is made from one matter, while the
man who applies the form, though he is one, makes many
5 tables. And the relation of the male to the female is
similar; for the latter is impregnated by one copulation,
but the male impregnates many females; yet these are
analogues of those first principles.
Plato, then, declared himself thus on the points in ques
tion;
it is evident from what has been said that he has used
only two causes, that of the essence and the material cause
10
(for
the Forms are the causes of the essence of all other
things, and the One is the cause of the essence of the
Forms) ;and it is evident what the underlying matter is, of
which the Forms are predicated in the case of sensible
things, and the One in the case of Forms, viz. that this is a
dyad, the great and the small. Further, he has assigned the
cause of good and that of evil to the elements, one to each
15 of the two, as we say1
some of his predecessors sought to
do, e. g. Empedocles and Anaxagoras.
Our review of those who have spoken about first prin- 7
ciples and reality and of the way in which they have
20 spoken, has been concise and summary ;but yet we have
learnt this much from them, that of those \vho speak about
4
principle and
*
causeno one has mentioned any principle
except those which have been distinguished in our work
on nature,2 but all evidently have some inkling of them^
though only vaguely. For some speak of the first prin
ciple as matter, whether they suppose one or more first
25 principles, and whether they suppose this to be a body or
to be incorporeal ;e. g. Plato spoke of the great and the
small, the Italians of the infinite, Empedocles of fire, earth,
water, and air, Anaxagoras of the infinity of things com
posed of similar parts. These, then, have all had a notion
of this kind of cause, and so have all who speak of air or
30 fire or water, or something denser than fire and rarer than
air;for some have said the prime element is of this kind.
3
1
Cf. 984b i5-i9, 32-b 10.2
Phys. ii. 3, 7.3
Cf. Diels, Vorsokratiker, ed. 3, i. 18. 8-21, 415. 32-416. 27. Thereference is probably to some follower of \naximenes.
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BOOK A. 7 988a
These thinkers grasped this cause only ;but certain
others have mentioned the source of movement, e. g. those
who make friendship and strife, or reason, or love, a principle.
The essence, i. e. the substantial reality, no one has expressed distinctly. It is hinted at chiefly by thosewho believe 35
in the Forms;for they do not suppose either that the Forms g88
b
are the matter of sensible things, and the One the matter of
the Forms, or that they are the source of movement (for
they say these are causes rather of immobility and of
being at rest), but they furnish the Forms as the essence of
every other thing, and the One as the essence of the Forms. 5
That for whose sake actions and changes and movements
take place, they assert to be a cause in a way, but not in
this way, i. e. not in the way in which it is its nature to be
a cause. For those who speak of reason or friendship
class these causes as goods ; they do not speak, however,
as if anything that exists either existed or came into being
for the sake of these, but as if movements started from 10
these. In the same way those who say the One or the
existent is the good, say that it is the cause of substance,
but not that substance either is or comes to be for the sake
of this. Therefore it turns out that in a sense they both
say and do not say the good is a cause;for they do not 15
call it a cause
qua goodbut
only incidentally.All these thinkers, then, as they cannot pitch on another
cause, seem to testify that we have determined rightly both
how many and of what sort the causes are. Besides this it
is plain that when the causes are being looked for, either
all four must be sought thus or they must be sought in one
of these four ways. Let us next discuss the possible diffi- *o
culties with regard to the way in which each of these
thinkers has spoken, and with regard to his situation rela
tively to the first principles.
8 Those, then, who say the universe is one and posit one
kind of thing as matter, and as corporeal matter which has
spatial magnitude, evidently go astray in many ways. For
they posit the elements of bodies only, not of incorporeal 35
things, though there are also incorporeal things. And in
c 2,
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988b METAPHYSICA
trying to state the causes of generation and destruction,
and in giving a physical account of all things, they do
away with the cause of movement. Further, they err in not
positing the substance, i.e. the essence, as the cause ofany
thing, and besides this in lightly calling any of the simple
30 bodies except earth the first principle, without inquiring
how they are produced out of one another, I mean fire,
water, earth, and air. For some things are produced out
of each other by combination, others by separation, and this
makes the greatest difference to their priority and pos-
35 teriority. For (i) in a way the property of being most
elementary of all would seem to belong to the first thing
g8ga from which they are produced by combination, and this
property would belong to the most fine-grained and subtle
of bodies. For this reason those who make fire the prin
ciple would be most in agreement with this argument.
But each of the other thinkers agrees that the element of5 corporeal things is of this sort. At least none ofthose who
named one element claimed that earth was the element,
evidently because of the coarseness of its grain. (Of the
other three elements each has found some judge on its side;
for some maintain that fire, others that water, others that
air is the element. Yet why, after all, do they not name
earth also, as most men do ? For people say all things are
10 earth. And Hesiod sayslearth was produced first of cor
poreal things ;so primitive and popular has the opinion
been.) According to this argument, then, no one would
be right who either says the first principle is any of the
elements other than fire, or supposes it to be denser than
15 air but rarer than water. But (2) if that which is later in
generation is prior in nature, and that which is concocted
and compounded is later in generation, the contrary of
what we have been saying must be true, water must be
prior to air, and earth to water.
So much, then, for those who posit one cause such as we
mentioned;but the same is true if one supposes more of
20
these,as
Fmpedocles says the matter of thingsis
fourbodies. For he too is confronted by consequences some of
1
Theog. 1 1 6.
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BOOK A. 8 989
which are the same as have been mentioned, while others
are peculiar to him. For we see these bodies produced
from one another, which implies that the same body
does not
always
remain fire or earth (we have spoken about
this in our works on naturel
) ;and regarding the cause of 25
movement and the question whether we must posit one or
two, he must be thought to have spoken neither correctly
nor altogether plausibly. And in general, change of quality
is necessarily done away with for those who speak thus,
for on their view cold will not come from hot nor hot from
cold. For if it did there would be something that acceptedthe contraries themselves, and there would be some one
entity that became fire and water, which Empedocles denies.2
As regards Anaxagoras, if one were to suppose that he 3
said there were two elements, the supposition would accord
thoroughly with an argument which Anaxagoras himself
did not state articulately, but which he must have accepted
if any one had led him on to it. True, to say that in the
beginning all things were mixed is absurd both on other
grounds and because it follows that they must have existed
before in an unmixed form, and because nature does not
allow any chance thing to be mixed with any chance
thing, and also because on this view modifications and
accidents could be separated from substances (for the same
things which are mixed can be separated ) ; yet if one
were to follow him up, piecing together what he means,
he would perhaps be seen to be somewhat modern in his 5
views. For when nothing was separated out, evidently
nothing could be truly asserted of the substance that then
existed. I mean, e. g.,that it was neither white nor black,
norgrey
norany
othercolour,
but ofnecessity
colourless;
for if it had been coloured, it would have had one of these
colours. And similarly, by this same argument, it was 10
flavourless, nor had it any similar attribute;for it could
not be either of any quality or of any size, nor could it be
any definite kind of thing. For if it were, one of the
particular forms would have belonged to it, and this is
impossible, since all were mixed together ; for the par-1 De Caelo, iii. 7.
2
989* 26 oAo>? ... 30 (prjaiv is possibly a gloss.
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989b METAPHYSICA
ticular form would necessarily have been already separated
15 out, but he says all were mixed except reason, and this
alone wras unmixed and pure.1 From this it follows, then,
that he mustsay
theprinciples
are the One(for
this is
simple and unmixed) and the Other, which is of such a
nature as we suppose the indefinite to be before it is defined
and partakes of some form. Therefore, while expressing
himself neither rightly nor clearly, he means something like
20 what the later thinkers say and what is now more clearly
seen to be the case.
But these thinkers are, after all, at home only in arguments about generation and destruction and movement
;
for it is practically only of this sort of substance that they
seek the principles and the causes. But those who extend
25 their vision to all things that exist, and of existing things
suppose some to be perceptible and others not perceptible,
evidently study both classes, which is all the more reason
why one should devote some time to seeing what is good in
their views and what bad from the standpoint of the inquiry
we have now before us.
The Pythagoreans treat of principles and elements
3o stranger than those of the physical philosophers (the reason
is that they got the principles from non-sensible things, for
theobjects
ofmathematics, except
those ofastronomy,
are
of the class of things without movement) ; yet their dis
cussions and investigations are all about nature;for they
99a
generate the heavens, and with regard to their parts and
attributes and functions they observe the phenomena, and use
up the principles and the causes in explaining these, which
implies that they agree with the others, the physical philo
sophers, that the real is just all that which is perceptible
5 and contained by the so-called heavens . But the causes
and the principles which they mention are, as we said,2
sufficient to act as steps even up to the higher realms of
reality, and are more suited to these than to theories about
nature. They do not tell us at all, however, how there can
be movement if limit and unlimited and odd and even are
10 the only things assumed, or how without movement and
1Fr. 12.
8
99b3i-3.
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BOOK A. 8 ggoa
change there can be generation and destruction, or the
bodies that move through the heavens can do what they do.
Further, if one either granted them that spatial magnitude consists of these elements, or this were proved, still
how would some bodies be light and others have weight ?
To judge from what they assume and maintain they are 15
speaking no more of mathematical bodies than of percep
tible;hence they have said nothing whatever about fire or
earth or the other bodies of this sort, I suppose because
they have nothing to say which applies peculiarly to per
ceptible things.
Further, how are we to combine the beliefs that the
attributes of number, and number itself, are causes of what 20
exists and happens in the heavens both from the beginning
and now, and that there is no other number than this
number out of which the world is composed ? When in
one particular region they place opinion and opportunity,
and, a little above or below, injustice and decision or mixture, and allege, as proof, that, each of these is a number,
and that there happens to be already in this place a plurality 25
of the extended bodies composed of numbers, because these
attributes ofnumber attach to the various places, this being
so, is this number, which we must suppose each of these
abstractions to be, the same number which is exhibited in
the material universe, or is it another than this ? Plato says
it is different; yet even he thinks that both these bodies 30
and their causes are numbers, but that the intelligible num
bers are causes, while the others are sensible.
9 Let us leave the Pythagoreans for the present ;for it is
enough to have touched on them as much as we have done.
But as for those who posit the Ideas as causes, firstly,in 99O
b
seeking to grasp the causes of the things around us, they
introduced others equal in number to these, as if a man who
wanted to count things thought he would not be able to do
it while they were few, but tried to count them when
he had added to their number. For the Forms are practi
cally equal to or not fewer than the things,in
tryingto
5
explain which these thinkers proceeded from them to the
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99ob METAPHYSICA
Forms. For to each thing there answers an entity which
has the same name and exists apart from the substances,
and so also in the case of all other groups there is a one
over
many,whether the
manyare in this world or are
eternal.
Further, of the ways in which we l
prove that the Forms
10exist, none is convincing ;
for from some no inference
necessarily follows, and from some arise Forms even of
things of which we think there are no Forms. For accord
ing to the arguments from the existence of the sciences
there will be Forms of all things of which there are sciences,
and according to the one over many argument there will
be Forms even of negations, and according to the argu
ment that there is an object for thought even when the
thing has perished, there will be Forms ofperishable things ;
15 for we have an image of these. Further, of the more accu
rate arguments, some lead to Ideas of relations, of which
we say there is no independent class, and others introduce
the*
third man .
2
And in general the arguments for the Forms destroy the
things for whose existence we are more zealous than for the
existence of the Ideas;for it follows that not the dyad
3 but
20 number is first, i. e. that the relative is prior to the abso
lute,4
besides all the otherpoints
on which certain
peopleby following out the opinions held about the Ideas have
come into conflict with the principles of the theory.
Further, according to the assumption on which our
belief in the Ideas rests, there will be Forms not only of
substances but also of many other things (for the concept is
25 single not only in the case of substances but also in the
other cases, and there are sciences not only of substance butalso of other things, and a thousand other such difficulties
confront them). But according to the necessities of the
1Aristotle speaks as a Platonist.
2Cf. Z. I039
a2, Soph. EL i;8
b36-179* 10, and Plato Farm. 132 AB,
D-ISSA.3
Sc. the*
indefinite 2 which Plato held to be one of the first prin
ciples of number.4
i.e. number, which is relative, is prior to the indefinite 2, which
Plato held to be an absolute first principle.
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BOOK A. 9 990b
case and the opinions held about the Forms, if Forms can
be shared in there must be Ideas of substances only. For
they are not shared in incidentally, but a thing must share 30
in its Form as in something
1
not predicated of a subject (by*
being shared in incidentally I mean that e. g.if a thing
shares in double itself, it shares also in eternal,but
incidentally ;for eternal happens to be predicable of the
double).
Therefore the Forms will be substance;but
the same terms indicate substance in this and in the ideal
world (or what will be the meaning of saying that there is 991
something apart from the particulars the one over many P).1
And if the Ideas and the particulars that share in them have
the same form, there will be something common to these;
for why should 2 be one and the same in the perishable
2 s or in those which are many but eternal, and not the
same in the 2 itself as in the particular 2 ? But if they 5
have not the same form, they must have only the name in
common, and it is as if one were to call both Callias and
a wooden image a man,without observing any com
munity between them.2
Above all one might discuss the question what on earth
the Forms contribute to sensible things, either to those that
are eternal or to those that come into being and cease to I0
be. Forthey
cause neither
movementnor
any changein
them. But again they help in no wise either towards the
knowledge of the other things (for they are not even the
substance of these, else they would have been in them), or
towards their being, if they are not in the particulars which
share in them; though if the) were, they might be thought
to be causes, as white causes whiteness in a white object 15
by entering into its composition. But this argument, whichfirst Anaxagoras and later Eudoxus and certain others
used, is very easily upset ;for it is not difficult to collect
many insuperable objections to such a view.
But, further, all other things cannot come from the
1This seems to be an enthymeme, the conclusion to be supplied
being that the Forms, since they are substances, must be of substances.
2 With 99ob2~99i
a8 cf. M. io;8
b34-io79
b3.
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99ia METAPHYSICA
20 Forms in any of the usual senses of from . And to say
that they are patterns and the other things share in them is
to use empty words and poetical metaphors. For what is
it
that works, looking to the Ideas ? And anything caneither be, or become, like another without being copied
25 from it, so that whether Socrates exists or not a man like
Socrates might come to be;and evidently this might be so
even if Socrates were eternal. And there will be several
patterns of the same thing, and therefore several Forms;
e. g. animal and two-footed and also* man himself will
be Forms of man. Again, the Forms are patterns not only
30 of sensible things, but of Forms themselves also;
i. e. the
genus, as genus of various species, will be so;therefore
the same thing will be pattern and copy.
ggib
Again, it would seem impossible that the substance and
that of which it is the substance should exist apart ; how,
therefore, could the Ideas, being the substances of things,
exist apart ? In the Phaedo lthe case is stated in this way
that the Forms are causes both of being and of becoming ;
yet when the Forms exist, still the things that share in them
5 do not come into being, unless there is something to origi
nate movement;and many other things come into being
(e.g. a house or a ring) of which we say there are no Forms.
Clearly, therefore, even the other things can both be andcome into being owing to such causes as produce the things
just mentioned.2
Again, if the Forms are numbers, how can they be
10 causes ? Is it because existing things are other numbers,
e. g. one number is man, another is Socrates, another
Callias ? Why then are the one set of numbers causes of the
other set ? It will not make any difference even if the
former are eternal and the latter are not. But if it is
because things in this sensible world (e.g. harmony) are
ratios of numbers, evidently the things between which they
are ratios are some one class of things. If, then, this the
15 matter is some definite thing,3
evidently the numbers
themselves too will be ratios of something to something
1
ioo c-E.2 With 991* 8-b 9 cf. M. io79
b 2-io8oa 8.
3
Reading in 991^ 14 &T)n TOVTO, 17 vA/;.
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BOOK A. 9 ggib
else. E. g. if Callias is a numerical ratio between fire and
earth and water and air, his Idea also will be a number of
certain other underlying things ;and man-himself, whether
it is a number in a sense ornot,
will still be a numerical
ratio of certain things and not a number proper, nor will
it be a kind of number merely because it is a numerical 20
ratio.1
Again, from many numbers one number is produced, but
how can one Form come from many Forms ? And if the
number comes not from the many numbers themselves but
from the units in them, e. g. in 10,000, how is it with the
units ? If they are specifically alike, numerous absurdities
will follow, and also if they are not alike (neither the units 25
in one number being themselves like one another nor those
in other numbers being all like to all) ;for in what will they
differ, as they are without quality ? This is not a plausible
view, nor is it consistent with our thought on the matter.
Further, they must set up a second kind of number
(with which arithmetic deals), and all the objects which
are called intermediate by some thinkers;
and how
do these exist or from what principles do they proceed ?
Or why must they be intermediate between the things in 30
this sensible world and the things-themselves ?
Further, the units in 2 must each come from a prior 2;
but this is impossible.
Further, why is a number, when taken all together, one ? 992a
Again, besides what has been said, if the units are diverse
the Platonists should have spoken like those who say there
are four, or two, elements;for each of these thinkers gives
the name of element not to that which is common, e.g.
to
body,but to fire
and earth, whether there is something 5
common to them, viz. body, or not. But in fact the
Platonists speak as if the One were homogeneous like fire
or water;and if this is so, the numbers will not be sub
stances.2
Evidently, if there is a One-itselfand this is a first
1i. e. the Idea is a numerical ratio in some underlying material. It
may perhaps be called a sort of (rt?) number, but strictly it is a
numerical ratio. Thepassage, however,
is
very difficult, and thecontradiction in 11. 19, 20 almost intolerable.2Sc. but ordinary mathematical numbers. Cf. M. 1081*5-12.
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gg2a METAPHYSICA
principle, one is being used in more than one sense;for
otherwise the theory is impossible.
ID When we wish to reduce substances to their principles,
we state that lines come from the short and long- (i. e. froma kind of small and great), and the plane from the broad
and narrow, and body from the deep and shallow. Yet
how then can either the plane contain a line, or the solid
a line or a plane ? For the broad and narrow is a different
15 class from the deep and shallow. Therefore, just as num
ber is not present in these, because the many and few are
different from these, evidently no other ofthe higher classes
will be present in the lower. But again the broad is not
a genus which includes the deep, for then the solid would
have been a species of plane.1
Further, from what prin
ciple will the presence of the points in the line be derived ?
20 Plato even used to object to this class of things as being
a geometrical fiction. He gave the name of principle of the
line and this he often posited to the indivisible lines. Yet
these must have a limit;therefore the argument from which
the existence of the line follows proves also the existence
of the point.
In general, though philosophy seeks the cause ofper-
25 ceptible things, we have given this up (for we say nothing
of the cause from which change takes its start), but whilewe fancy we are stating the substance of perceptible things,
we assert the existence of a second class of substances,
while our account of the way in which they are the sub
stances of perceptible things is empty talk;for
*
sharingf
,
as we said before,2 means nothing.
Nor have the Forms any connexion with what we see to
30 be the cause in the case of the arts, that for whose sake both
all mind and the whole of nature are operative,3 with this
cause which we assert to be one of the first principles ;but
mathematics has come to be identical with philosophy for
modern thinkers, though they say that it should be studied
for the sake of other things.4
1 With 992* 10-19 cf. M. 1085*9-19.2
991*20-22.3Sc. the final cause.
4Cf. Plato, Rep. vii. 531 D, 533 B-E.
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BOOK A. 9 992b
Further, one might suppose that the substance which
according to them underlies as matter is too mathematical,
and is a predicate and differentia of the substance, i. e. of
the matter, rather than matter itself ; i. e. the great and thesmall are like the rare and the dense which the physical
philosophers speak of, calling these the primary differentiae 5
of the substratum;for these are a kind of excess and defect.
And regarding movement, if the great and the small are to
be movement, evidently the Forms will be moved;but if
they are not to be movement, whence did movement come ?
The whole study of nature has been annihilated.
And what is thought to be easy to show that all things
are one is not done;for what is proved by the method of 10
setting out instances1is not that all things are one but that
there is a One-itself, if we grant all the assumptions. And
not even this follows, if we do not grant that the universal
is a genus ;and this in some cases it cannot be.
Nor can it be explained either how the lines and
planes and solids that come after the numbers exist or
can exist, or what significance they have; for these canT5
neither be Forms (for they are not numbers), nor the
intermediates (for those are the objects of mathematics),
nor the perishable things. This is evidently a distinct fourth
class.2
In general, if we search for the elements of existing
things without distinguishing the many senses in which
things are said to exist, we cannot find them, especially if
the search for the elements of which things are made is con- 30
ducted in this manner. For it is surely impossible to dis
cover what acting or being acted on,or the straight ,
is made of, but if elements can be discovered at all, it is
only the elements of substances;therefore either to seek the
elements of all existing things or to think one has them is
incorrect.
And how could we learn the elements of all things ?
Evidently we cannot start by knowing anything before. 25
For as he who is learning geometry, though he may know
1 For this Platonic method cf. Z. iO3ib2i, M. io86b 9, N. iogo
a17.
2Cf. M. ic8ob 23-30, 1085*7-9.
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992b METAPHYSICA
other things before, knows none of the things with which
the science deals and about which he is to learn, so is it in
all other cases. Therefore if there is a science of all things,
such as some assert to exist, he who is learning this will
3 know nothing before. Yet all learning is by means of pre
misses which are (either all or some of them) known before,
whether the learning be by demonstration or by defini
tions;for the elements of the definition must be known
before and be familiar;and learning by induction proceeds
993a
similarly. But again, if the science were actually innate, it
were strange that we are unaware of our possession of the
greatest of sciences.
Again, how is one to come to know what all things are
made of, and how is this to be made evident ? This also
affords a difficulty; for there might be a conflict of opinion,
5 as there is about certain syllables ;some say za is made out
of s and d and<z,
while others
sayit is a distinct sound and
none of those that are familiar.
Further, how could we know the objects of sense without
having the sense in question ? Yet we ought to, if the
elements of which all things consist, as complex sounds
10 consist of the elements proper to sound, are the same.
It is evident, then, even from what we have said before, 10that all men seem to seek the causes named in the Physics?-
and that we cannot name any beyond these;but they seek
these vaguely ;and though in a sense they have all been
described before, in a sense they have not been described at
15 all. For the earliest philosophy is, on all subjects, like one
who lisps, since it is young and in its beginnings. For
even Empedocles says2 bone exists by virtue of the ratio
in it. Now this is the essence and the substance of the
thing. But it is similarly necessary that flesh and each of
the other tissues should be the ratio of its elements, or that
20 not one of them should;for it is on account of this that
both flesh and bone and everything else wall exist, and not
on account of the matter, which he names, fire and
1
>7-
2
Diels, Vorsokratiker, ed. 3, fr. 96 and i. 214. 22-215. 6.
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BOOK A. 10 993a
earth and water and air. But while he would necessarily
have agreed if another had said this, he has not said it
clearly.
On these questions our views have been expressed before ;
but let us return to enumerate the difficulties that might be 25
raised on these same points ;
1for perhaps we may get from
them some help towards our later difficulties.
1 The reference is to Bk. B.
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BOOK a
30 THE investigation of the truth is in one way hard, in i
another easy. An indication of this is found in the fact
that no one is able to attain the truth adequately, while, on
993 the other hand, we do not collectively fail, but every one
says something- true about the nature of things, and while
individually we contribute little or nothing to the truth, bythe union of all a considerable amount is amassed. There
fore, since the truth seems to be like the proverbial door,1
5 which no one can fail to hit, in this respect it must be easy,
but the fact that we can have a whole truth and not the
particular part we aim at shows the difficulty of it.
Perhaps, too, as difficulties are of two kinds, the cause of
the present difficulty is not in the facts but in us. For as
10 the eyes of bats are to the blaze of day, so is the reason in
our soul to the things which are by nature most evident
of all.
It is just that we should be grateful, not only to those
with whose views we may agree, but also to those who have
expressed more superficial views;for these also contributed
something, by developing before us the powers of thought.
15 It is true that if there had been no Timotheus we should
have been without much of our lyric poetry ;but if there
had been no Phrynis there would have been no Timotheus.
The same holds good of those who have expressed views
about the truth;for from some thinkers we have inherited
certain opinions, while the others have been responsible forthe appearance of the former.
It is right also that philosophy should be called know-
20 ledge of the truth. For the end of theoretical knowledge
is truth, while that of practical knowledge is action (for even
if they consider how things are, practical men do not study
the eternal, but what is relative2 and in the present). Now
1Cf. Leutsch and Schneidewin, Faroemiographi Craed, ii. 678.
2
Reading in 993b 22 dAX 6 rrpos .
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BOOK a. I 993b
we do not know a truth without its cause;and a thing has
a quality in a higher degree than other things if in virtue
of it the similar quality belongs to the other things as well
(e.g. fire is the hottest of things ; for it is the cause of the 25
heat of all other things) ;so that that which causes deriva
tive truths to be true is most true. Hence the principles
of eternal things must be always most true (for they are not
merely sometimes true, nor is there any cause of their
being, but they themselves are the cause of the being of
other things), so that as each thing is in respect of being, so 3
is it in respect of truth.
But evidently there is a first principle, and the causes of 994a
things are neither an infinite series nor infinitely various in
kind. For (i) neither can one thing proceed from another,
as from matter, ad infinitum (e. g. flesh from earth, earth
from air, air from fire, and so on without stopping), nor 5
can the sources of movement form an endless series (man
for instance being acted on by air, air by the sun, the sun by
Strife,1 and so on without limit). Similarly the final causes
cannot go on ad infinitum, walking being for the sake
of health, this for the sake of happiness, happiness for the
sake of something else, and so one thing always for the sake
of another. And the case of the essence is similar. For in 10
the case of intermediates, which have a last term and a term
prior to them, the prior must be the cause of the later
terms. For if we had to say which ofthe three is the cause,
we should say the first; surely not the last, for the final
term is the cause of none;nor even the intermediate, for it 15
is the cause only of one.(It
makes no difference whether
there is one intermediateor more, nor whether they are
infinite or finite in number.) But ofseries which are infinite
in this way, and of the infinite in general, all the parts down
to that now present are alike intermediates;so that if there
is no first there is no cause at all.
Nor can there be an infinite process downwards, with
a beginning in the upward direction, so that water should 20
proceed from fire, earth from water, and so always some
1 The illustration is taken from the cosmology of Empedocles.646-28
)
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994a METAPHYSICA
other kind should be produced. For one thing comes
from another in two ways not in the sense in which
4
from means after (as we say from the Isthmian games
come the Olympian ), but either (i) asthe
man comes fromthe boy, by the boy s changing, or
(ii)as air comes from
35 water. By as the man comes from the boy we mean *
as
that which has come to be from that which is coming to be,
or as that which is finished from that which is being
achieved (for as becoming is between being and not being,
so that which is becoming is always between that which is
and that which is not ; for the learner is a man of science in
the making, and this is what is meant when we say that
sofrom a learner a. man of science is being made) ;on the
other hand, coming from another thing as water comes
from air implies the destruction of the other thing. This
is why changes of the former kind are not reversible, and
the boy does not come from the man (for it is not that
which comes to be something that comes to be as a result
994bof coming to be, but that which exists after the coming to
be;for it is thus that the day, too, comes from the morning
in the sense that it comes after the morning ;which is the
reason why the morning cannot come from the day) ;but
changes of the other kind are reversible. But in both cases
it is
impossible that the number of terms should be infinite.
For terms of the former kind, being intermediates,1 must
5 have an end, and terms of the latter kind change back into
one another;for the destruction of either is the generation
of the other.
At the same time it is impossible that the first cause,
being eternal, should be destroyed ;for since the process of
becoming is not infinite in the upward direction, that which
is the first thing by whose destruction something came to
be must be non-eternal. 2
1Cf.
a27 f.
2This paragraph is very obscure. Aristotle has in
aii-i9 given a
general argument which applies to all the four causes, to show that
there must always be a first cause. This, he assumes, must be
eternal. He now applies this argument to the prime material cause,
and shows that it must be indestructible. There are two difficulties in
the paragraph :
(i) It seems pointless to say that the first cause must be inde-
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BOOK a. 2 994b
Further, the final caiise is an end, and that sort of end
which is not for the sake of something* else, but for whose
sake everything- else is;so that if there is to be a last term to
of this sort, the process will not be infinite ; but if there is
no such term, there will be no final cause, but those who
maintain the infinite series eliminate the Good without
knowing it (yet no one would try to do anything ifhe were
not going to come to a limit) ;nor would there be reason in
the world; the reasonable man, at least, always acts for 15
a purpose, and this is a limit;for the end is a limit.
But the essence, also, cannot be reduced to another
definition which is fuller in expression.1 For the original
definition is always more of a definition, and not the later
one;and in a series in which the first term has not the
required character, the next has not it either. Further, 2o
those who speak thus destroy science;for it is not possible
to have this till one comes to the
unanalysable
terms.
And knowledge becomes impossible ;for how can one
apprehend things that are infinite in this way ?2 For this is
not like the case of the line, to whose divisibility there is no
stop, but which we cannot think if we do not make a
stop (for which reason one who is tracing the infinitely
divisible line cannot be counting the possibilities of section),
but the whole line also must be apprehended by something 35
in us that does not move from part to part. Again, nothing
infinite can exist;and if it could, at least the notion of
infinity is not infinite.3
But(2)
if the kinds of causes had been infinite in number,
then also knowledge would have been impossible ;for we
structible because it is eternal. Ground and consequent appear to be
identical. But probably the object is to show that the first cause mustbe to its effects not as water to air but as boy to man. It developsinto them, and is not destroyed when they come into being.
(2) The clause beginning with eW seems, as is often the case in
Aristotle, to be elliptical. The meaning probably is : Since the process of becoming is not infinite in the upward direction, (there mustbe an eternal first cause, but) that which is the first thing by whosedestruction something came to be cannot be eternal.
1i. e. one can reduce the definition of man as
*
rational animal to
rational sensitive living substance,but one cannot carry on this
process ad infinituin,2
i. e. actually infinite.3
i. e. does not contain an infinite number of marks.
D 2
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994b METAPHYSICA
think we know, only when we have ascertained the causes,
30 but that which is infinite by addition cannot be gone through
in a finite time.
The effect which lectures produce on a hearer depends 3
on his habits;for we demand the language we are accus-
995atomed to, and that which is different from this seems not in
keeping but somewhat unintelligible and foreign because of
its unwontedness. For it is the customary that is intelli
gible. The force of habit is shown by the laws, in which
5 the legendary and childish elements prevail over our know
ledge about them, owing to habit. Thus some people do
not listen to a speaker unless he speaks mathematically,
others unless he gives instances, while others expect him to
cite a poet as witness. And some want to have everything
done accurately, while others are annoyed by accuracy,
either because they cannot follow the connexion of thought
10 or because they regardit
as pettifoggery. For accuracy has
something of this character, so that as in trade so in argu
ment some people think it mean. Hence one must be
already trained to know how to take each sort ofargument,
since it is absurd to seek at the same time knowledge and
the way of attaining knowledge ;and it is not easy to get
even one of the two.
1 5 The minute accuracy of mathematics is not to be demandedin all cases, but only in the case of things which have no
matter. Hence its method is not that of natural science;
for presumably the whole of nature has matter. Hence we
must inquire first what nature is : for thus we shall also see
what natural science treats of [and whether it belongs to
one science or to more to investigate the causes and the
20 principles of things].1
1 This clause has probably been wrongly inserted from 995b5-6.
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BOOK B
I WE must, with a view to the science which we are seek
ing, first recount the subjects that should be first discussed.
These include both the other opinions that some have held 25
on the first principles, and any point besides these that
happens to have been overlooked. For those who wish to
get clear of difficulties it is advantageous to discuss the
difficulties well;for the subsequent free play of thought
implies the solution of the previous difficulties, and it is not
possible to untie a knot of which one does not know. But 30
the difficulty of our thinking points to a4 knot in the
object ;for in so far as our thought is in difficulties, it is in
like case with those who are bound;
for in either case it is
impossible to go forward. Hence one should have surveyed
all the difficulties beforehand, both for the purposes we have
stated and because people who inquire without first stating
the difficulties are like those who do not know where they 35
have to go ; besides, a man does not otherwise know even
whether he has at any given time found what he is looking
for or not; for
theend
is
not clear to such a man, while to him 995^who has first discussed the difficulties it is clear. Further,
he who has heard all the contending arguments, as if they
were the parties to a case, must be in a better position for
judging.
The first problem concerns the subject1 which we dis
cussed in our prefatory remarks. It is this(i) whether
5
the investigation of the causes belongs to one or to more
sciences,2 and
(2)whether such a science should survey only
the first principles of substance, or also the principles on
which all men base their proofs, e. g. whether it is possible
at the same time to assert and deny one and the same thing
or not, and all other such questions ;
:i and (3)if the science 10
in question deals with substance, whether one science deals
1Sc. the four causes.
2Cf. 996** i8-b 26.
3Cf. 996
b26-997
ai5.
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995b METAPHYSICA
with all substances, or more than one,1 and it more, whether
all are akin, or some of them must be called forms of Wis
dom and the others something else. And (4) this itself is
also one of the things that must be discussed whethersensible substances alone should be said to exist or others
15 also besides them, and whether these others are of one kind
or there are several classes of substances, as is supposed
by those who believe both in Forms and in mathematical
objects intermediate between these and sensible things.2
Into these questions, then, as we say, we must inquire, and
also (5) whether our investigation is concerned only with
substances or also with the essential attributes of substances.3
20 Further, with regard to the same and other and like and un
like and contrariety, and with regard to prior and posterior
and all other such terms about which the dialecticians try
to inquire, starting their investigation from probable pre
mises only, whose business is it to inquire into all these ?
25 Further, we must discuss the essential attributes of these
themselves;and we must ask not only what each of these
is, but also whether one thing always has one contrary.4
Again (6), are the principles and elements of things the
genera, or the parts present in each thing, into which it is
divided;
5 and (7) if they are the genera, are they the genera
that are predicated proximately of the individuals, or the
30 highest genera, e. g. is animal or man the first principle and
the more independent of the individual instance ?6 And
(8) we must inquire and discuss especially whether there is,
besides the matter, any thing that is a cause in itself or not,
and whether this can exist apart or not, and whether it is
one or more in number, and whether there is something
35 apart from the concrete thing (by the concrete thing I mean
the matter with something already predicated ofit),
or
there is nothing apart, or there is something in some cases
though not in others, and what sort of cases these are.7
gg6a
Again (9) we ask whether the principlesare limited in num-
1Cf. 997*15-25.
2Cf.
997
a
34-998* 19.
The reference is to Plato.3
Cf. 997;1
25-34.4
Cf. r. ioo3b
22-ioc>5
a18.
5Cf. 99S
a 2o-b 14.6
Cf. 998b14-999*23.
7Cf. 999* 24~
b24.
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BOOK B. i 996
her or in kind, both those in the definitions and those in the
substratumj
1 and (10) whether the principles of perishable
and of imperishable things are the same or different;and
whether they are all imperishable or those of perishable
things are perishable.2 Further (n) there is the question
which is hardest of all and most perplexing, whether unity 5
and being, as the Pythagoreans and Plato said, are not
attributes of something else but the substance of existing
things, or this is not the case, but the substratum is some
thing else, as Empedocles says, love;as some one else
3
says, fire; while another 4 says water or air.5 Again
(12) we ask whether the principles are universal or like
individual things,6 and (13) whether they exist potentially or 10
actually7
,and further, whether they are potential or actual
in any other sense than in reference to movement;8
for
these questions also would present much difficulty. Further
(14), are numbers and lines and figures and points a kind of
substance or not, and if they are substances are they
separate from sensible things or present in them ?9 With 1 5
regard to all these matters not only is it hard to get
possession of the truth, but it is not easy even to think out
the difficulties well.
2 (i) First then with regard to what we mentioned first,
does it belong to one or to more sciences to investigate all
the kinds of causes ? How could it belong to one science 20
to recognize the principles if these are not contrary ?
Further, there are many things to which not all the prin
ciples pertain. For how can a principle of change or the
nature of the good exist for unchangeable things, since
everything that in itself and by its own nature is good is an
end, and a cause in the sense that for its sake the other 25
things both come to be and are, and since an end or pur
pose is the end of some action, and all actions imply change ?
So in the case of unchangeable things this principle could not
1
Cf. 999b24-iooo
a4.
2Cf. icooa s~iooi
a3.
3
Hippasus and Heraclitus.4
Thales (water) ;Anaximenes and Diogenes of Apollonia (air).
6
Cf. iooia
4-^25.e
Cf. ioo3a
5-i;.7Cf. ioo2b 32-ioo3
a5.
8Cf. e. 6.
9Cf. IOOIb 26-I002b
II.
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996a METAPHYSICA
exist, nor could there be a good-itself. This is why in
mathematics nothing is proved by means of this kind ot
30 cause, nor is there any demonstration of this kind
because it is better, or worse;indeed no one even men
tions anything of the kind. And so for this reason some
of the Sophists, e.g. Aristippus, used to ridicule mathe
matics;for in the arts (he maintained), even in the indus
trial arts, e. g. in carpentry and cobbling, the reason always
35 given is because it is better, or worse \ but the mathe
matical sciences take no account of goods and evils.
gg6
b
But if there are several sciences of the causes, and adifferent science for each different principle, which of these
sciences should be said to be that which we seek, or which
of the people who possess them has the most scientific
5 knowledge of the object in question ? The same thing mayhave all the kinds of causes, e. g. the moving cause of
a house is the art or the builder, the final cause is the func
tion it fulfils, the matter is earth and stones, and the form
is the definition. To judge from our previous discussionJ
of the question which of the sciences should be called Wis
dom, there is reason for applying the name to each of them.
10 For inasmuch as it is most architectonic and authoritative
and the other sciences, like slave-women, may not even
contradict it, the science of the end and of the
good
is of
the nature of Wisdom (for the other things are for the sake
of the end). But inasmuch as it was described 2as dealing
writh the first causes and that which is in the highest sense
object of knowledge, the science of substance* must be of
the nature of Wisdom. For since men may know the same
15 thing in many ways, we say that he who recognizes what
a thing is by its being so and so knows more fully than hewrho recognizes it by its not being so and so, and in the
former class itself one knows more fully than another, and
he knows most fully who knows what a thing is, not he who
knows its quantity or quality or what it can by nature do
or have done to it. And further in all other cases also we
think that the knowledge of each even ofthe things of which
1Cf. A. 982*8-19.
2ib. 30-
b2.
3i. e. essence.
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BOOK B. 2 996
demonstration is possiblel
is present only when we know
what the thing is, e. g. what squaring a rectangle is, viz. that 20
it is the finding of a mean;and similarly in all other cases.
And we know about becomings and actions and about every
change when we know the source ofthe movement ;and
this is other than and opposed to the end. Therefore it
would seem to belong to different sciences to investigate 25
these causes severally.2
But(2), taking the starting-points of demonstration as well
as the causes, it is a disputable question whether they are the
object of one science or of more (by the starting-pointsof
demonstration I mean the common beliefs, on which all
men base their proofs) ;e. g. that everything must be either
affirmed or denied, and that a thing cannot at the same
time be and not be, and all other such premisses: the 3
question is whether the same science deals with them as
withsubstance,
or a differentscience,
and if it is not one
science, which of the two must be identified with that which
we now seek. It is not reasonable that these topics should
be the object ofone science;for why should it be peculiarly
appropriate to geometry or to any other science to under
stand these matters ? If then it belongs to every science 35
alike, and cannot belong to all, it is not peculiar to the 997*
science which investigates substances, any more than to
any other science, to know about these topics. And, at the
same time, in what way can there be a science of the first
principles ? For we are aware even now what each ofthem
in fact is (at least even other sciences use them as familiar) ; 5
but ifthere is a demonstrative science which deals with them,
there will have to be an underlying kind, and some of them
must be demonstrable attributes and others must be axioms
(for it is impossible that there should be demonstration
about all of them) ;for the demonstration must start from
certain premisses and be about a certain subject and prove
1 The meaning is that whether the essence is known directly (as in
the case of substances) or by means of demonstration (as in the case of
attributes or of events like thunder or eclipse), knowledge of the
essence is the primary knowledge.2 With 996* i8-b 26 cf. 995
b4-6, K. 1059** 20-23 (with 996
a 2i-b I cf.
34-8).
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997a METAPHYSICA
certain attributes. Therefore it follows that all attributes
10 that are proved must belong to a single class; for all
demonstrative sciences use the axioms.
But if the science of substance and the science which
deals with the axioms are different, which of them is by
nature more authoritative and prior ? The axioms are most
universal and are principles of all things. And if it is not
the business of the philosopher, to whom else will it belong
to inquire what is true and what is untrue about them ?l
15 (3) In general, do all substances fall under one science
or under more than one ? If the latter, to what sort of substance is the present science to be assigned ? On the other
hand, it is not reasonable that one science should deal with all.
For then there would be one demonstrative science dealing
with all attributes. For every demonstrative science
20investigates with regard to some subject its essential attri
butes, starting from the common beliefs.2 Therefore to
investigate the essential attributes of one class of things,
starting from one set of beliefs, is the business of one
science. For the subject belongs to one science, and the
premisses belong to one. whether to the same or to another;
so that the attributes do so too, whether they are investigated
by these sciences or by one compounded out of them.3
25(5)
4
Further,does our
investigationdeal with substances
alone or also with their attributes ? I mean for instance, if
the solid is a substance and so are lines and planes, is it the
business of the same science to know these and to know
the attributes of each of these classes (the attributes about
which the mathematical sciences offer proofs), or of a differ-
so ent science ? If of the same, the science of substance also
must be a demonstrative science ; but it is thought that there
is no demonstration of the essence of things. And if ot
another, what will be the science that investigates the attri
butes of substance ? This is a very difficult question.5
1 With 996b26-997* 15 cf. 995
b6-10, 1059** 23-6. For the answer
cf. r. 32
Cf. 996b 28.
8 With 997*15-25 cf. 995b10-13, io59
a26~9. For the answer cf. r.
1004*2-9,E. i.
4I number the problems as in ch. i.
5 With 997*25-34 cf. 995b18-20, 1059*29-34. For the answer cf.
r. I003b22-ioo5
a18.
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BOOK B. 2 997a
(4) Further, must we say that sensible substances alone
exist, or that there are others besides these ? And are sub- 35
stances of one kind or are there in fact several kinds of
substances, as those say who assert the existence both of the 997Forms and of the intermediates, with which they say the
mathematical sciences deal ? The sense in which we l
say the Forms are both causes and self-dependent sub
stances has been explained in our first remarks about them;
2
while the theory presents difficulties in many ways, the 5
most paradoxical thing of all is the statement that there
are certain things besides those in the material universe, and
that these are the same as sensible things except that they
are eternal while the latter are perishable. For they say
there is a man-himself and a horse-itself and health-itself,
with no further qualification, a procedure like that of the
people who said there are gods, but in human form. For TO
they
werepositing nothing
but eternal men, nor are the
Platonists making the Forms anything other than eternal
sensible things.
Further, if we are to posit besides the Forms and the
sensibles the intermediates between them, we shall have
many difficulties. For clearly on the same principle there
will be lines besides the lines-themselves and the sensible
lines, and so with each of the other classes of things;
so 15
that since astronomy is one of these mathematical sciences
there will also be a heaven besides the sensible heaven, and
a sun and a moon (and so with the other heavenly bodies)
besides the sensible. Yet how are we to believe in these
things ? It is not reasonable even to suppose such a body
immovable, but to suppose it moving is quite impossible.
And similarly with the things of which optics and mathe- 20
matical harmonics treat;for these also cannot exist apart
from the sensible things, for the same reasons. For if there
are sensible things and sensations intermediate between
Form and individual, evidently there will also be animals
intermediate between animals-themselves and the perish
able animals. We might also raise the question, with 25
reference to which kind of existing things we must look for
1
Cf. note on A. 99ob9.
2Cf. A. 6 and 9.
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997b METAPHYSICA
these sciences of intermediates. If geometry is to differ
from mensuration only in this, that the latter deals with
things that we perceive, and the former with things that are
not perceptible, evidently there will also be a science otherthan medicine, intermediate between medical-science-itself
and this individual medical science, and so with each of the
3 other sciences. Yet how is this possible ? There would have
to be also healthy things besides the perceptible healthy
things and the healthy-itself. And at the same time not
even this is true, that mensuration deals with perceptible and
perishable magnitudes ; for then it would have perished
when they perished.
But on the other hand astronomy cannot be dealing
with perceptible magnitudes nor with this heaven above
35 us. For neither are perceptible lines such lines as the
998a
geometer speaks of (for no perceptible thing is straight or
round in the way in which he defines straight and1 round
;for a hoop touches a straight edge not at a
point, but as Protagoras used to say it did, in his refutation
ofthe geometers),1 nor are the movements and spiral orbits
5 in the heavens like those of which astronomy treats, nor
have geometrical points the same nature as the actual stars.
Now there are some who say that these so-called inter
mediates between the Forms and the perceptible things
exist, not apart from the perceptible things, however, but
in these;
2the impossible results of this view would take too
10long to enumerate, but it is enough to consider even such
points as the following : It is not reasonable that this should
be so only in the case of these intermediates, but clearly
the Forms also might be in the perceptible things ;for both
statements are parts of the same theory. Further, it follows
from this theory that there are two solids in the same place,
and that the intermediates are not immovable, since they
15 are in the moving perceptible things. And in general to
what purpose would one suppose them to exist indeed, but
1
Possibly in a work Hepi TWVMa6r]piiTa>v,
for which cf. Diog.
Laert. ix. 55.2 The reference is to a school of semi-Pythagorean, semi-Platonic
thinkers.
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BOOK B. 2 998*
to exist in perceptible things ? For the same paradoxical
results will follow which we have already mentioned ;there
will be a heaven besides the heaven, only it will be not apart
but in the same place;
which is still more impossible.
1
3 (6) Apart from the great difficulty of stating the case 2
truly with regard to these matters, it is very hard to say,
with regard to the first principles, whether it is the genera
that should be taken as elements and principles, or rather
the primary constituents of a thing ;e. g. it is the primary
parts of which articulate sounds consist that are thought tobe elements and principles of articulate sound, not the
common genus articulate sound;and we give the name 2 5
of elements to those geometrical propositions, the proofs
of which are implied in the proofs of the others, either of all
or of most. Further, both those who say there are several
elements of corporeal things and those who say there is
one, say the parts of which bodies are compounded andconsist are principles ;
e. g. Empedocles says fire and water 30
and the rest are the constituent elements of things, but does
not describe these as genera of existing things. Besides
this, if we want to examine the nature of anything else, we
examine the parts of which, e. g.,a bed consists and how 99&
b
they are put together, and then we know its nature.
To judge from these arguments, then, the principles of
things would not be the genera ;but ifwe know each thing
by its definition, and the genera are the principles or 5
starting-points of definitions, the genera must also be the
principles of definable things. And if to get the knowledge of
the species according to which things are named is to get
the
knowledgeof
things,the
generaare at least
starting-points of the species. And some also of those who say
unity or being,2 or the great and the small,
3are elements of 10
things, seem to treat them as genera.
But, again, it is not possible to describe the principles in
both ways. For the formula of the essence is one;but
1 With 997a34-998
a19 cf. 995
b13-18, I059
a38-
b2i. For the
answer cf. A. 6-lo, M, N.2 The reference is to the Pythagoreans and Plato (cf. 996*6).3 The reference is to Plato (cf. A. 98;
b20).
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998b METAPHYSICA
definition by genera will be different from that which states
the constituent parts of a thing.1
(7) Besides this, even if the genera are in the highest
15 degree principles, should one regard the first of the generaas principles, or those which are predicated directly of the
individuals ? This also admits of dispute. For if the
universals are always more of the nature of principles,
evidently the uppermost of the genera are the principles ;
for these are predicated of all things. There will, then, be
as many principles of things as there are primary genera,
20 so that both being and unity will be principles and sub
stances;for these are most of all predicated of all existing
things. But it is not possible that either unity or being
should be a single genus of things ;for the differentiae of
any genus must each of them both have being and be one,
but it is not possible for the genus taken apart from its
25 species (any more than for the species of the genus) to be
predicated of its proper differentiae;so that if unity or
being is a genus, no differentia will either have being or be
one. But if unity and being are not genera, neither will
they be principles, if the genera are the principles. Again,
the intermediate kinds, in whose nature the differentiae are
included, will on this theory be genera, down to the indivisible
species;
but as it is, some are thought to be genera and3 others are not thought to be so. Besides this, the differ
entiae are principles even more than the genera ;and if
these also are principles, there comes to be practically an
infinite number of principles, especially if we suppose the
999a
highest genus to be a principle. But again, if unity ?s
more of the nature of a principle, and the indivisible is one,
and everything indivisible is so either in quantity or in
species, and that which is so in species is the prior, and
genera are divisible into species (for man is not the genus
5 of individual men), that which is predicated directly of the
individuals will have more unity. Further, in the case of
things in which the distinction of prior and posterior is
present, that which is predicable of these things cannot be
something apart from them(e. g.
if two is the first of
1 With 998* 2o-b 14 cf. 995** 27-9. For the answer cf. Z. 10, 13.
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BOOK B. 3 999a
numbers, there will not be a Number apart from the kinds
of numbers;and similarly there will not be a Figure apart
from the kinds of figures ;and if the genera of these things
10
do not exist apart from the species, the genera of other
things will scarcely do so;for genera of these things are
thought to exist if any do). But among the individuals one
is not prior and another posterior. Further, where one
thing is better and another worse, the better is always prior ;
so that of these also no genus can exist.
From these considerations, then, the species predicated of J 5
individuals seem to be principles rather than the genera.
But again, it is not easy to say in what sense these are to
be taken as principles. For the principle or cause must
exist alongside of the things of which it is the principle,
and must be capable of existing in separation from them;
but for what reason should we suppose any such thing to
exist alongside of the individual, except that it is predicated 20
universally and of all ? But if this is the reason, the things
that are more universal must be supposed to be more of the
nature of principles ;so that the highest genera would be
the principles.1
4 (8) There is a difficulty connected with these, the hardest
of all and the most necessary to examine, and of this the 25
discussion now awaits us. If, on the one hand, there is
nothing apart from individual things, and the individuals
are infinite in number, how then is it possible to get know
ledge of the infinite individuals ? For all things that we
come to know, we come to know in so far as they have
some unity and identity, and in so far as some attribute
belongs to them universally.
But if this is necessary, and there must be something
apart from the individuals, it will be necessary that the 30
genera exist apart from the individuals, either the lowest
or the highest genera ;but we found by discussion just now
that this is impossible.2
Further, if we admit in the fullest sense that something
1 With 998bI4~999
a23 cf. 995
b29-31. For the answer cf. Z. 12.
iO38a19, and 13. With this and the previous problem cf. loco 15 21-
1060* i.2Ch. 3.
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999* METAPHYSICA
exists apart from the concrete thing, whenever something-
is predicated of the matter, must there, if there is some
thing apart, be something apart from each set of individuals,
999
b or from some and not fromothers,
or from none ?l
(A)If
there is nothing apart from individuals, there will be no
object of thought, but all things will be objects of sense,
and there will not be knowledge of anything, unless we say
that sensation is knowledge.2
Further, nothing will be
eternal or unmovable;for all perceptible things perish and
5are in movement. But if there is nothing eternal, neither
can there be a process of coming to be ; for there must be
something that comes to be, i. e. from which something
comes to be, and the ultimate term in this series cannot
have come to be, since the series has a limit and since
nothing can come to be out of that which is not. Further,
if generation and movement exist there must also be a limit;
10 for no movement is infinite, but every movement has an end,
and that which is incapable of completing its coming to be
cannot be in process of coming to be;and that which has
completed its coming to be must be as soon as it has come
to be.3
Further, since the matter exists,4 because it is un-
generated, it is a fortiori reasonable that the substance or
essence, that which the matter is at any time coming to be,
should exist;
forif
neither essence nor matteris
to be,
r5 nothing will be at all, and since this is impossible there
must be something besides the concrete thing, viz. the shape
or form.
But again (B) if we are to suppose this, it is hard to say
in which cases we are to suppose it and in which not. For
evidently it is not possible to suppose it in all cases;we
could not suppose that there is a house besides the particular
20 houses. Besides this, will the substance of all the indi
viduals, e. g. of all men, be one ? This is paradoxical, for
1 The question which individuals have something apart correspond
ing to them suggests to Aristotle the further question whether any
have. Thus the end of the sentence takes a form inconsistent with the
beginning.2 The reference is to Protagoras (cf. PI. Theaet. 152 -153 A).3Sc. and thus there is a limit to its coming to be.
4Sc. before the concrete thing.
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BOOK B. 4 999b
all the things whose substance is one are one. But are the
substances many and different ? This also is unreasonable.
At the same time, how does the matter become each of the
individuals,and how is the concrete
thing
these two
elements ?l
(9) Again, one might ask the following question also
about the first principles. If they are one in kind only, 35
nothing will be numerically one, not even unity-itself and
being-itself ;and how will knowing exist, if there is not to
be something common to a whole set of individuals ?
But if there is a common element which is numerically
one, and each of the principles is one, and the principles
are not as in the case of perceptible things different for
different things (e. g. since this particular syllable is the
same in kind whenever it occurs, the elements of it are also
the same in kind; only in kind, for these also, like the 30
syllable, are numerically different in different contexts), if
it is not like this but the principles of things are numeri
cally one, there will be nothing else besides the elements
(for there is no difference of meaning between numerically
one and individual;for this is just what we mean by the
individual the numerically one, and by the universal we
mean that which is predicable of the individuals). There- ioooa
fore it will be just as if the elements of articulate sound
were limited in number;
all the language in the world
would be confined to the ABC, since there could not be two
or more letters of the same kind.2
(10) One difficulty which is as great as any has been 5
neglected both by modern philosophers and by their pre
decessors whether the principles of perishable and those
ofimperishable things are the same or different. If they
are the same, how are some things perishable and others
imperishable, and for what reason ? The school of Hesiod
and all the theologians thought only of what was plausible
to themselves, and had no regard to us. For, asserting the 10
1 With 999a24-
b24 cf. 995
b31-6, io6oa 3-27,
b23-8. For the
answer cf. Z.
8, 13, 14,
A.
6-10,M. 10.
2 With 999b24-iooo
a4 cf. 996*1-2, 1060 b
28-30. For the answercf. Z. 14, A. 4, 5, M. 10.
645-28 E
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ioooa METAPHYSICA
first principles to be gods and born of gods, they say that
the beings which did not taste of nectar and ambrosia
became mortal;and clearly they are using words which are
familiarto themselves, yet what they have said about the
very application of these causes is above our comprehen-
15 sion. For if the gods taste of nectar and ambrosia for their
pleasure, these are in no wTise the causes of their existence
;
and if they taste them to maintain their existence, how can
gods who need food be eternal? But into the subtleties
of the mythologists it is not worth our while to inquire
seriously ; those, however, who use the language of proof
20 we must cross-examine and ask why. after all, things which
consist of the same elements are, some of them, eternal in
nature, while others perish. Since these philosophers
mention no cause, and it is unreasonable that things should
be as they say, evidently the principles or causes of things
cannot be the same. Even the man whom one might sup-
25 pose to speak most consistently Empedocles, even he
has made the same mistake;for he maintains that strife is
a principle that causes destruction^ but even strife would
seem no less to prodtice everything, except the One;for
all things excepting God proceed from strife. At least he
says :
From which all that was and is and will be hereafter30 Trees, and men and women, took their growth,
And beasts and birds and water-nourished fish,
And long-aged gods.1
The implication is evident even apart from these words;
iooobfor if strife had not been present in things, all things would
have been one, according to him;for when they have come
together,then strife stood outermost.
2 Hence it also
follows on his theory that God most blessed is less wise
5 than all others;for he does not know all the elements
;for
he has in him no strife, and knowledge is of the like by the
like.* For by earth, he says,
we see earth, by water water,
By ether godlike ether, by fire wasting fire,
Loveby love,
and strife
by gloomystrife.
3
1Fr. 21.
2Fr. 36.
3Fr. 109.
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BOOK B. 4 iooob
But and this is the point we started from this at least
is evident, that on his theory it follows that strife is as much l
the cause of existence as of destruction. And similarly
love is not specially the cause of existence;for in collecting
things into the One it destroys all other things. And at
the same time Empedocles mentions no cause of the change
itself, except that things are so by nature.
But when strife at last waxed great in the limbs of the
Sphere,And sprang to assert its rights as the time was fulfilled
Which is fixed for them in turn by a mighty oath. 1 15
This implies that change was necessary ;but he shows no
cause of the necessity. But yet so far at least he alone
speaks consistently ;for he does not make some things
perishable and others imperishable, but makes all perishable
except the elements. 2 The difficulty we are speaking of 20
now is,
whysome
thingsare
perishableand others are
not,if they consist of the same principles.
Let this suffice as proof of the fact that the principles
cannot be the same. But if there are different principles,
one difficulty is whether these also will be imperishable or
perishable. For if they are perishable, evidently these also
must consist of certain elements (for all things that perish, 25
perish by being resolved into the elements of which they
consist) ;so that it follows that prior to the principles there
are other principles. But this is impossible, whether the
process has a limit or proceeds to infinity. Further, how
will perishable things exist, if their principles are to be
annulled ? But if the principles are imperishable, why will
things composed of some imperishable principles be perish
able, while those composed of the others are imperishable ? 30
This is not probable, but is either impossible or needs much
proof. Further, no one has even tried to maintain different
principles ; they maintain the same principles for all things.
But they swallow the difficulty we stated first3as if they iooi
a
took it to be something trifling.4
1Fr. 30.
2Cf.
Diels, Vorsokratiker,
ed. 3, i.
209.
11-21.3 ioooa 5~
b 21.4 With ioooa 5-icoi
a3 cf. 996
a2-4, 1060*27-36. For the answer
cf. Z. 7-10.
E 2
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iooia METAPHYSICA
(n) The inquiry that is both the hardest of all and the
5 most necessary for knowledge of the truth is whether being
and unity are the substances of things, and whether each of
them, without being anything else, is being or unity respec
tively, or we must inquire what being and unity are, with
the implication that they have some other underlying nature.
For some people think they are of the former, others think
they are of the latter character. Plato and the Pythagoreans10 thought being and unity were nothing else, but this was
their nature, their essence being just unity and being. But
the natural philosophers take a different line;
e. g. Empe-docles as though reducing it to something more intel
ligible says what unity is;for he would seem to say it is
love : at least, this is for all things the cause of their being
15 one. Others say this unity and being, of which things
consist and have been made, is fire,1 and others say it is air.
2
Asimilar view is
expressed bythose
who makethe elements
more than one;for these also must say that unity and being
are precisely all the things which they say are principles.
(A) If we do not suppose unity and being to be sub-
20 stances, it follows that none of the other universals is
a substance;for these are most universal of all, and if there
is no unity-itself or being-itself, there will scarcely be in any
other case anything apart from what are called the indi-
25 viduals. Further, if unity is not a substance, evidently
number also will not exist as an entity separate from the
individual things; for number is units, and the unit is
precisely a certain kind of one.
But (B) if there is a unity-itself and a being-itself, unity
and being must be their substance;for it is not something
else that is predicated universally of the things that are and
are one, but just unity and being. But if there is to be
30 a being-itself and a unity-itself, there is much difficulty in
seeing how there will be anything else besides these,
I mean, how things will be more than one in number. For
what is different from being does not exist, so that it
1
Hippasus and Heraclitus.3 Anaximenes and Diogenes of Apollonia.
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BOOK B. 4 iooia
necessarily follows, according to the argument of Parmenides,
that all things that are are one and this is being.
There are objections to both views. For whether unity iooib
is not a substance or there is a unity-itself, number cannotbe a substance. We have already
l said why this result
follows if unity is not a substance;and if it is, the same
difficulty arises as arose2 with regard to being. For whence
is there to be another one besides unity-itself? It must be 5
not-one;but all things are either one or many, and of the
many each is one.
Further, if unity-itself is indivisible, according to Zeno s
postulate3
it will be nothing. For that which neither when
added makes a thing greater nor when subtracted makes it
less, he asserts to have no being, evidently assuming that
whatever has being is a spatial magnitude. And if it is 10
a magnitude, it is corporeal ;for the corporeal has being
in every dimension, while the other objects of mathematics,
e. g. a plane or a line, added in one way will increase what
they are added to, but in another way will not do so,4 and
a point or a unit does so in no way. But, since his theory
is of a low order, and an indivisible thing can exist in such
a way as to have a defence even against him (for the indi- 15
visible when added will make the number, though not the
size, greater), yethow can a
magnitude proceedfrom one
such indivisible or from many ? It is like saying that the
line is made out of points.
But even if one supposes the case to be such that, as 20
some say, number proceeds from unity-itself and something
else which is not one, none the less we must inquire whyand how the product will be sometimes a number and some
times a magnitude, if the not-one was inequality5
and wasthe same principle in either case. For it is not evident how
magnitudes could proceed either from the one and this
principle, or from some number and this principle.6
25
1 a24-27.
2 a3i-
bi.
5Cf. Diels, Vorsokratiker,t&. 3, i. 170. 16-38.
4e. g. a line added to another at the end makes it longer, but one
which lies beside another makes it no broader.
5 The reference is to Plato s theory (cf. M. io8l a 24).6 With iooi a
4-b25 cf. 996*4 9.
For the answer cf. Z. io4ob
16-24, I. 2.
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iooib METAPHYSICA
(14) A question connected with these is whether numbers 5
and bodies and planes and points are substances of a kind,
or not. If they are not, it baffles us to say what being1
is
and what the substances of things are. For modifications
30 and movements and relations and dispositions and ratios do
not seem to indicate the substance of anything ;for all are
predicated of a subject, and none is a this . And as to the
things which might seem most of all to indicate substance,
water and earth and fire and air, of which composite bodies
ioo2a
consist, heat and cold and the like are modifications of
these, not substances, and the body which is thus modifiedalone persists as something real and as a substance. But,
on the other hand, the body is surely less of a substance
5 than the surface, and the surface than the line, and the line
than the unit and the point. For the body is bounded by
these;and they are thought to be capable of existing with
out body, but body incapable of existing without these.
This is why, while most of the philosophers and the earlier
among them thought that substance and being were iden
tical with body, and that all other things were modifications
10 of this, so that the first principles of bodies were the first
principles of being, the more recent and those who were
held to be wiser l
thought numbers were the first principles.
As we said, then, if these are not substance, there is no
substance and no being at all;for the accidents of these it
cannot be right to call beings.
15 But if this is admitted, that lines and points are substance
more than bodies, but we do not see to what sort of bodies
these could belong (for they cannot be in perceptible
bodies), there can be no substance. Further, these are all
evidently divisions of body, one in breadth, another in
20 depth, another in length. Besides this, no sort of shape is
present in the solid more than any other;so that if the
Hermes is not in the stone, neither is the half of the cube
in the cube as something determinate;therefore the surface
is not in it either;for if any sort of surface were in
it,the
surface which marks off the half of the cube would be in it
25 too. And the same account applies to the line and to the
1 The Pythagoreans and Plato are probably meant.
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^BOOK B. 5 ioo2a
point and the unit. Therefore, if on the one hand body is
in the highest degree substance, and on the other hand
these things are so more than body, but these are not even
instances of substance,1
it baffles us to say what being is
and what the substance of things is. For besides what has
been said, the questions of generation and destruction con
front us with further paradoxes. For if substance, not 30
having existed before, now exists, or having existed before,
afterwards does not exist, this change is thought to be
accompanied by a process of becoming or perishing ;but
points and lines and surfaces cannot be in process either of
becoming or of perishing, when they at one time exist and
at another do not. For when bodies come into contact or
are divided, their boundaries simultaneously become one in iooab
the one case when they touch, and two in the other when
they are divided;so that when they have been put together
one boundary does not exist but has perished, and when
they have been divided the boundaries exist which before
did not exist (for it cannot be said that the point, which is
indivisible, was divided into two). And if the boundaries
come into being and cease to be, from what do they come
into being ? A similar account may also be given of the 5
now in time;for this also cannot be in process of coming
into being or of ceasing to be, but yet seems to be alwaysdifferent, which shows 2
that it is not a substance. And
evidently the same is true of points and lines and planes ;
for the same argument applies, since they are all alike 10
either limits or divisions.3
6 In general one might raise the question why after all,
besides perceptible things and the intermediates,
4
we haveto look for another class of things, i. e. the Forms which
we 5
posit. If it is for this reason, because the objects
of mathematics, while they differ from the things in this
1Sc. not to speak of their being the most real substances.
2
Reading in Ioo2b 7-8 eu/m, s owe(<os
OVK. Ab).
3 For the answer cf. M. 1-3 (esp. io9ob5-13), 6-9, N. 1-3, 5, 6.
With problems (li), (14) cf. io6oa
36-b
19.*For these cf. A. 987^14-18.
5Sc. Platonists.
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ioo2b METAPHYSICA
i 5world in some other respect, differ not at all in that there
are many of the same kind, so that their first principles
cannot be limited in number (just as the elements of all the
language in this sensible world are not limited in number,but in kind, unless one takes the elements of this individual
aosyllable or of this individual articulate sound whose
elements will be limited even in number;so is it also in
the case of the intermediates;for there also the members
of the same kind are infinite in number), so that if there are
not besides perceptible and mathematical objects others
such as some maintain the Forms to be, there will be no
substance which is one in number, but only in kind, nor
will the first principles of things be determinate in number,
25 but only in kind : if then this must be so, the Forms also
must therefore be held to exist. Even if those who support
this view do not express it articulately, still this is what
they mean,and
theymust be
maintainingthe Forms
justbecause each of the Forms is a substance and none is by
accident.
30 But if we are to suppose both that the Forms exist and
that the principles are one in number, not in kind, we have
mentioned 1 the impossible results that necessarily follow.2
(13) Closely connected with this is the question whether
the elements exist potentially or in some other manner. If
in some other way, there will be something else prior to the
ioo3a
first principles ;for the potency is prior to the actual cause,
and it is not necessary for everything potential to be actual.
But if the elements exist potentially, it is possible that
everything that is should not be. For even that wrhich is
not yet is capable of being ;for that which is not comes to
be, but nothing that is incapable of being comes to be.3
5 (12) We must not only raise these questions about the
first principles, but also ask whether they are universal or
wrhat we call individuals. If they are universal, they will
not be substances;for everything that is common indicates
1
999b27-iooo
a4.
2
(15)is
a question not raisedin
ch.I
but akin to problems (4), (8),
(14).3 With ioo2b 32-1003* 5 cf. 996*10-11. For the answer cf. e. 8,
A. 6, 7.
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BOOK B. 6 ioo3a
not a this but a such,but substance is a this . And
if we are to be allowed to lay it down that a common predi
cate is a this and a single thing, Socrates will be several 10
animals himself and man and animal , if each of these
indicates a this and a single thing.
If, then, the principles are universals, these results follow;
if they are not universals but of the nature of individuals,
they will not be knowable;for the knowledge of anything
is universal. Therefore if there is to be knowledge of the 15
principles there must be other principles prior to them,
namely those that are universally predicated of them. 1
1 With 1003*5-17 cf. 996*9-10, io6ob 19-23. For the answer
cf. Z. 13, 15, M. 10.
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BOOK F
THERE is a science which investigates being- as being i
and the attributes which belong to this in virtue of its own
nature. Now this is not the same as any of the so-called
special sciences;for none of these others treats universally
of being as being. They cut off a part of being and investi-
25 gate the attribute of this part ;this is what the mathematical
sciences for instance do. Now since we are seeking thefirst principles and the highest causes, clearly there must
be some thing to which these belong in virtue of its own
nature. If then those who sought the elements of existing
things were seeking these same principles, it is necessary
3othat the elements must be elements of being not by accident
but just because it zs being. Therefore it is of being as
being that we also must grasp the first causes.
There are many senses in which a thing may be said to 2
4 be,but all that is is related to one central point, one
definite kind of thing, and is not said to be by a mere
ambiguity. Everything which is healthy is related to
35 health, one thing in the sense that it preserves health,
another inthe sense that
it
produces it, anotherin
thesense that it is a symptom of health, another because it is
ioo3bcapable of it. And that which is medical is relative to the
medical art, one thing being called medical because it
possesses it, another because it is naturally adapted to it,
another because it is a function of the medical art. And we
5shall find other words used similarly to these. So, too,
there are many senses in which a thing is said to be, but
all refer to one starting-point ;some things are said to
be because they are substances, others because they are
affections of substance, others because they are a process
towards substance, or destructions or privations or qualities
of substance, or productive or generative of substance, or of
things which are relative to substance, or negations of one
10 of these things or of substance itself. It is for this reason
that we say even of non-being that it is non-being. As,
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BOOK T. 2 1003
then, there is one science which deals with all healthy
things, the same applies in the other cases also. For not
only in the case of things which have one common notion
does the investigation belong to one science, but also in thecase of things which are related to one common nature
;
for even these in a sense have one common notion. It is 15
clear then that it is the work of one science also to study
the things that are, qua being. But everywhere science
deals chiefly with that which is primary, and on which the
other things depend, and in virtue of which they get their
names. If, then, this is substance, it will be of substances that
the philosopher must grasp the principles and the causes.
Now for each one class of things, as there is one percep
tion, so there is one science, as for instance grammar, being20
one science, investigates all articulate sounds. Hence to
investigate all the species of being qua being is the work
of a science which is generically one, and to investigate the
several species is the work of the specific parts ofthe science.
If, now, being and unity are the same and are one thing
in the sense that they are implied in one another as prin
ciple and cause are, not in the sense that they are explained
by the same definition (though it makes no difference even 25
if we suppose them to be like that in fact this would even
strengthenour
case);for
* one man and man are the
same thing, and so are existent man and man,and the
doubling of the words in one man and one existent man
does not express anything different(it
is clear that the two
things are not separated either in coming to be or in ceas
ing to be) ;and similarly one existent man adds nothing 3
to4
existent man,so that it is obvious that the addition in
these cases means the same thing, and unity is nothing
apart from beingl
;and
if, further, the substance of each
thing is one in no merely accidental way, and similarly is
from its very nature something that is : all this being so,
there must be exactly as many species of being as of unity.
And to investigate the essence of these is the work of a
1
The argument is obscured by doubts as to the reading, but seemsto be that being and unity are not severed from the particular thingwhich is and is one, and .*. are not severed from one another.
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ioo3b METAPHYSICA
35 science which is generically one I mean, for instance, the
discussion of the same and the similar and the other con
cepts of this sort;and nearly all contraries may be referred
ioo4
a
to this origin; let us take them as having been investigated
in the Selection of Contraries .
And there are as many parts of philosophy as there are
kinds of substance, so that there must necessarily be amongthem a first philosophy and one which follows this. For
5 being falls immediately into genera ;for which reason the
sciences too will correspond to these genera. For the
philosopher is like the mathematician, as that word is used ;
for mathematics also has parts, and there is a first and a
second science and other successive ones within the sphere
of mathematics.2
Now since it is the work of one science to investigate
10opposites, and plurality is opposed to unity and it belongs
to one science to
investigate
the
negation
and the
privationbecause in both cases we are really investigating the one
thing of which the negation or the privation is a negation
or privation (for we either say simply that that thing is
not present, or that it is not present in some particu
lar class;in the latter case difference is present over and
above what is implied in negation ;for negation means just
15 the absence of the thing in question, while in privation there
is also employed an underlying nature of which the priva
tion is asserted 3
): in view of all these facts, the contraries
of the concepts we named above, the other and the dis
similar and the unequal, and everything else which is
derived either from these or from plurality and unity,
must fall within the province of the science above named.
20 And contrariety is one of these concepts ;for contrariety
is a kind of difference, and difference is a kind of other
ness. Therefore, since there are many senses in which
a thing is said to be one, these terms also will have
1Cf. Fr. I478
b35-I479
a5, I497
a32-149^43-
2 With ioo4a2-9 cf. B. 995
b10-13, 997
a15-25, E. i.
8i. e.
negationis
simplythe
negationof an attribute
;in
privationsome member of a definite class is said not to have the attribute in the
form appropriate to that class. I conjecture that TO> f.vl or TO> iv\r]
should be omitted in 1004* 13-14.
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BOOK T. 2 ioo4a
many senses, but yet it belongs to one science to know
them all;for a term belongs to different sciences not if it
has different senses, but if it has not one meaning and its
definitions cannot be referred to one central meaning. And 25
since all things are referred to that which is primary, as for
instance all things which are called one are referred to the
primary one, we must say that this holds good also of the
same and the other and of contraries in general ;so that
after distinguishing the various senses of each, we must then
explain by reference to what is primary in the case of each
of the predicates in question, saying how they are related
to it;for some will be called what they are called because 30
they possess it, others because they produce it, and others
in other such ways.
It is evident, then, that it belongs to one science to be able
to give an account of these concepts as well as of substance
(this was one of the questions in our book of problems),1
and that it is the function of the philosopher to be able to
investigate all things. For if it is not the function of the ioo4b
philosopher, who is it who will inquire whether Socrates
and Socrates seated are the same thing, or whether one
thing has one contrary, or what contrariety is, or how many
meanings it has ? And similarly with all other such ques
tions.
Since, then,these are essential modifications of
unity 5
qua unity and of being qua being, not qua numbers or lines
or fire, it is clear that it belongs to this science to investi
gate both the essence of these concepts and their properties.
And those who study these properties err not by leaving
the sphere of philosophy,2 but by forgetting that substance,
of which they have no correct idea, is prior to these other
things. For number qua number has peculiar attributes, I0
such as oddness and evenness, commensurability and
equality, excess and defect, and these belong to numbers
either in themselves or in relation to one another. And
similarly the solid and the motionless and that which is in
motion and the weightless and that which has weight have
other peculiar properties. So too there are certain pro- 15
1i. e. B. 995
b18-27, 997
a25-34.
2Sc. which they do not do.
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ioo4b METAPHYSICA
parties peculiar to being as such, and it is about these that
the philosopher has to investigate the truth. An indication
of this may be mentioned : dialecticians and sophists
assume the same guise as the philosopher, for sophistic is
Wisdom which exists only in semblance, and dialecticians
20 embrace all things in their dialectic, and being is common
to all things ;but evidently their dialectic embraces these
subjects because these are proper to philosophy. For
sophistic and dialectic turn on the same class of things as
philosophy, but this differs from dialectic in the nature of
the faculty required and from sophistic in respect of the
35 purpose of the philosophic life. Dialectic is merely critical
where philosophy claims to know, and sophistic is what
appears to be philosophy but is not.
Again, in the list of contraries one of the two columns 1
is privative,and all contraries are reducible to being and
non-being,and to
unityand
plurality,as for instance rest
belongs to unity and movement to plurality. And nearly
30 all thinkers agree that being and substance are composed
of contraries;at least all name contraries as their first prin
ciples some name odd and even,2 some hot and cold,
3
some limit and the unlimited,4 some love and strife.
5 And
all the others as well are evidently reducible to unity and
ioosa plurality (this reduction we must take for granted 6), and the
principles stated by other thinkers fall entirely under these
as their genera. It is obvious then from these considera
tions too that it belongs to one science to examine being
qua being. For all things are either contraries or com
posed of contraries, and unity and plurality are the starting-
5 points of all contraries. And these belong to one science,
whether they have or have not one single meaning. Prob
ably the truth is that they have not; yet even if one has
several meanings, the other meanings will be related to the
primary meaning (and similarly in the case of the con
traries), even if being or unity is not a universal and the
1
Cf. note on A. 986
a
23.
2
The Pythagoreans.3 Parmenides in thek
Way of Opinion .
4 The Platonists.6
Empedocles.fi
Cf. Fr. 1 4;8b36-i479
a5-
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BOOK P. 2 ioosa
same in every instance or is not separable from the particu
lar instances (as in fact it probably is not;the unity is in 10
some cases that of common reference, in some cases that of
serialsuccession).
And for this reason it does notbelong-
to the geometer to inquire what is contrariety or complete
ness or unity or being or the same or the other, but only to
presuppose these concepts and reason from this starting-
point. Obviously then it is the work of one science to
examine being qua being, and the attributes which belong
to it qua being, and the same science will examine not
only substances but also their attributes, both those above 15
named l and the concepts prior and posterior ,
*
genus
and species ,whole and part ,
and the others of this
sort.2
3 We must state whether it belongs to one or to different
sciences to inquire into the truths which are in mathematics
calledaxioms,
and into substance.Evidently,
theinquiry
20
into these also belongs to one science, and that the science
of the philosopher ;for these truths hold good for every
thing that is, and not for some special genus apart from
others. And all men use them, because they are true of
being qtia being and each genus has being. But men use 25
them just so far as to satisfy their purposes ;that
is, as far
as the genus to which their demonstrations refer extends.
Therefore since these truths clearly hold good for all things
qua being (for this is what is common to them), to him who
studies being q^ia being belongs the inquiry into these as
well. And for this reason no one who is conducting a
special inquiry tries to say anything about their truth or 30
falsity, neither the geometer nor the arithmetician. Some
natural philosophers indeed have done so, and their pro
cedure was intelligible enough ;for they thought that they
alone were inquiring about the whole of nature and about
being. But since there is one kind of thinker who is above
even the natural philosopher (for nature is only one particu
lar genus of being), the discussion of these truths also will 35
11. 12.
2 With ioo3b22-ioo5
a 18 cf. B. 995b18-27, 997*25-34. With the
whole ch. cf. K. 3.
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ioosa METAPHYSICA
belong to him whose inquiry is universal and deals with
I0 5b
primary substance. Physics also is a kind of Wisdom, but
it is not the first kind. 1 And the attempts of some ofthose
who discuss the terms on which truth should be accepted,2
are due to a want of training in logic ;for they should know
these things already when they come to a special study,
and not be inquiring into them while they are listening to
lectures on it.
5 Evidently then it belongs to the philosopher, i. e. to him
who is studying the nature of all substance, to inquire also
into the principles of syllogism. But he who knows bestabout each genus must be able to state the most certain
10principles of his subject, so that he whose subject is exist
ing things qtta existing must be able to state the most
certain principles of all things. This is the philosopher,
and the most certain principle of all is that regarding which
it is impossible to be mistaken;for such a principle must
be both the best known (for all men may be mistaken
about things which they do not know), and non-hypothe-T 5 tical. For a principle which every one must have who
understands anything that is, is not a hypothesis ;and that
which every one must know who knows anything, he must
already have when he comes to a special study. Evidently
then such a
principle
is the most certain of all;
which
principle this is, let us proceed to say. It is, that the same
attribute cannot at the same time belong and not belong to
20 the same subject and in the same respect ;we must pre
suppose, to guard against dialectical objections, any further
qualifications which might be added. This, then, is the
most certain of all principles, since it answers to the defini-
^c, tion given above. For it is impossible for any one to believe the same thing to be and not to be, as some think
25 Heraclitus says. For what a man says, he does not neces
sarily believe;and if it is impossible that contrary attri
butes should belong at the same time to the same subject
(the usual qualifications must be presupposed in this pre
miss too), and if an opinion which contradicts another is
1 With ioo5aiQ-
b2 cf. K. 4.2 The reference may be to Antisthenes.
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BOOK T. 3 ioosb
contrary to it, obviously it is impossible for the same man
at the same time to believe the same thing to be and not to
be;for if a man were mistaken on this point he would have 3
contrary opinions at the same time. It is for this reasonthat all who are carrying out a demonstration reduce it to
this as an ultimate belief; for this is naturally the starting-
point even for all the other axioms.1
4 There are some who, as we said,2 both themselves assert 35
that it is possible for the same thing to be and not to be,
and say that people can judge this to be the case.3
And ioo6
among others many writers about nature use this language.
But wre have now posited that it is impossible for anything v
at the same time to be and not to be, and by this means
have shown that this is the most indisputable of all prin
ciples.4 Some indeed demand that even this shall be 5
demonstrated,5 but this they do through want of education,
for not to know of what things one should demand demon
stration, and of what one should not, argues want of educa
tion. For it is impossible that there should be demonstration
of absolutely everything (there would be an infinite regress,
so that there would still be no demonstration) ;but if there 10
are things of which one should not demand demonstration,
these persons could not say what principle they maintain
to be more self-evident than the present one.
We can, however, demonstrate negatively even that this
view 6is impossible )
if our opponent will only say some
thing ;and if he says nothing, it is absurd to seek to give
an account of our views to one who cannot give an account
of anything, in so far as he cannot do so. For such a man,
as such,is
from the start no better than a vegetable. Now 15
negative demonstration I distinguish from demonstra
tion proper, because in a demonstration one might be
1 With ch. 3 cf. B. 995b6-10, 996
b26-997
a15. With
ioc>5
b8-34 cf.
K. io6i b 34-io62a2(with ioo5
b23~6 cf. io62a 31-5).
2
Apparently a loose reference to ioo5b23-5.
3 The Megaric school may be referred to.
4i.e. we have shown that since A cannot be both B and not-jB, no
one can think A is both B and not-j5 (icos
b
22-32).6 The reference may be to Antisthenes.6 That the same thing can be and not be.
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ioo6a METAPHYSICA
thought to be begging the question, but if another person
is responsible for the assumption we shall have negative
proof, not demonstration. 1 The starting-point for all such
arguments is not the demand that our opponent shall say20 that something either is or is not (for this one might per
haps take to be a begging of the question), but that he shall
say something which is significant both for himself and for
another;for this is necessary, if he really is to say any
thing. For, if he means nothing, such a man will not be
capable of reasoning, either with himself or with another.
But if any one grants this, demonstration will be possible ;
2 5 for we shall already have something definite. The person
responsible for the proof, however, is not he who demon
strates but he who listens;for while disowning reason he
listens to reason. And again he who admits this has
admitted that something is true apart from demonstration
[so
that not
everything
will be*
so and not so].
First then this at least is obviously true, that the word
34 be or not be has a definite meaning, so that not every
thing will be so and not so \2
Again, if man has one
meaning, let this be two-footed animal; by having one
meaning I understand this : if man means c X\ then ifAis a man X will be what being a man means for him.
(It makes no difference even if one were to say a wordhas several meanings, if only they are limited in number
;
ioo6bfor to each definition there might be assigned a different
word. For instance, we might say that man has not one
meaning but several, one of which would have one defini
tion, viz.*
two-footed animal,while there might be also
several other definitions ifonly they were limited in number;
for a peculiar name might be assigned to each of the
5 definitions. If, however, they were not limited but one were
to say that the word has an infinite number of meanings,
obviously reasoning would be impossible ;for not to have
one meaning is to have no meaning, and if words have no
meaning our reasoning with one another, and indeed with
10 ourselves, has been annihilated;for it is
impossible
to think
1 With 11. s-i 8 cf. K. 1062*2-5.2 For so and not so cf. PI. Theaet. 183 A.
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BOOK F. 4 ioo6b
of anything if we do not think of one thing ;but if this is
possible, one name might be assigned to this thing.)
Let it be assumed then, as was said at the beginning,1
that the name has a meaning and has one meaning ; it is
impossible, then, that being a man should mean precisely
not being a man,if
( man not only signifies something
about one subject but also has one significance (for we do 15
not identify having one significance with4
signifying
something about one subject ,since on that assumption
even musical and white and man would have had one
significance, so that all things would have been one ;for
they would all have had the same significance).
And it will not be possible to be and not to be the same
thing, except in virtue of an ambiguity, just as if one whom
we call* man
,others wrere to call not-man
;but the point
20
in question is not this, whether the same thing can at the
same time be and not be a man in name, but whether it can
in fact. Now if man and not-man mean nothing dif
ferent, obviously not being a man will mean nothing
different from being a man;so that
*
being a man will
be not being a man;for they will be one. For being one 25
means this being related as raiment and 4
dress are, if
their definition is one. And if being a man and being
a not-man are to be one, they must mean one thing. Butit was shown earlier
2that they mean different things.
Therefore, if it is true to say of anything that it is a man, it
must be a two-footed animal (for this was what man
meant 3
) ;and if this is necessary, it is impossible that the 30
same thing should not at that time be a two-footed animal;
for this is what being necessary meansthat it is im
possible for the thing not to be. It is, then, impossible that
it should be at the same time true to say the same thing is
a man and is not a man.
The same account holds good with regard to not being
a man,for being a man and *
being a not-man mean ioo7a
different things, since even being white and being a man
are different;for the former terms are much more opposed,
so that they must a fortiori mean different things. And1 a
2i, 31.2
11. 11-15.3
in a3if-
F 2
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ioo7a METAPHYSICA
if any one says that white means one and the same thing
5 as man, again we shall say the same as what was said
before,1that it would follow that all things are one, and not
only opposites.But if this is
impossible,then
what wehave maintained will follow, if our opponent will only
answer our question.
Andif, when one asks the question simply, he adds the
10 contradictories, he is not answering the question. For there
is nothing to prevent the same thing from being both a man
and white and countless other things : but still, if one asks
whether it is or is not true to say that this is a man, our
opponent must give an answer which means one thing, and
not add that it is also white and large . For, besides other
reasons, it is impossible to enumerate its accidental attri-
15 butes, which are infinite in number;
let him, then,
enumerate either all or none. Similarly, therefore, even if
the same thing is a thousand times a man and a not-man,
he must not, in answering the question whether this is a
man, add that it is also at the same time a not-man, unless
he is bound to add also all the other accidents, all that the
subject is or is not;and if he does this, he is not observing
the rules of argument.2
20 And in general those who say this do away with sub
stance andessence.
For theymust
saythat all attributes
are accidents, and that there is no such thing as being
essentially a man or* an animal . For if there is to be
any such thing as being essentially a man this will not be
being a not-man or not being a man (yet these are
25 negations of it3
) ;for there was one thing which it meant,
and this was the substance of something. And denoting
the substance of a thing means that the essence of the thing
is nothing else. But if its being essentially a man is to be
the same as either being essentially a not-man or essentially
not being a man, then its essence will be something else.
Therefore our opponents must say that there cannot be
1 ioo6b i7.
2 With ioo6a i8-ioo;a 20 cf. K. 1062* 5-20 (with ioo6b 28-34 cf.
1062* 20-3).3Sc. and hence (on the view attacked) should be compatible with it.
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BOOK T. 4 ioo7a
such a definition of anything, but that all attributes are 30
accidental;for this is the distinction between substance and
accident white is accidental to man, because though he
is
white,whiteness is not his essence. But if all statements
are accidental, there will be nothing primary about which
they are made, if the accidental always implies predication 35
about a subject. The predication, then, must go on ad in- ioo7b
finitum. But this is impossible ;for not even more than two
terms can be combined in accidental predication. For (i)
an accident is not an accident of an accident, unless it be
because both are accidents of the same subject. I mean,for instance, that the white is musical and the latter is white,
only because both are accidental to man. But(2) Socrates 5
is musical, not in this sense, that both terms are accidental
to something else. Since then some predicates are acci
dental in this and some in that sense, (a) those which are
accidental in the latter sense, in which white is accidental to
Socrates, cannot form an infinite series in the upward direc
tion;
1e. g. Socrates the white has not yet another acci
dent;for no unity can be got out of such a sum. Nor 10
again (b) will*
white have another term accidental to it,
e. g.*
musical . For this is no more accidental to that than
that is to this;and at the same time we have drawn the
distinction, that while some predicates are accidental in this
sense, others are so in the sense in which musical is acci
dental to Socrates;and the accident is an accident of an
accident not in cases of the latter kind, but only in cases of T 5
the other kind, so that not all terms will be accidental.2
There must, then, even so be something which denotes sub
stance. And if this is so, it has been shown that contra
dictoriescannot
bepredicated
at thesame time.
Again, if all contradictory statements are true of the
same subject at the same time, evidently all things will be
one. For the same thing will be a trireme, a wall, and a 20
man, if ofeverything it is possible either to affirm or to deny
1i. e. in the direction of predicates, which are naturally wider or
higher than the subject.2
Sense (i) reduces to sense (2), and in this an infinite number ofaccidents combined together is impossible ;
there must be substance
somewhere.
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ioo7b METAPHYSICA
anything (and this premiss must be accepted by those who
share the views of Protagoras). For if any one thinks that
the man is not a trireme, evidently he is not a trireme;so
that he also is a trireme, if, as they say, contradictory
25 statements are both true. And we thus get the doctrine of
Anaxagoras,1that all things are mixed together ;
so that
nothing really exists. They seem, then, to be speaking of
the indeterminate, and, while fancying themselves to be
speaking of being, they are speaking about non-being ;for
it is that which exists potentially and not in complete
reality
that is indeterminate. Butthey
mustpredicate
of
every subject the affirmation or the negation of every attri-
3 bute. For it is absurd if of each subject its own negation
is to be predicable, while the negation of something else
which cannot be predicated of it is not to be predicable of
it;for instance, if it is true to say of a man that he is not
a man, evidently it is also true to say that he is either a
trireme or not a trireme. If, then, the affirmative2
can be35 predicated, the negative must be predicable too
;and if the
affirmative is not predicable, the negative, at least, will be
ioo8a more predicable than the negative of the subject itself. If,
then, even the latter negative is predicable, the negative of
*
trireme will be also predicable ; and, if this is predicable,
the affirmative will be so too.3
Those, then, who maintain this view are driven to this
conclusion, and to the further conclusion that it is not
necessary either to assert or to deny. For if it is true
5 that a thing is a man and a not-man, evidently also it will be
neither a man nor a not-man. For to the two assertions
there answer two negations, and if the former 4is treated as
asingle proposition compounded
out oftwo,
the latter also
is a single proposition opposite to the former.5
Again, either the theory is true in all cases, and a thing
is both white and not-white, and existent and non-existent,
and all other assertions and negations are similarly com-
1Fr. i.
2Sc. trireme .
8 With ico7b i8-ioo8a 2 cf. K. io62a
23-30.4Sc. that the thing is a man and a not-man.
5 With 11. 6-7 cf. K. io62a 36-b
;.
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BOOK T. 4 ioo8a
patible, or the theory is true of some statements and not of 10
others. And if not of all, the exceptions will be contradic
tories of which admittedly only one is true;but if of all,
again
either the
negation
will be true wherever the asser
tion is, and the assertion true wherever the negation is, or
the negation will be true where the assertion is, but the
assertion not always true where the negation is. And (a) 15
in the latter case there will be something which fixedly
zs not, and this will be an indisputable belief;and if non-
being is something indisputable and knowable, the oppo
site assertion will be more knowable. But (6) if it is equally
possible also to assert all that it is possible to deny, one must
either be saying what is true when one separates the pre
dicates (and says, for instance, that a thing is white, arid
again that it is not-white), or not. And if(i)
it is not true 2
to apply the predicates separately, our opponent is not say
ing what he professes to say, and also nothing at all exists;
but how could non-existent things speak or walk, as he
does ? Also all things would on this view be one, as has
been already said,1 and man and God and trireme and their
contradictories will be the same. For if contradictories can 25
be predicated alike of each subject, one thing will in no
wise differ from another;for if it differ, this difference will
be something true and peculiar to it. And(ii)
ifone maywith truth apply the predicates separately, the above-
mentioned result follows none the less, and, further, it
follows that all would then be right and all would be in
error, and our opponent himself confesses himself to be in
error. And at the same time our discussion with him is 30
evidently about nothing at all;for he says nothing. For
hesays
neither
yes
nor no,but
yesand no
;and
again he denies both of these and says neither yes nor
no;
for otherwise there would already be something
definite.
Again, it when the assertion is true, the negation is false,
and when this is true, the affirmation is false, it will not be 35
possible to assert and deny the same thing truly at the same
1 ioc6b 17, ioo7a6.
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ioo8b METAPHYSICA
ioo8btime. But perhaps they might say this was the very ques
tion at issue.
Again, is he in error who judges either that the thing is
so or that it is notso,
and is heright
whojudges
both ? If
he is right, what can they mean by saying that the nature
5 of existing things is of this kind ? And if he is not right,
but more right than he who judges in the other way, being
will already be of a definite nature, and this will be true,
and not at the same time also not true. But if all are alike
both wrong and right, one who is in this condition will not
be able either to speak or to say anything intelligible ; for
10 he says at the same time both yes and no . And if he
makes no judgement but*
thinks and 4
does not think,in
differently, what difference will there be between him and
a vegetable? Thus, then, it is in the highest degree evident
that neither any one of those who maintain this view nor
any one else is really in this position. For why does a
man walk to Megara and not stay at home, when he thinks
J 5 he ought to be walking there? Why does he not walk
early some morning into a well or over a precipice, if one
happens to be in his way ? Why do we observe him
guarding against this, evidently because he does not think
that fallingin is alike good and not good ? Evidently, then,
hejudges
onething
to be better and another worse. And
if this is so, he must also judge one thing to be a man and
20 another to be not-a-man, one thing to be sweet and another
to be not-sweet. For he does not aim at and judge all
things alike, when, thinking it desirable to drink water or
to see a man, he proceeds to aim at these things ; yet he
ought, if the same thing were alike a man and not-a-man.
But, as was said, there is no one who does not obviously2 5 avoid some things and not others. Therefore, as it seems,
all men make unqualifiedjudgements, if not about all things,
still about what is better and worse.1 And if this is not
knowledge but opinion, they should be all the more anxious
about the truth, as a sick man should be more anxious about
30 his health than one who is healthy ;for he who has opinions
1 With 11. 12-27 cf. K. io63a28-35.
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BOOK T. 4 ioo8fc
is, in comparison with the man who knows, not in a healthy
state as far as the truth is concerned.
Again, however much all things may be so and not so,
still there is a more and a less in the nature of things;
for
we should not say that two and three are equally even, nor
is he who thinks four things are five equally wrong with
him who thinks they are a thousand. If then they are not 35
equally wrong, obviously one is less wrong and therefore
more right. If then that which has more of any quality is
nearer the norm, there must be some truth to which the 1009*
more true is nearer. And even if there is not, still there is
already something better founded and liker the truth, and
we shall have got rid ofthe unqualified doctrine which would
prevent us from determining anything in our thought. 5
5 From the same opinion proceeds the doctrine of Prota
goras, and both doctrines must be alike true or alike untrue.
For on the one hand, if all opinions and appearances are
true, all statements must be at the same time true and false.
For many men hold beliefs in which they conflict with one
another, and think those mistaken who have not the same 10
opinions as themselves;so that the same thing must both
be and not be. And on the other hand, if this is so, all
opinions must be true;for those who are mistaken and
those who are right are opposed to one another in their
opinions ;if then, reality is such as the view in question
supposes, all will be right in their beliefs.
Evidently, then, both doctrines proceed from the same 15
way of thinking. But the same method of discussion must
not be used with all opponents; for some need persuasion,
and others compulsion. Those who have been driven to
this position by difficulties in their thinking can easily be
cured of their ignorance ;for it is not their expressed argu
ment but their thought that one has to meet. But those 20
who argue for the sake of argument can be cured only by
refuting the argument as expressed in speech and in words.1
Those who really feel the difficulties have been led to
this
opinion byobservation of the sensible world,
(i) They1 With 11. 16-22 cf. K. io6s
b7-i6.
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ioo9a METAPHYSICA
think that contradictories or contraries are true at the same
time, because they see contraries coming into existence out
25 of the same thing1
. If, then, that which is not cannot come
to be, the thing must have existed before as both contraries
alike, as Anaxagoras says all is mixed in all, and Demo-
critus too;
for he says the void and the full exist alike in
every part, and yet one of these is being, and the other
30 non-being.1 To those, then, whose belief rests on these
grounds, we shall say that in a sense they speak rightly and
in a sense they err. For *
that which is has two meanings,
so that in some sense a thing can come to be out of that
which is not, while in some sense it cannot, and the same
thing can at the same time be in being and not in being
but not in the same respect. For the same thing can be
35 potentially at the same time two contraries, but it cannot
actually.2 And again we shall ask them to believe that
among existing things there is also another kind of sub
stance to which neither movement nor destruction nor
generation at all belongs.
ioo9b And (2) similarly some have inferred from observation
of the sensible world the truth of appearances. For they
think that the truth should not be determined by the large
or small number of those who hold a belief, and that the
same thing is thought sweet by some when they taste it,
5 and bitter by others, so that if all were ill or all were mad,
and only two or three were well or sane, these would be
thought ill and mad, and not the others.
And again, they say that many of the other animals
receive impressions contrary to ours;and that even to the
senses of each individual, things do not always seem the
same. Which, then, of these impressions are true and10 which are false is not obvious; for the one set is no more
true than the other, but both are alike. And this is why
Democritus, at any rate, says that either there is no truth or
to us at least it is not evident.
And in general it is because these thinkers suppose
knowledge
to be sensation, and this to be a physical altera-
1 With 11. 6-1 6, 22-30 cf. K. io62b 12-24.2 With 11. 30-6 cf. K. 1062*24-33.
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BOOK T. 5 ioo9b
tion, that they say that what appears to our senses must be
true;for it is for these reasons that both Empedocles and 1
5
Democritus and, one may almost say, all the others have
fallen victims to opinions of this sort. For Empedoclessays that when men change their condition they change
their knowledge ;
For wisdom increases in men according to what is before
them. 1
And elsewhere he says that
Sofar
as their nature changed, so far to them always20
Came changed thoughts into mind. 2
And Parmenides also expresses himself in the same way :
For as at each time the much-bent limbs are composed,So is the mind of men
;for in each and all men
Tis one thing thinks the substance of their limbs :
For that of which there is more is thought.:i
A saying of Anaxagoras to some of his friends is also 25
related, that things would be for them such as they sup
posed them to be. And they say that Homer also evidently
had this opinion, because he made Hector, when he was
unconscious from the blow, lie*
thinking other thoughts ,
4
which implies that even those who are bereft of thought 30
havethoughts, though
not the samethoughts. Evidently,
then, if both are forms of knowledge, the real things also
are at the same time both so and not so V5 And it is in this
direction that the consequences are most difficult. For if
those who have seen most of such truth as is possible for us
(and these are those who seek and love it most) if these35
have such opinions and express these views about the truth,
isit not natural that beginners in philosophy should lose
heart ? For to seek the truth would be to follow flying
game.
But the reason why these thinkers held this opinion is ioioa
that while they were inquiring into the truth of that which
is, they thought that which is was identical with the
1
Fr. 106.2
Fr. 108.3
Fr. 16.*
Cf. //. xxiii. 698, which does not, however, refer to Hector.6 With a
38-b33 cf. K. 1063* 35~
b7.
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ioa METAPHYSICA
sensible world;
in this, however, there is largely present
the nature of the indeterminate of that which exists in the
peculiar sense which we have explained ;
1 and therefore,
while they speak plausibly, they do not say what is true
5 (for it is fitting to put the matter so rather than as Epichar-
musput it against Xenophanes2
;.And again, because they
saw that all this world of nature is in movement, and that
about that which changes no true statement can be made,
they said that ofcourse, regarding that which everywhere in
every respect is changing, nothing could truly be affirmed.
10 It was this belief that blossomed into the most extreme of
the views above mentioned, that of the professed Hera-
cliteans, such as was held by Cratylus, who finally did not
think it right to say anything but only moved his finger,
and criticized Heraclitus for saying that it is impossible to
step twice into the same river;
3for he thought one could
not do it even once.
J 5 But we shall say in answer to this argument also, that
while there is some justification for their thinking that the
changing, when it is changing, does not exist, yet it is after
all disputable ;for that which is losing a quality has some
thing of that which is being lost, and of that which is
coming to be, something must already be. And in general
if a thing is perishing, there will be present something that20 exists
;and if a thing is coming to be, there must be some
thing from which it comes to be and something by which
it is generated, and this process cannot go on ad infinitum.
But, leaving these arguments, let us insist on this, that it is
not the same thing to change in quantity and in quality.
Grant that in quantity a thing is not constant;
still it is in
25 respect of its form that we know each thing.4 And again,
it would be fair to criticize those who hold this view for
asserting about the whole material universe what they saw
only in a minority even of sensible things. For only that
region of the sensible world which immediately surrounds
1Cf. ioo9
a32.
2Fr.
252
Kaibel.
Epicharmus mayhave said that Xenophanes
views were neither plausible nor true,or that they were true but
not plausible .
3Fr. 91.
4 With 11. 22-5 cf- K . io63a 22-8.
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BOOK r. 5 ioioa
us is always in process of destruction and generation ;but 3
this is so to speak not even a fraction of the whole, so
that it would have been juster to acquit this part of the
world because of the other part, than to condemn the other
because of this.1 And again, obviously we shall make to
them also the same reply that we made long ago ;
2 we
must show them and persuade them that there is something
whose nature is changeless. Indeed, those who say that 35
things at the same time are and are not, should in conse
quence say that all things are at rest rather than that they
are in movement;for there is nothing into which they can
change, since all attributes belong already to all subjects.
Regarding the nature of truth, we must maintain that not ioiob
everything which appears is true; firstly, because even if
sensation at least of the object peculiar to the sense in
question is not false, still appearance is not the same as
sensation.
Again,
it is fair to
express surprise
at our
opponents raising the question whether magnitudes are as
great, and colours are of such a nature, as they appear to 5
people at a distance, or as they appear to those close at
hand, and whether they are such as they appear to the
healthy or to the sick, and whether those things are heavy
which appear so to the weak or those which appear so to
the strong, and those things true which appear to the
sleeping or to the waking. For obviously they do not
think these to be open questions ;no one, at least, if when 10
he is in Libya he has fancied one night that he is in Athens,
starts for the concert hall. And again with regard to the
future, as Plato says,3
surely the opinion of the physician
and that of the ignorant man are not equally weighty, for
instance, on the question whether a man will get well or
not. And again, among sensations themselves the sensa- 15
tion of a foreign object and that of the appropriate object,
or that of a kindred object and that of the object of the
sense in question,4 are not equally authoritative, but in the
1 With 11. 25-32 cf. K. 1063* 10-17.2
Cf. 1009*36-8. 3 Cf. Theaetetus 178 6-179 A.4
E.g. the awareness which smell gives us of savour and of odour
respectively.
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ioiob METAPHYSICA
case of colour sight, not taste, has the authority, and in
the case of flavour taste, not sight ;each of which senses
never says at the same time of the same object that it
simultaneously is so and not so.
But not even at different
20 times does one sense disagree about the quality, but only
about that to which the quality belongs. I mean, for
instance, that the same wine might seem, if either it or one s
body changed, at one time sweet and at another time not
sweet;but at least the sweet, such as it is when it exists,
25has never yet changed, but one is always right about it, and
that which is to be sweet is of necessity of such and such
a nature.1 Yet all these views destroy this necessity, leaving
nothing to be of necessity, as they leave no essence of
anything ;for the necessary cannot be in this way and also
in that, so that if anything is of necessity, it will not be both
so and not so .
3o And,in
general,if
onlythe sensible
exists,
there would
be nothing if animate things were not;for there would be
no faculty of sense. Now the view that neither the sensible
qualities nor the sensations would exist is doubtless true
(for they are affections of the perceiver), but that the sub
strata which cause the sensation should not exist even apart
35 from sensation is impossible. For sensation is surely not
the sensation of itself, but there is something beyond the
sensation, which must be prior to the sensation;for that
ionawhich moves is prior in nature to that which is moved, and
if they are correlative terms, this is no less the case.
There are, both among those who have these convictions 6
and among those who merely profess these views, some who
5 raise a difficulty by asking, who is to be the judge of the
healthy man, and in general who is likely to judge rightly
on each class of questions. But such inquiries are like
puzzling over the question whether we are now asleep or
awake. And all such questions have the same meaning.
These people demand that a reason shall be given for
everything;
2for they seek a starting-point, and they seek
1 With 11. 1-26 cf. K. io62b 33-io63aio.
2 The reference may be to Antisthenes.
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BOOK T. 6 ion*
to get this by demonstration, while it is obvious from their 10
actions that they have no conviction. But their mistake is
what we have stated it to be; they seek a reason for things
for which no reason can be given ; for the starting-point of
demonstration is not demonstration.
These, then, might be easily persuaded of this truth, for
it is not difficult to grasp ;but those who seek merely 15
compulsion in argument seek what is impossible ;for they
demand to be allowed to contradict themselves a claim
which contradicts itself from the very first.1 But if not all
things are relative, but some are self-existent, not every
thing that appears will be true;for that which appears is
apparent to some one ; so that he who says all things that
appear are true, makes all things relative. And, therefore, 20
those who ask for an irresistible argument, and at the same
time demand to be called to account for their views, must
guard themselves by saying that the truth is not that what
appears exists, but that what appears exists for him to
whom it appears, andw/ien, and to the sense to which^ and
under the conditions under which it appears. And if they
give an account of their view, but do not give it in this way,
they will soon find themselves contradicting themselves.
For it is possible that the same thing may appear to be 25
honey to the sight, but not to the taste, and that, since wehave two eyes, things may not appear the same to each,
if their sight is unlike. For to those who for the reasons
named some time ago2
say that what appears is true, and 30
therefore that all things are alike false and true, for things
do not appear either the same to all men or always the same
to the same man, but often have contrary appearances at
the same time (for touch says there are two objects whenwe cross our fingers, while sight says there is one),
3to
these we shall say yes, but not to the same sense and in
the same part of it and under the same conditions and at 35
the same time,so that what appears will be with these
qualifications true. But perhaps for this reason those who ionb
argue thus not because they feel a difficulty but for the sake
1 With 11. 3-16 cf. K. 1063*7-16.a
Cf. ioo9a38-ioio
a15.
3 With 11. 31-4 cf. K. io62b 33-io63a 10.
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IOIIb METAPHYSICA
of argument, should say that this is not true, but true for
this man. And as has been said x
before, they must make
5 everything relative relative to opinion and perception, so
that nothing either has come to be or will be without someone s first thinking so. But if things have come to be or
will be,2
evidently not all things will be relative to opinion.
Again, if a thing is one, it is in relation to one thing or to
a definite number of things; and if the same thing is both
half and equal, it is not to the double that the equal is corre
lative.3
If, then, in relation to that which thinks, man and
10 that which is thought are the same, man will not be that
which thinks, but only that which is thought. And if each
thing is to be relative to that which thinks, that which
thinks will be relative to an infinity of specifically different
things.
Let this, then, suffice to show (i) that the most indis
putableof all beliefs is that
contradictorystatements are
not at the same time true, and (2) what consequences follow
from the assertion that they are, and(3) why people do
15 assert this. Now since it is impossible that contradictories
should be at the same time true ofthe same thing, obviously
contraries also cannot belong at the same time to the same
thing. For of contraries, one is a privation no less than it
is a contrary and a privation of the essential nature ; and
privation is the denial of a predicate to a determinate genus.
20 If, then, it is impossible to affirm and deny truly at the same
time, it is also impossible that contraries should belong to
a subject at the same time, unless both belong to it in par
ticular relations, or one in a particular relation and one
without qualification.4
But on the other hand there cannot be an intermediate 7
between contradictories, but of one subject we must either
25 affirm or deny any one predicate. This is clear, in the first
place, if we define what the true and the false are. To say
of what is that it is not, or of what is not that it is, is false,
2Sc. without some one s first thinking so.
3Sc. but the equal to the equal, the half to the double.
4 With 11. 17-22 cf. K. io63b17-19-
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BOOK r. 7 ionb
while to say of what is that it is, and of what is not that it
is not, is true;so that he who says of anything that it is, or
that it is not, will say either what is true or what is false;
but neither what is nor what is not is said to be or not to
be.1
Again, the intermediate between the contradictories
will be so either in the way in which grey is between black 3o
and white,2 or as that which is neither man nor horse is
between man and horse, (a) If it were of the latter kind,
it could not change into the extremes (for change is from
not-good to good, or from good to not-good), but as
a matter of fact when there is an intermediate it is always
observed to change into the extremes. For there is no change
except to opposites3 and to their intermediates.
(<5)
But if it 35
is really intermediate,4 in this way too there would have to be
a change to white, which was not from not-white;but as it
is, this is never seen. Again, every object of understanding ioi2a
or reason the understanding either affirms or denies this is
obvious from the definition whenever it says what is true
or false. When it connects in one way by assertion or nega
tion, it says what is true, and when it does so in another way,
what is false. Again, there must be an intermediate between 5
// contradictories, if one is not arguing merely for the sake
of argument ;so that it will be possible for a man to say
what is neither true noruntrue,
and there will be a middle
between that which is and that which is not, so that there
will also be a kind of change intermediate between genera
tion and destruction. Again, in all classes in which the
negation of an attribute involves the assertion of its con
trary, even in these there will be an intermediate;
for 10
instance, in the sphere of numbers there will be number
which is neither odd nor not-odd. But this is impossible,
as is obvious from the definition. Again, the process will
go on ad infinitum, and the number of realities will be
1Sc. by those who say there is an intermediate between contradic
tories. Hence such a statement is neither true nor false, which is
absurd.2
Though of course it differs from this case in being between con
tradictories,not contraries.
3Sc. contrary, not contradictory opposites.
4Sc. as grey is between black and white.
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ioi2a METAPHYSICA
not only half as great again, but even greater. For again
it will be possible to deny this intermediate with reference
both to its assertion and to its negation,1 and this new term
will be some definite
thing;for its essence is
something15 different. Again, when a man, on being asked whether
a thing is white, says4 no
,he has denied nothing except
that it is;and its not being is a negation.
Some people have acquired this opinion as other para
doxical opinions have been acquired ;when men cannot
refute eristical arguments, they give in to the argument and
20 agree that the conclusion is true. This, then, is why someexpress this view
;others do so because they demand
a reason for everything.2 And the starting-point in dealing
with all such people is definition. Now the definition rests
on the necessity of their meaning something ;for the form
of words ofwhich the word is a sign will be its definition.3
While the doctrine of Heraclitus, that all things are and are
25 not, seems to make everything true, that of Anaxagoras,
that there is an intermediate between the terms of a contra
diction, seems to make everything false;for when things
are mixed, the mixture is neither good nor not-good, so
that one cannot say anything that is true.
In view of these distinctions it is obvious that the one- 8
30 sided theories which some people express about all things
cannot be valid on the one hand the theory that nothing
is true (for, say they, there is nothing to prevent every
statement from being like the statement the diagonal of
a square is commensurate with the side),on the other hand
the theory that everything is true. These views are practi
cally the same as that of Heraclitus;for he who says that
35l
all things are true and all are false also makes each of
1012 these statements separately, so that since they are impos
sible, the double statement must be impossible too. Again,
there are obviously contradictories which cannot be at the
same time truenor on the other hand can all statements
1i. e. if there is a term B which is neither A nor not-A, there will
be a new term C which is neither B nor not-jS*.2 The reference may be to Antisthenes.5 With ionb
23-loi2a24 cf. K. io63
b19-24.
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BOOK P. 8 ioi2b
be false; yet this would seem more possible in the light of
what has been said. But against all such views we must5
postulate, as we said above,1 not that something is or is
not, but that something has a meaning, so that we must
argue from a definition, viz. by assuming what falsity or
truth means. If that which it is true to affirm is nothing
other than that which it is false to deny, it is impossible
that all statements should be false;for one side of the con- 10
tradiction must be true. Again, if it is necessary with
regard to everything either to assert or to deny it,it is
impossible that both should be false;for it is one side of
the contradiction that is false. Therefore all such views
are also exposed to the often expressed objection, that they
destroy themselves. For he who says that everything is I 5
true makes even the statement contrary to his own true,
and therefore his own not true (for the contrary statement
denies that it is true), while he who says everything is false
makes himself also false.2 And if the former person excepts
the contrary statement, saying it alone is not true, while
the latter excepts his own as being not false, none the less 20
they are driven to postulate the truth or falsity ofan infinite
number ofstatements;for that which says the true statement
is true is true, and this process will go on to infinity.
Evidently, again,those
who sayall
thingsare at rest are
not right, nor are those who say all things are in move
ment. For if all things are at rest, the same statements
will always be true and the same always false, but this
obviously changes ;for he who makes a statement, himself 25
at one time was not and again will not be. And if all
things are in motion, nothing will be true; everything
therefore will be false. But it has been shown that this is
impossible. Again, it must be that which is that changes;
for change is from something to something. But again
it is not the case that all things are at rest or in motion
sometimes, and nothing for ever;for there is something 30
which always moves the things that are in motion, and the
first mover is itself unmoved.
1Cf. ioo6a 18-22.
2 With a24-
b 18 cf. K. io63b24-35 (with
b13-18 cf. io62b 7-9).
G 2
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BOOK A
4 BEGINNING means(i) that part of a thing from which i
35 one would start first, e. g. a line or a road has a beginning
ioi3ain either of the contrary directions. (2) That from which
each thing wrould best be originated, e. g. even in learning
we must sometimes begin not from the first point and the
beginning of the subject, but from the point from which we
should learn most easily. (3) That from which, as an
immanent part, a thing first comes to be, e. g. as the keel
5 of a ship and the foundation of a house, while in animals
some suppose the heart, others the brain, others some other
part, to be of this nature. (4) That from which, not as an
immanent part, a thing first comes to be, and from which
the movement or thechange naturally
first
begins,as a
child comes from its father and its mother, and a fight
10 from abusive language. (5) That at whose will that which
is moved is moved and that which changes changes, e. g.
the magistracies in cities, and oligarchies and monarchies
and tyrannies, are called apxafV and so are tne arts&
and of
these especially the architectonic arts. (6) That from which
15 a thing can first be known, this also is called the beginning
of the thing, e. g. the hypotheses are the beginnings of
demonstrations. (Causes are spoken of in an equal number
of senses;for all causes are beginnings.) It is common,
then, to all beginnings to be the first point from which
a thing either is or comes to be or is known;but of these
some are immanent in the thing and others are outside.
20 Hence the nature of a thing is a beginning, and so is the
element of a thing, and thought and will, and essence, and
the final cause for the good and the beautiful are the
beginning both of the knowledge and of the movement of
many things.
Cause means (i)that from which, as immanent 2
1 The double meaning of apxn beginning and government-
cannot be reproduced in English.
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BOOK A. 2 ioi3a
material, a thing comes into being, e. g. the bronze is the 25
cause of the statue and the silver of the saucer, and so are
the classes which include these. (2) The form or pattern,
i.
e. the definition of the essence, and the classes whichin
clude this (e. g. the ratio 2 : i and number in general are
causes of the octave), and the parts included in the definition.
(3) That from which the change or the resting from change
first begins ;e. g. the adviser is a cause of the action, and 3
the father a cause of the child, and in general the maker
a cause of the thing made and the change-producing of the
changing. (4) The end, i. e. that for the sake of which a
thing is;
e. g. health is the cause of walking. For Whydoes one walk ? we say ;
that one may be healthy ;and
in speaking thus we think we have given the cause. The 35
same is true of all the means that intervene before the end,
when something else has put the process in motion, as e. g.
thinning or purging or drugs or instruments intervene
before health is reached;for all these are for the sake of
the end, though they differ from one another in that some
are instruments and others are actions.
These, then, are practically all the senses in which causes
are spoken of, and as they are spoken of in several senses
it follows both that there are several causes of the same 5
thing,
and in no accidental sense(e. g. both the art of
sculpture and the bronze are causes of the statue not in respect
of anything else but qua statue; not, however, in the same
way, but the one as matter and the other as source of the
movement), and that things can be causes of one another
(e.g. exercise of good condition, and the latter of exercise;
not, however, in the same way, but the one as end and the 10
other as source of movement). Again, the same thing is
the cause of contraries;for that which when present causes
a particular thing, we sometimes charge, when absent, with
the contrary, e. g. we impute the shipwreck to the absence
of the steersman, whose presence was the cause of safety 5
and both the presence and the privation are causes as 15
sources of movement.
All the causes now mentioned fall under four senses
which are the most obvious. For the letters are the cause
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ioi3b METAPHYSICA
of syllables, and the material is the cause of manufactured
things, and fire and earth and all such things are the causes of
bodies, and the parts are causes of the whole, and the hypo-20 theses are causes of the conclusion, in the sense that they are
that out of which these respectively are made;but of these
some are cause as the siibstratum (e. g. the parts), others as
the essence (the whole, the synthesis, and the form). The
semen, the physician, the adviser, and in general the agent,
25 are all soiirces of change or of rest. The remainder are
causes as the end and the good of the other things ;for that
for the sake of which otherthings
are tends to be the best
and the end of the other things ;let us take it as making
no difference whether \ve call it good or apparent good.
These, then, are the causes, and this is the number of
their kinds, but the varieties of causes are many in number,
though when summarized these also are comparatively few.
30 Causes are spoken of in many senses, and even of those
which are of the same kind some are causes in a prior andothers in a posterior sense, e. g. both the physician and
the professional man are causes of health, and both the ratio
2:1 and number are causes of the octave, and the classes
that include any particular cause are always causes of the
particular effect. Again, there are accidental causes and
35 the classes which include these;
e. g. while in one sense
the sculptor causes the statue, in another sense*
Poly-
clitus causes it, because the sculptor happens to be
ioi4aPolyclitus ;
and the classes that include the accidental
cause are also causes, e. g. man or in general animal
is the cause of the statue, because Polyclitus is a man, and
man is an animal. Of accidental causes also some are more
5
remote or nearer thanothers, as,
forinstance,
if the white
and *
the musical were called causes of the statue, and not
only Polyclitus or man . But besides all these varieties
of causes, whether proper or accidental, some are called
causes as being able to act, others as acting ;e. g. the cause
of the house s being built is a builder, or a builder who is
10 building. The same variety of language will be found with
regard to the effects of causes ; e. g. a thing may be called
the cause of this statue or of a statue or in general of an
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BOOK A. 2 ioi4a
image, and of this bronze 1 or of bronze or of matter in
general ;and similarly in the case of accidental effects.
Again, both accidental and proper causes may be spoken of
incombination
;
e.
g. we may saynot
Polyclitusnor the
sculptor ,but *
Polyclitus the sculptor .
Yet all these are but six in number, while each is spoken 15
of in two ways ;for (A) they are causes either as the indi
vidual, or as the genus, or as the accidental, or as the genus
that includes the accidental, and these either as combined,2
or as taken simply ;and (B) all may be taken as acting or
as having a capacity. But they differ inasmuch as the act- 20
ing causes, i. e. the individuals, exist, or do not exist, simul
taneously with the things of which they are causes, e. g.
this particular man who is healing, with this particular man
who is recovering health, and this particular builder with
this particular thing that is being built;but the potential
causes are not always in this case;for the house does not
perish at the same time as the builder.325
3 Element means(i) the primary component immanent
in a thing, and indivisible in kind into other kinds;
e. g.
the elements of speech are the parts of which speech con
sists and into which it is ultimately divided, while they are
no longer divided into other forms of speech different in
kind from them. If they are divided, their parts are of the 30
same kind, as a part of water is water (while a part of the
syllable is not a syllable). Similarly those who speak of
the elements of bodies mean the things into which bodies
are ultimately divided, while they are no longer divided into
other things differing in kind;and whether the things of
this sort are one ormore, they
call these elements. The 35
so-called elements of geometrical proofs, and in general the
elements of demonstrations, have a similar character;
for
the primary demonstrations, each of which is implied in
many demonstrations, are called elements of demonstra- ioi4b
1 For this way of speaking cf. Phys. II. I94a33.
2Sc. the
particular propercause with the
particular accidental,or
the general proper with the general accidental.J With this chapter cf. Phys. I94
b23-I95
b 21.
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ioi4b METAPHYSICA
tions;and the primary syllogisms, which have three terms
and proceed by means of one middle, are of this nature.
(2) People also transfer the word element from this
meaningand
applyit to that
which, beingone and
small,5 is useful for many purposes ;
for which reason what is small
and simple and indivisible is called an element. Hence
come the facts that the most universal things are elements
(because each of them being one and simple is present in
a plurality of things, either in all or in as many as possible *),
and that unity and the point are thought by some to be
first principles. Now, since the so-called genera are
universal and indivisible (for there is no definition of them),10 some say the genera are elements, and more so than the
differentia, because the genus is more universal;for where
the differentia is present, the genus accompanies it, but
where the genus is present, the differentia is not always so.
It is common to all the meanings that the element of each
15 thing is the first component immanent in each.
*
Nature means (i) the genesis of growing things the 4
meaning which would be suggested if one were to pro
nounce the v infyva-is long.
2
(2) That immanent part of a
growing thing, from which its growth first proceeds. (3) The
source from which the primary movement in each natural
20 object is present in it in virtue of its own essence. Those
things are said to grow which derive increase from some
thing else by contact and either by organic unity, or by
organic adhesion as in the case of embryos. Organic unity
differs from contact;for in the latter case there need not
be anything besides the contact, but in organic unities
there is
somethingidentical in both
parts,which makes
3 5 them grow together instead of merely touching, and be one
in respect of continuity and quantity, though not ofquality.
(4)*
Nature means the primary material of which any
natural object consists or out of which it is made, which is
1
TJon 7r\i(TTois shows that A. is not thinking of the strict universals
of science but of the rough generalizations of dialectic. Cf. the use of
o-TOLXfiov in the Topics , and Diels, Elementum, p. 29.2This (i. e. growth )
is the etymological sense of(frvo-is.
to grow ,has v long in most of its forms.
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BOOK A. 4 ioi4b
relatively unshaped and cannot be changed from its own
potency, as e. g. bronze is said to be the nature of a statue
and of bronze utensils, and wood the nature of wooden
things ;
and so in all other cases ; for when a product is 3
made out of these materials, the first matter is preserved
throughout. For it is in this way that people call the
elements of natural objects also their nature, some naming
fire, others earth, others air, others water, others something
else of the sort, and some naming more than one of these,
and others all of them. (5)Nature means the essence of 35
natural objects, as with those who say the nature is the
primary mode of composition, or as Empedocles1
says :
Nothing that is has a nature, ioi5a
But only mixing and parting of the mixed,
And nature is but a name given them by men.
Hence as regards the things that are or come to be by
nature, though thatfrom which they naturally come to beor are is already present, we say they have not their nature
yet, unless they have their form or shape. That which 5
comprises both of these2exists by nature, e. g. the animals
and their parts ;and not only is the first matter nature
(and this in two senses, either the first, counting from the
thing, or the first in general ;e. g. in the case of works in
bronze, bronze is first with reference to them, but in general
perhaps water is first, if all things that can be melted are
water), but also the form or essence, which is the end of the 10
process of becoming. (6) By an extension ofmeaning from
this sense of nature every essence in general has come to
be called a nature,because the nature of a thing is one
kind of essence.
From what has been said, then, it is plain that nature in
the primary and strict sense is the essence of things which
have in themselves, as such, a source of movement;for the 15
matter is called the nature because it is qualified to receive
this, and processes of becoming and growing are called
nature because they are movements proceeding from this.
And nature in this sense is the source of the movement of1Fr. 8.
2Matter and form.
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ioi5a METAPHYSICA
natural objects, being present in them somehow, either
potentially or in complete reality.
20 We call necessary (i) (a) that without which, as a con- 5
dition, a thing1
cannot live;
e. g. breathing and food are
necessary for an animal;for it is incapable of existing with
out these; (6) the conditions withoutwhich goodcannot be or
come to be, or without which we cannot get rid or be freed
of evil;
e. g. drinking the medicine is necessary in order
25 that we may be cured of disease, and a man s sailing to
Aeginais
necessaryin order that he
may gethis
money.(2) The compulsory and compulsion, i. e. that which im
pedes and tends to hinder, contrary to impulse and pur
pose. For the compulsory is called necessary (whence the
necessary is painful, as Evenus l
says : For every necessary
30 thing is ever irksome),and compulsion is a form of neces
sity, as Sophocles2
says : But force necessitates me to this
act. And necessity is held to be something that cannot be
persuaded and rightly, for it is contrary to the movement
which accords with purpose and with reasoning. (3) We
say that that which cannot be otherwise is necessarily as it
35 is. And from this sense of necessary all the others are
somehow derived;for a thing is said to do or suffer what
ioi5b
is necessary in the sense of compulsory, only when it can
not act according to its impulse because of the compelling
force, which implies that necessity is that because of which
a thing cannot be otherwise;and similarly as regards the
conditions of life and of good ;for when in the one case
5 good, in the other life and being, are notpossible without cer
tain conditions, these are necessary, and this kind of cause
is a sort ofnecessity. Again,
demonstration is a neces
sary thing because the conclusion cannot be otherwise, if
there has been demonstration in the unqualified sense;and
the causes of this necessity are the first premisses, i.e. the
fact that the propositions from which the syllogism proceeds
cannot be otherwise.
Now some things owe their necessity to something other
10 than themselves ; others do not, but are themselves the
1Fr. 8 Killer.
2Electra 256.
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BOOK A. 5 ioisb
source of necessity in other things. Therefore the necessary
in the primary and strict sense is the simple ;for this does
not admit of more states than one, so that it cannot even be
in one state and also in another ; for if it did it would already
be in more than one. If, then, there are any things that are
eternal and unmovable, nothing compulsory or against their 15
nature attaches to them.
6 One means (i) that which is one by accident, (2) that
which is one by its own nature, (i) Instances of the acci
dentally one are Coriscus and what is musical , and musical
Coriscus (for it is the same thing to say4
Coriscus and what
is musical,and 4
musical Coriscus),
and what is musical
and what is just ,and ;
musical Coriscus and just Coriscus .
For all of these are called one by virtue of an accident, what 20
is just and what is musical because they are accidents of
one substance, what is musical and Coriscus because the
one is an accident of the other;and similarly in a sense
( musical Coriscus is one with4
Coriscus because one of the
parts of the phrase is an accident of the other, i. e. musical 25
is an accident of Coriscus;and * musical Coriscus is one
with just Coriscus because one part of each is an accident
of one and the same subject. The case is similar if the
accidentis
predicated of a genus or of any universal name,e. g. if one says that man is the same as musical man
;for 3
this is either because musical is an accident of man, which
is one substance, or because both are accidents of some
individual, e. g. Coriscus. Both, however, do not belong to
him in the same way, but one presumably as genus and
included in his substance, the other as a state or affection
of the substance.
The things, then, that are called one in virtue ofan accident, 35
are called so in this way. (2) Of things that are called one
in virtue of their own nature some (a) are so called because
they are continuous, e. g. a bundle is made one by a band, ioi6a
and pieces of wood are made one by glue ;and a line, even
if it is bent, is called one if it is continuous, as each part of
the body is, e. g. the leg or the arm. Of these themselves,
the continuous by nature are more one than the continuous
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ioi6a METAPHYSICA
5 by art. A thing is called continuous which has by its own
nature one movement and cannot have any other;and the
movement is one when it is indivisible, and it is indivisible
in respect oftime. Those things are continuous bytheir
ownnature which are one not merely by contact
;for if you put
pieces of wood touching one another, you will not say these
are one piece of wood or one body or one continuum ofany
other sort. Things, then, that are continuous in any way10 are called one, even if they admit of being bent, and still
more those which cannot be bent;
e. g. the shin or the
thigh is more one than the leg, because the movement of
the leg need not be one. And the straight line is more one
than the bent;but that which is bent and has an angle we
call both one and not one, because its movement may be
15 either simultaneous or not simultaneous;but that of the
straight line is always simultaneous, and no part of it which
has magnitude1rests while another moves, as in the bent line.
(b) (i) Things are called one in another sense because their
substratum does not differ in kind;
it does not differ in
the case of things whose kind is indivisible to sense.
The substratum meant is either the nearest to, or the
20 farthest from, the final state. For, on the one hand, wine
is said to be one and water is said to be one, qua indivisible
inkind
;
and, on the other hand, all juices,e.
g.oil and
wine, are said to be one, and so are all things that can be
melted, because the ultimate substratum of all is the same;
for all of these are water or air.
(ii)Those things also are called one whose genus is one
25 though distinguished by opposite differentiae these too
are all called one because the genus which underlies the
differentiae is one (e. g. horse, man, and dog form a unity,
because all are animals), and indeed in a way similar to that
in which the matter is one.2 These are sometimes called
one in this way, but sometimes it is the higher genus that
is said to be the same(if they are infimae species of their
30 genus) the genus above the proximate genera ;e. g. the
1 Any point may remain fixed while the line rotates round it;but
a point has no magnitude.2
Cf. (b) (i) above.
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BOOK A. 6 ioi6a
isosceles and the equilateral are one and the samefigure
because both are triangles ;but they are not the same
triangles.1
(c) Two things are called one, when the definition whichstates the essence of one is indivisible from another defini
tion which shows us the other (though in itself every
definition is divisible).Thus even that which has increased 35
or is diminishing is one, because its definition is one, as, in
the case of plane figures, is the definition of their form. In ioi6b
general those things the thought of whose essence is indi
visible, and cannot separate them either in time or in place
or in definition, are most of all one, and of these especially
those which are substances. For in general those things
that do not admit of division are called one in so far as they
do not admit of it;
e. g. if two things are indistinguishable 5
qua man, they are one kind of man;if qua animal, one kind
of animal;
if qua magnitude, one kind of magnitude.
Now most things are called one because they either do or
have or suffer or are related to something else that is one,
but the things that are primarily called one are those whose
substance is one, and one either in continuity or in form
or in definition;
for we count as more than one either
things that are not continuous, or those whose form is not 10
one,or those
whosedefinition is not one.
While in a sense we call anything one if it is a quantity
and continuous, in a sense we do not unless it is a whole,
i. e. unless it has unity of form;
e. g. if we saw the parts of
a shoe put together anyhow we should not call them one
all the same (unless because of their continuity) ;we do 15
this only if they are put together so as to be a shoe and to
have already a certain single form. This is why the circle is
of all lines most truly one, because it is whole and complete.
(3) The essence ofwhat is one is to be some kind ofbegin
ning of number;for the first measure is the beginning, since
that by which wre first know each class is the first measure
1
Horse, man, and dog are one, because all are animals. But if we
are to call them one something^ we cannot call them one (kind of)
animal, but must go to the higher genus and call them one (kind of)
living thing.
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ioi6b METAPHYSICA
20 of the class;the one, then, is the beginning of the knowable
regarding each class. But the one is not the same in all
classes. For here it is a quarter-tone, and there it is the
vowel or the consonant;
and there is another unit of weightand another of movement. But everywhere the one is
indivisible either in quantity or in kind. Now that which
25is indivisible in quantity is called a unit if it is not divisible
in any dimension and is without position, a point if it is not
divisible in any dimension and has position, a line if it is
divisible in one dimension, a plane if in two, a body it
divisible in quantity in all i. e. in three dimensions. And,
reversing the order, that which is divisible in two dimensions
is a plane, that which is divisible in one a line, that which is
30 in no way divisible in quantity is a point or a unit, that
which has not position a unit, that which has position a
point.
Again, some things are one in number, others in species,
others in genus, others by analogy ;in number those whose
matter is one, in species those whose definition is one, in
genus those to which the same figure of predication applies,1
by analogy those which are related as a third thing is to
35 a fourth. The latter kinds of unity are always found when
the former are;
e. g. things that are one in number are also
one in species, while things that are one in species are not
ioi7a
all one in number;but things that are one in species are all
one in genus, while things that are so in genus are not all
one in species but are all one by analogy ;while things that
are one by analogy are not all one in genus.
Evidently many will have meanings opposite to those
ofl one
;some things are many because they are not con-
5 tinuous, others because their matter either the proximate
matter or the ultimate is divisible in kind, others because
the definitions which state their essence are more than one.
Things are said to be (i)in an accidental sense, (2) by 7
their own nature.
(i)In an accidental sense, e.g., we say
*
the righteous
doer is musical , and the man is musical , and the musician
1Sc. the same category. Cf. note on A. 986
a23.
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BOOK A. 7 ioi7a
is a man, just as we say the musician builds
,because the 10
builder happens to be musical or the musician to be a builder;
for here one thing is another means one is an accident of
another . So in the cases we have mentioned;for when
we say the man is musical and the musician is a man,
or he who is pale is musical or*
the musician is pale ,the 15
last two mean that both attributes are accidents of the same
thing ;the first that the attribute is an accident of that
which ts;while
*
the musical is a man means that musical
is an accident of a man. (In this sense, too, the not-pale is
said to be, because that of which it is an accident ts.) Thuswhen one thing is said in an accidental sense to be another,
this is either because both belong to the same thing, and 20
this w, or because that to which the attribute belongs z>,or
because the subject which has as an attribute that of which
it is itself predicated, itself is.
(2) The kinds of essential being are precisely those that
are indicated by the figures of predication ;l for the senses
of being are just as many as these figures. Since, then,
some predicates indicate what the subject is, others its 25
quality, others quantity, others relation, others activity or
passivity, others its where,others its when
, being has
a meaning answering to each of these. For there is no
difference between the man is recovering and *
the man
recovers,nor between the man is walking or cutting
and the man walks or cuts;and similarly in all other 30
cases.
(3) Again, being and is mean that a statement is
true, not being that it is not true but false, and this alike
in the case of affirmation and of negation ;e. g.
*
Socrates
is musical means that this is
true,
or Socrates is not-
pale means that this is true;but the diagonal of the
square is not commensurate with the side means that it is
false to say it is.
(4) Again, being and that which is mean that some 35
of the things we have mentioned are potentially, others ioi7b
in complete reality.2 For we say both of that which sees
1 i. e. the categories. Cf. note on A. 986* 23.
2
Omitting prjTov in 1017^ I.
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ioi7b METAPHYSICA
potentially and of that which sees actually, that it is seeing ,
and both of that which can actualize its knowledge and ot
5 that which is actualizing it,that it knows, and both of that to
wr
hich rest is already present and of that which can rest, thatit rests. And similarly in the case ofsubstances
;we say the
Hermes is in the stone, and the half of the line is in the line,
and we say of that wThich is not yet ripe that it is corn.
When a thing is potential and when it is not yet potential
must be explained elsewhere.1
I0 We call substance(i)
the
simple bodies,i. e. earth and 8
fire and water and everything of the sort, and in general
bodies and the things composed of them, both animals and
divine beings, and the parts of these. All these are called
substance because they are not predicated of a subject but
everything else is predicated of them. (2) That which,
15 being present in such things as are not predicated of a sub
ject, is the cause of their being, as the soul is of the beingof an animal. (3) The parts which are present in such
things, limiting them and marking them as individuals, and
by whose destruction the whole is destroyed, as the body is
by the destruction of the plane, as some 2
say, and the plane
20 by the destruction of the line;and in general number is
thought by some 2to be of this nature
;for if it is destroyed,
they say, nothing exists, and it limits all things. (4) The
essence, the formula of which is a definition, is also called
the substance of each thing.
It follows, then, that substance has two senses, (A) the
ultimate substratum, which is no longer predicated of any
thing else, and (B) that which, being a this,
is also
25
separable
3 and of this nature is the
shapeor form of each
thing.
The same means (i)that which is the same in an acci- 9
dental sense, e. g. the pale and the musical are the same
because they are accidents of the same thing, and a man
and musical because the one is an accident of the other;
and the musical is a man because it is an accident ot
30 the man. (The complex entity is the same as either of the
1e. 7.
2 The Pythagoreans and Plato.3
Cf. H. 1042* 29.
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BOOK A. 9 ioi7b
simple ones and each of these is the same as it;for both
1
the man and the musical are said to be the same as the
musical man,and this the same as they.) This is why all
of these statements are made not universally ; for it is not
true to say that every man is the same as the musical (for35
universal attributes belong to things in virtue of their own
nature, but accidents do not belong to them in virtue of
their own nature) ;but of the individuals the statements ioi8
a
are made without qualification. For 4
Socrates and musi
cal Socrates are thought to be the same;but
*
Socrates
is not predicable of more than one subject, and therefore we
do not say every Socrates as we say*
every man .
Some things are said to be the same in this sense, others
(2)are the same by their own nature, in as many senses as
that which is one by its own nature is so;for both the 5
things whose matter is one either in kind or in number,
and those whose essence is one, are said to be the same.
Clearly, therefore, sameness is a unity of the being either
of more than one thing or of one thing when it is treated as
more than one, i. e. when we say a thing is the same as
itself;for we treat it as two.
Things are called other if either their kinds or their 10
matters or the definitions of their essence are more than
one;
and in general
(
other has meanings opposite to thoseof the same .
Different is applied (i)to those things which though
other are the same in some respect, only not in number but
either in species or in genus or by analogy ; (2) to those
whose genus is other, and to contraries, and to all things
that have their otherness in their essence.
Those things are called like which have the same attri- 15
butes in every respect, and those which have more attributes
the same than different, and those whose quality is one;
and that which shares with another thing the greater number
or the more important of the attributes (each of them one
of two contraries) in respect of which things are capable of
altering, is like that other thing.1 The senses of unlike
are opposite to those of like .
1Such attributes are hot and cold, wet and dry, rough and smooth,
645-28]-[
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ioi8a METAPHYSICA
20 The term opposite is applied to contradictories, and to 10
contraries, and to relative terms, and to privation and
possession, and to the extremes from which and into which
generation and dissolution take place;
and the attributesthat cannot be present at the same time in that which is
receptive of both, are said to be opposed, either themselves
or their constituents. Grey and white colour do not belong
at the same time to the same thing ;hence their constituents
are opposed.1
2 5 The term contrary is applied (i) to those attributes
differing in genus which cannot belong at the same time to
the same subject, (2) to the most different of the things in
the same genus, (3)to the most different of the attributes
in the same recipient subject, (4)to the most different of the
30 things that fall under the same faculty, (5) to the things
whose difference is greatest either absolutely or in genus or
in species. The other things that are called contrary are
so called, some because they possess contraries of the above
kind, some because they are receptive of such, some because
they are productive of or susceptible to such, or are pro
ducing or suffering them, or are losses or acquisitions, or
35 possessions or privations, of such. Since one and being
have many senses, the other terms which are derived from
these, and therefore same,
*
other,
and contrary,
mustcorrespond, so that they must be different for each category.
The term other in species is applied to things which
being of the same genus are not subordinate the one to the
ioi8bother, or which being in the same genus have a difference,
2
or which have a contrariety in their substance;and con
traries are other than one another in species (either all
contraries or those which are so called in the primary
sense:5
),and so are those things whose definitions differ in
5tiie infima species of the genus (e. g.
man and horse are
hard and soft, white and black, sweet and bitter. The more important
pairs of contraries, in Aristotle s view, are the first two.1 We cannot say grey and white are opposites, but we say the consti
tuents of grey (black and white) are opposites.2 This definition is wider than the previous one, since it includes
species subordinate one to the other.3
Cf.a25-31 in distinction from 31-35.
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BOOK A. 10
indivisible in genus, but their definitions are different), and
those which being- in the same substance have a difference.1
The same in species has the various meanings opposite to
these.
II The words prior and posterior are applied (i) to
some things (on the assumption that there is a first, i. e.
a beginning, in each class) because they are nearer some 10
beginning determined either absolutely and by nature, or
by reference to something or in some place or by certain
people ;e. g. things are prior in place because they are
nearer either to some place determined by nature (e. g. the
middle or the last place), or to some chance object ;and
that which is farther is posterior. Other things are prior
in time;some by being farther from the present, i. e. in 1 5
the case of past events (for the Trojan war is prior to the
Persian, because it is farther from the present), others by
being nearer the present, i. e. in the case of future events
(for the Nemean games are prior to the Pythian, if we treat
the present as beginning and first point, because they are
nearer the present). Other things are prior in movement;
for that wrhich is nearer the first mover is prior (e. g. the 20
boy is prior to the man) ;and the prime mover also is
a beginning absolutely. Others are prior in power ;for
that which exceeds in power, i.e. the more powerful, is
prior ;and such is that according to whose will the other
i. e. the posterior must follow, so that if the prior does not
set it in motion the other does not move, and if it sets it in
motion it does move;and here will is a beginning. Others 25
are prior in arrangement ;these are the things that are
placed at intervals in reference to some one definite thing
1 No satisfactory explanation of this clause has been proposed.Alexander suggests that Aristotle may mean that individuals with the
same specific essence differ in individual essence; but in ordinary
language (which alone Aristotle is examining in A) these would not be
called erep f idd. He also suggests that the reference may be to bodies
such as earth and water which are eYepa e idfi without being contrarylike fire and water; but these could hardly be said to be ev 177 avrf/
ovo-iq. Asclepius suggests more plausibly that the reference may be to
different elements in the essence of complex substances, e.g. to heat
and cold in the essence of man. Cf. vovs and amOr^is in the humansoul. But probably the reference is to attributes present at different
times in the same substance.
H 2
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ioi8b METAPHYSICA
according to some rule, e.g. in the chorus the second man
is prior to the third, and in the lyre the second lowest string
is prior to the lowest;for in the one case the leader and in
the other themiddle string
is thebeginning.
30 These, then, are called prior in this sense, but (2) in
another sense that which is prior for knowledge is treated
as also absolutely prior ;of these, the things that are prior
in definition do not coincide with those that are prior in rela
tion to perception. For in definition universals are prior, in
relation to perception individuals. And in definition also
the accident is prior to the whole, e. g. musical to musi-
35 cal man,for the definition cannot exist as a whole without
the part ; yet musicalness cannot exist unless there is some
one who is musical.
(3) The attributes of prior things are called prior, e. g.
straightness is prior to smoothness;for one is an attribute
of a line as such, and the other of a surface.
1019 Some things then are called prior and posterior in this sense,
others(4)
in respect of nature and substance, i. e. those which
can be without other things, while the others cannot be with
out them, a distinction which Plato used.1
(Ifwe consider
5 the various senses of being ,
2
firstly the subject is prior, so
that substance is prior; secondly, according as potency orcom
plete reality is taken into account, different things are prior,for some things are prior in respect of potency, others in re
spect of complete reality, e. g.in potency the halfline is prior
to the whole line, and the part to the whole, and the matter to
the concrete substance, but in complete reality these are pos-
10 terior;for it is only when the whole has been dissolved that
they will exist in complete reality.) In a sense, therefore,
all things that are called prior and posterior are so called
with reference to this fourth sense;for some things can
exist without others in respect of generation, e. g. the
whole without the parts, and others in respect of dissolu
tion, e.g. the part without the whole. And the same is
true in all other cases.
1 The reference is to an oral utterance of Plato, or perhaps to the
Platonic AicupeVay. Cf. Divisiones Aristoteleae, ed. Mutschmann,
pp. xvii, xviii.2
Cf. ch. 7.
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BOOK A. 12 1019*
12 Potency means (i) a source of movement or change, 15
which is in another thing than the thing moved or in the
same thing qua other;
e. g. the art of building is a potency
which is not in the
thingbuilt, while the art of
healing,which is a potency, may be in the man healed, but not in
him qua healed. Potency then means the source, in
general, of change or movement in another thing or in the
same thing qua other, and also (2)the source of a thing s 20
being moved by another thing or by itself qua other. For
in virtue of that principle, in virtue of which a patient
suffers anything, we call it capable of suffering;
and this
we do sometimes if it suffers anything at all, sometimes not
in respect of everything it suffers, but only if it suffers a
change for the better. (3) The capacity of performing this
well or according to intention;for sometimes we say of
those who merely can walk or speak but not well or not
as they intend, that they cannot speak or walk. So too 35
(4) in the case of passivity. (5) The states in virtue of
which things are absolutely impassive or unchangeable, or
not easily changed for the worse, are called potencies ;for
things are broken and crushed and bent and in general
destroyed not by having a potency but by not having one 30
and by lacking something, and things are impassive with
respect to such processes if they are scarcely and slightly
affected by them, because of a potency and because they
can do something and are in some positive state.
*
Potency having this variety of meanings, so too the
potent or*
capable}in one sense will mean that which
can begin a movement (or a change in general, for even
that which can bring things to rest is a potent thing)
in anotherthing
or in itself
quaother
;
andin
one sense 35that over which something else has such a potency ;
and in ioi9b
one sense that which has a potency of changing into some
thing, whether for the worse or for the better (for even that
which perishes is thought to be 4
capable of perishing, for
it would not have perished if it had not been capable of it;
but, as a matter of fact, it has a certain disposition and
cause and principle which fits it to suffer this ; sometimes it 5
is thought to be of this sort because it has something,
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ioi9b METAPHYSICA
sometimes because it is deprived of something ;but if
privation is in a sense*
having orf
habit, everything will
be capable by having something, so that things are capable
both
by having
a
positive
habit andprinciple,
andby
having the privation of this, if it is possible to have a
privation ;and if privation is not in a sense habit
,
10 capable is used in two distinct senses); and a thing
is capable in another sense because neither any other thing.
nor itself qua other, has a potency or principle which can
destroy it. Again, all of these are capable either merely
because the thing might chance to happen or not to happen,or because it might do so well. This sort of potency is
found even in lifeless things, e. g.in instruments
;for we say
one lyre can speak, and another cannot speak at all, if it
has not a good tone.
15 Incapacity is privation of capacity i.e. of such a prin
ciple as has been described either in general or in the case
of something that would naturally have the capacity, or
even at the time when it would naturally already have it;
for the senses in which we should call a boy and a man and
a eunuch incapable of begetting are distinct. Again, to
either kind of capacity there is an opposite incapacity
20 both to that which only can produce movement and to that
which canproduce
it well.
vSome things, then, are called dSvvara in virtue of this
kind of incapacity, while others are so in another sense;
i. e. both SVVCLTOV and aSvvarovaare used as follows. The
impossible is that of which the contrary is of necessity true,
e. g. that the diagonal of a square is commensurate with the
25 side is impossible, because such a statement is a falsity of
which the contrary is not only true but also necessary ; that
it is commensurate, then, is not only false but also of
necessity false. The contrary of this, the possible, is found
when it is not necessary that the contrary is false, e. g. that
a man should be seated is possible ;for that he is not
30 seated is not of necessity false. The possible, then, in one
sense, as has been said, means that which is not of necessity
1
Aristotle passes now to Swarov and dbuvarov in the sense of possible
and impossible .
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BOOK A. 12 1019
false;in one, that which is true
;in one, that which may be
true. A potency or power1
in geometry is so called
by a change of meaning. These senses of capable or
possible involve no reference to potency. But the senses 35
which involve a reference to potency all refer to the primary
kind of potency ;and this is a source of change in another iO2o
a
thing or in the same thing qua other. For other things
are called capable ,some because something else has such
a potency over them, some because it has not, some because
it has it in a particular way. The same is true ofthe things
that are
incapable.
Therefore the
proper
definition of the
primary kind of potency will be a source of change in 5
another thing or in the same thing q2ia other .
13 Quantum means that which is divisible into two or
more constituent parts of which each is by nature a one
and a this . A quantum is a plurality if it is numerable,
a magnitude if it is measurable. Plurality means that ">
which is divisible potentially into non-continuous parts,
magnitude that which is divisible into continuous parts ;
of magnitude, that which is continuous in one dimension is
length, in two breadth, in three depth. Of these, limited
plurality is number, limited length is a line, breadth a sur
face, depth a solid.
Again,some
things
are called
quanta
in virtue of their
own nature, others incidentally ;e. g. the line is a quantum 15
by its own nature, the musical is one incidentally. Of the
things that are quanta by their own nature some are so
as substances, e. g. the line is a quantum (for a certain kind
of quantum is present in the definition which states what it
is),and others are modifications and states of this kind of
substance, e. g. much and little, long and short, broad and 20
narrow, deep and shallow, heavy and light, and all other such
attributes. And also great and small, and greater and smaller,
both in themselves and when taken relatively to each other,
are by their own nature attributes of what is quantitative ;
but these names are transferred to other things also. Of 2 5
things that are quanta incidentally, some are so called in
1 The reference is to squares and cubes.
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ioaoa METAPHYSICA
the sense in which it was said that the musical and the white
were quanta, viz. because that to which musicalness and
whiteness belong is a quantum, and some are quanta in the
way in which movement and time are so;for these also are
30 called quanta of a sort and continuous because the things
of which these are attributes are divisible. I mean not that
which is moved, but the space through which it is moved;
for because that is a quantum movement also is a quantum,
and because this is a quantum time is one.
Qualitymeans
(i)the differentia of the
essence,e.
g. 14man is an animal of a certain quality because he is tvvo-
35 footed, and the horse is so because it is four-footed;and a
circle is a figure of particular quality because it is without
iO2Obangles, which shows that the essential differentia is a
quality. This, then, is one meaning of quality the differ
entia of the essence, but (2) there is another sense in which
it applies to the unmovable objects of mathematics, the
sense in which the numbers have a certain quality, e. g. the
composite numbers which are not in one dimension only,
5 but of which the plane and the solid are copies (these are
those which have two or three factors) ;and in general that
which exists in the essence of numbers besides quantity is
quality ;for the essence of each is what it is once, e. g. that
of 6 is not what it is twice or thrice, but what it is once;
for 6 is once 6.
(3)All the modifications of substances that move
(e. g.
10 heat and cold, whiteness and blackness, heaviness and light
ness, and the others of the sort) in virtue of which, when
they change, bodies are said to alter. (4) Quality in
respectof
virtue and vice and, in general, of evil and good.Quality, then, seems to have practically two meanings, and
one of these is the more proper. The primary quality is the
15 differentia of the essence, and of this the quality in numbers
is a part ;for it is a differentia of essences, but either not of
things that move or not ofthem qua moving. Secondly, there
are the modifications ofthings that move,<?ua moving,and the
differentiae ofmovements. Virtue and vice fall among these
modifications;for they indicate differentiae of the move-
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BOOK A. 14 io2ob
ment or activity, according to which the things in motion 20
act or are acted on well or badly ;for that which can be
moved or act in one way is good, and that which can do so
in another the contrary way is vicious. Good and evil
indicate quality especially in living things, and among these
especially in those which have purpose.2 5
Things are relative(i)as double to half, and treble to
a third, and in general that which contains something else
many times to that which is contained many times in some
thing else, and that which exceeds to that which is exceeded;
(2)as that which can heat to that which can be heated, and
that which can cut to that which can be cut, and in general
the active to the passive ; (3) as the measurable to the 30
measure, and the knowable to knowlege, and the per
ceptible to perception.
(i) Relative terms of the first kind are numerically
related eitherindefinitely or definitely, to numbers them
selves or to i. E.g. the double is in a definite numerical
relation to i, and that which is many times as great is in
a numerical, but not a definite, relation to i, i. e. not in this 35
or in that numerical relation to it;
the relation of that io2ia
which is half as big again as something else to that some
thing is a definite numerical relation to a number;that
H ~\~ I
which is - - times something else is in an indefinite rela
tion to that something, as that which is many times as
great is in an indefinite relation to i;the relation of that
which exceeds to that which is exceeded is numerically
quite indefinite;for number is always commensurate, and 5
4 number is not predicated of that which is not commen
surate, but that which exceeds is,in relation to that which
is exceeded, so much and something more;and this some
thing is indefinite;for it can, indifferently, be either equal
or not equal to that which is exceeded. All these relations,
then, are numerically expressed and are determinations
of number, and so in another way are the equal and the like
and the same. For all refer tounity.
Thosethings
are 10
the same whose substance is one;
those are like whose
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io2ia METAPHYSICA
quality is one;those are equal whose quantity is one
;and
i is the beginning and measure of number, so that all these
relations imply number, though not in the same way.
15 (2) Thingsthat are active or
passive implyan active or
a passive potency and the actualizations of the potencies ;
e. g. that which is capable of heating is related to that which
is capable of being heated, because it can heat it, and,
again, that which heats is related to that which is heated
and that which cuts to that which is cut, in the sense that
they actually do these things. But mimerical relations are
not actualized except in the sense which has been else-
20 where *stated
;actualizations in the sense of movement
they have not. Of relations which imply potency some
further imply particular periods of time, e. g.that which has
made is relative to that which has been made, and that
which will make to that which will be made. For it is in
this way that a father is called the father of his son;for the
one has acted and the other has been acted on in a certain
25 way.2
Further, some relative terms imply privation of
potency, i. e.*
incapable and terms of this sort, e.g.*
in
visible .
Relative terms which imply number or potency, there
fore, are all relative because their very essence includes in
its
nature a reference to something else, not because something else involves a reference to it
;but
(3)that which is
30 measurable or knowable or thinkable is called relative
because something else involves a reference to it. For4
that which is thinkable implies that the thought of it is
possible, but the thought is not relative to that of which
it is the thought ;for we should then have said the same
thing twice. Similarly sight is the sight of something, not4
of that of which it is the sight (though of course it is true
io2ibto say this) ;
in fact it is relative to colour or to something
else of the sort. But according to the other way of speak
ing the same thing would be said twice, the sight is of
that of which it is.
1 The reference may be to the H(p\ (Sewi/ and theIle/ji rfys-
ru>v
2i.e. there need not be any present relation to justify the use of the
relative form of words in this case;there is always the past relation.
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BOOK A. 15 io2ib
Things that are by their own nature called relative are
called so sometimes in these senses, sometimes if the classes
that include them are of this sort; e.g. medicine is a rela- 5
tive term because its genus, science, is thought to be arelative term. Further, there are the properties in virtue
of which the things that have them are called relative, e. g.
equality is relative because the equal is, and likeness
because the like is. Other things are relative by accident;
e. g. a man is relative because he happens to be double of
something and double is a relative term;or the white is 10
relative, if the same thing happens to be double and white.
16 What is called complete is(i) that outside which it is
not possible to find any, even one, of its parts ;e. g. the
complete time of each thing is that outside which it is not
possible to find any time which is a part proper to it.
(2)That which in respect of excellence and goodness cannot 15
be excelled in its kind;
e. g. we have a complete doctor or
a complete flute-player, when they lack nothing in respect of
the form of their proper excellence. And thus, transferring
the word to bad things, we speak of a complete scandal
monger and a complete thief; indeed we even call them
good, i. e. a good thief and a good scandal-monger. And 20
excellence is acompletion
;for each
thingis
completeand
every substance is complete, when in respect of the form
of its proper excellence it lacks no part of its natural
magnitude. (3) The things which have attained their end,
this being good, are called complete; for things are complete
in virtue of having attained their end. Therefore, since the 25
end is something ultimate, we transfer the word to bad
things and say a thing has been completely spoilt, and completely destroyed, when it in no wise falls short of destruc
tion and badness, but is at its last point. This is why
death, too, is by a figure of speech called the end, because
both are lastthings. But the ultimate purpose is also an
end. Things, then, that are called complete in virtue of 3
their own nature are so called in all these senses, some
because in respect of goodness they lack nothing and can
not be excelled and no part proper to them can be found out-
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io2ib METAPHYSICA
side them, others in general because they cannot be exceeded
in their several classes and no part proper to them is out-
io22aside them
;the others presuppose these first two kinds, and
are called complete because they either make or have something of the sort or are adapted to it or in some way or
other involve a reference to the things that are called com
plete in the primary sense.
Limit means (i) the last point of each thing, i.e. the 17
first point beyond which it is not possible to find any part,
5 and the first point within which every part is ; (2) the form,
whatever it may be, of a spatial magnitude or of a thing
that has magnitude ; (3) the end of each thing (and of this
nature is that towards which the movement and the action
are, not that from which they are, though sometimes it is
both, that from which and that to which the movement is,
i. e. the final cause) ; (4)the substance of each thing, and
the essence of each;for this is the limit of knowledge ;
10 and if of knowledge, of the object also. Evidently, there
fore,4
limit has as many senses as beginning ,and yet
more;for the beginning is a limit, but not every limit is a
beginning.
That in virtue of which has several meanings : 18
J 5(i)
the form or substance of each thing, e.g. that in virtue
of which a man is good is the good itself, (2) the proximate
subject in which it is the nature of an attribute to be found,
e.g. colour in a surface. That in virtue of which
, then,
in the primary sense is the form, and in a secondary sense
the matter of each thing and the proximate substratum of
each. In general that in virtue of which will be found20 in the same number of senses as
;
cause;for we say in
differently (3)*
in virtue of what has he come ? or for
what end has he come ?;and (4)
*
in virtue of what has he
inferred wrongly, or inferred ? or* what is the cause ofthe
inference, or of the wrong inference ? Further (5) KaO ol
is used in reference to position, e. g. at which he stands
1Aristotle here mentions the original local sense of KCI& o. No
English word or phrase has quite the same ambiguity.
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BOOK A. 18 io22a
or*
along which he walks;
for all such phrases indicate
place and position.
Therefore in virtue of itself must likewise have several
meanings. The following belong to a thing in virtue of 25
itself: (i) the essence of each thing, e.g. Callias is in
virtue of himself Callias and what it was to be Callias;
(2) whatever is present in the what,e. g. Callias is in virtue
of himself an animal. For animal is present in his
definition;
Callias is a particular animal.(3) Whatever
attribute a thing receives in itself directly or in one of its
parts ;e.
g.a surface is white in virtue of itself, and a man 3
is alive in virtue of himself; for the soul, in which life
directly resides, is a part of the man. (4) That which has
no cause other than itself;man has more than one cause-
animal, two-footed but yet man is man in virtue of himself.
(5) Whatever attributes belong to a thing alone, and in so 35
far as
they belongto it
merely byvirtue of itselfconsidered
apart by itself.
19 Disposition means the arrangement of that which has 1022
parts, in respect either of place or of potency or of kind;
for there must be a certain position, as even the word dis
position shows.
204
Having1
means (i) a kind of activity of the haver andof what he has something like an action or movement.
For when one thing makes and one is made, between them 5
there is a making ;so too between him who has a garment
and the garment which he has there is a having. This sort
of having, then, evidently we cannot have;for the process
will go on to infinity, if it is to be possible to have the
having of what we have. (2) Having orl
habit means 10
a disposition according to which that which is disposed is
either well or ill disposed, and either in itself or with refer
ence to something else;
e. g. health is a habit;for it is
such a disposition. (3) We speak of a habit if there is
a portion of such a disposition ;and so even the excellence
of the parts is a habit*
of the whole thing.
1 The word e|ts does duty for having ,habit
,and permanent
state .
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io22b METAPHYSICA
15 Affection*
means( i) a quality in respect of which a thing 21
can be altered, e. g. white and black, sweet and bitter, heavi
ness and lightness, and all others of the kind. (2) The
actualization of these the already accomplished altera
tions. (3) Especially, injurious alterations and movements,
20 and, above all, painful injuries. (4) Misfortunes and pain
ful experiences when on a large scale are called affections.
We speak of privation (i) if something has not one of 22
the attributes which a thing might naturally have, even if
this thing itself would not naturally have it;
e. g. a plant is
said to be deprived of eyes. (2) If, though either the
thing itself or its genus would naturally have an attri-
25 bute, it has it not;
e. g.a blind man and a mole are in
different senses deprived of sight ;the latter in contrast
with its genus,1 the former in contrast with his own normal
nature.(3)
If,
though
it wouldnaturally
have the attribute,
and when it would naturally have it, it has it not;for blind
ness is a privation, but one is not blind at any and every
age, but only if one has not sight at the age at which one
30 would naturally have it. Similarly a thing is called blind
if it has not sight in the medium in which, and in respect of
the organ in respect of which, and with reference to the
object with reference to which, and in the circumstances in
which, it would naturally have it. (4) The violent taking
away of anything is called privation.
Indeed there are just as many kinds of privations as there
are of words with negative prefixes; for a thing is called
unequal because it has not equality though it would natur
ally have it, and invisible either because it has no colour at
35 all or because it has a poor colour, and apodous either
because it has no feet at all or because it has imperfect feet.
Again, a privative term may be used because the thing has
J023a
little of the attribute (and this means having it in a sense
imperfectly), e. g.kernel-less
;or because it has it not
easily or not well (e. g. we call a thing uncuttable not only
if it cannot be cut but also if it cannot be cut easily or
well) ;or because it has not the attribute at all
;for it is
1i.e.* animal .
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BOOK A. 22 1023
not the one-eyed man but he who is sightless in both eyes
that is called blind. This is why not every man is good or 5
bad, just or unjust ,
but there is also an intermediate state.
23To have or hold means many things : (i)
to treat
a thing according to one s own nature or according to one s
own impulse ;so that fever is said to have a man, and 10
tyrants to have their cities, and people to have the clothes
they wear. (2) That in which a thing is present as in
something receptive of it is said to have the thing ;e. g. the
bronze has the form of the statue, and the body has the
disease. (3) As that which contains hold the things con
tained;for a thing is said to be held by that in which it is as
in a container;
e.g. we say that the vessel holds the liquid 15
and the city holds men and the ship sailors;and so too
that the whole holds the parts. (4) That which hinders a
thing from moving or acting according to its own impulse
is said to holdit,
as pillars hold the incumbent weights, and
as the poets make Atlas hold the heavens,1
implying that 20
otherwise they would collapse on the earth, as some of
the natural philosophers also say.2
In this way also that
which holds things together is said to hold the things it
holds together, since they would otherwise separate, each
accordingto its own
impulse.*
Being in something has similar and corresponding
meanings to holding or having .
35
24 To come from something means (i) to come from
something as from matter, and this in two senses, either in
respect of the highest genus or in respect of the lowest
species ;e. g. in a sense all
things
that can be melted come
from water, but in a sense the statue comes from bronze.
(2)As from the first moving principle ;
e. g. what did the 30
fight come from ? From abusive language, because this
was the origin of the fight. (3) From the compound of
matter and shape, as the parts come from the whole, and the
verse from the Iliad, and the stones from the house; (in
every such case the whole is a compound of matter and
1Cf. Hes. Theog. 517.
&
Cf. De Caelo 284* 20-26.
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io23a METAPHYSICA
shape,) for the shape is the end, and only that which attains
35 an end is complete. (4)As the form from its part, e. g.
man from two-footed and syllable from letter;for this
is a different sense from that in which the statue comes
ic23bfrom bronze
;for the composite substance comes from the
sensible matter, but the form also comes from the matter of
the form. Some things, then, are said to come from some
thing else in these senses;but (5) others are so described if
one ofthese senses is applicable to a part of that other thing ;
e.
g.
the child comes from its father and mother, andplants
come from the earth, because they come from a part of
5 those things. (6) It means coming after a thing in time,
e. g. night comes from day and storm from fine weather,
because the one comes after the other. Of these things
some are so described because they admit of change into
one another, as in the cases now mentioned;some merely
because they are successive in time, e. g. the voyage took
place from the equinox, because it took place after the
10 equinox, and the festival of the Thargelia comes from the
Dionysia, because after the Dionysia.
Part means (i) (a) that into which a quantum can in 25
any way be divided;for that which is taken from a quan
tum qua quantum is always called a part of it, e. g. two is
I5called in a sense a part of three. It means (), of the parts
in the first sense, only those which measure the whole;
this is why two, though in one sense it is, in another is not,
called a part of three.(2)
The elements into which a kind
might be divided apart from the quantity are also called parts
of it;for which reason we
say
the
species
are
parts
of the
genus. (3) The elements into which a whole is divided,
or of which it consists the whole meaning either the
20 form or that which has the form;
e. g. of the bronze sphere
or of the bronze cube both the bronze i. e. the matter in
which the form is and the characteristic angle are parts.
(4) The elements in the definition which explains a thing
are also parts of the whole ; this is why the genus is called
a part of the species, though in another sense the species is
3 5 part of the genus.
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BOOK A. 26 i023b
|a6A whole means (i) that from which is absent none of
the parts of which it is said to be naturally a whole, and (2)
that which so contains the things it contains that they form
a unity; and this in two senses either as being each sever
ally one single thing, or as making up the unity between
them. For (a) that which is true of a whole class and is
said to hold good as a whole (which implies that it is a kind
of whole) is true of a whole in the sense that it contains 3
many things by being predicated of each, and by all of
them, e.g. man, horse, god, being severally one single
thing, because all are living things. But (b) the continuous
and limited is a whole, when it is a unity consisting of
several parts, especially ifthey are present only potentially,1
but, failing this, even if they are present actually. Of these
things themselves, those which are so by nature are wholes
in a higher degree than those which are so by art, as we 35
said2in the case of unity also, wholeness being in fact a sort
of oneness.
Again (3),of quanta that have a beginning and a io24
a
middle and an end, those to which the position does not
make a difference are called totals, and those to which it
does, wholes. Those which admit of both descriptions
are both wholes and totals. These are the things whose
nature remains the sameafter
transposition,but
whose formdoes not, e. g. wax or a coat
; they are called both wholes 5
and totals;for they have both characteristics. Water and
all liquids and number are called totals, but the whole
number or the whole water one does not speak of, ex
cept by an extension of meaning. To things, to which quaone the term total is applied, the term all is applied
when they are treated as separate ; this total number, all 10
these units.
27 It is not any chance quantitative thing that can be said to
be mutilated;
it must be a whole as well as divisible.
For not only is two not mutilated if one of the two ones
is taken away (for the part removed by mutilation is never
1i. e. if they are only distinguishable, not distinct.
2Cf. ioi6a 4.
845-28 J
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io24a METAPHYSICA
equal to the remainder), but in general no number is thus
mutilated;for it is also necessary that the essence remain
;
15 if a cup is mutilated, it must still be a cup ;but the number
is no longer the same. Further, even if things consist of
unlike parts, not even these things can all be said to be
mutilated, for in a sense a number has unlike parts (e. g.
two and three) as well as like;but in general of the things
to which their position makes no difference, e. g. water or
fire, none can be mutilated;to be mutilated, things must be
such as in virtue of their essence have a certain position.
20Again, they must be continuous
;for a musical scale con
sists of unlike parts and has position, but cannot become
mutilated. Besides, not even the things that are wholes
are mutilated by the privation of any part. For the parts
removed must be neither those which determine the essence
nor any chance parts, irrespective of their position ;e. g.
acup
is not mutilated if it is boredthrough,
butonly
if the
25 handle or a projecting part is removed, and a man is muti
lated not if the flesh or the spleen is removed, but if an
extremity is, and that not every extremity but one which
when completely removed cannot grow again. Therefore
baldness is not a mutilation.
The termc
race or genus is used(i)
if generation of 28
30 things which have the same form is continuous, e. g.*
while
the race of men lasts means while the generation of them
goes on continuously .
(2)It is used with reference to
that which first brought things into existence;for it is thus
that some are called Hellenes by race and others lonians,
because the former proceed from Hellen and the latter frorr
Ion as their first begetter. And the wordis
used in refer-35 ence to the begetter more than to the matter, though people
also get a race-name from the female, e. g. the descendants
of Pyrrha&
.
1
(3) There is genus in the sense in which
iO24b
plane is the genus of plane figures and solid of solids ;
for each of the figures is in the one case a plane ofsuch and
such a kind, and in the other a solid of such and such a
kind ; and this is what underlies the differentiae. Again1Aristotle thinks that the male supplies the efficient and the formal,
the female the material cause of generation.
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BOOK A. 28 io24b
(4),in definitions the first constituent element, which is in
cluded in the what,
is the genus, whose differentiae the 5
qualities are said to be. Genus then is used in all these
ways, (i)in reference to continuous generation of the same
kind, (2) in reference to the first mover which is of the
same kind as the things it moves, (3) as matter;for that to
which the differentia or quality belongs is the substratum,
which we call matter.
Those things are said to be other in genus whose 10
proximate substratum is different, and which are not
analysed the one into the other nor both into the same
thing (e. g. form and matter are different in genus) ;and
things which belong to different categories of being (for
some of the things that are said to be signify essence,
others a quality, others the other categories we have before
distinguishedl
) ;these also are not analysed either into one 1 5
another or into some one thing.
29 The false means (i)that which is false as a thing, and
that (a) because it is not put together or cannot be put
together, e. g. that the diagonal of a square is commen
surate with the side or*
that you are sitting ;for one of 20
these is false always, and the other sometimes;
it is in these
two senses thatthey
are non-existent.(6)
There arethings
which exist, but whose nature it is to appear either not to
be such as they are or to be things that do not exist, e. g.
a sketch or a dream;for these are something, but are not
the things the appearance of which they produce in us.
We call things false in this way, then, either because they 25
themselves do not exist, or because the appearance which
results from them is that of something that does not exist.
(2)A false account is the account ofnon-existent objects,
in so far as it is false. Hence every account is false when
applied to something other than that of which it is true;
e. g. the account of a circle is false when applied to a
triangle. In a sense there is one account of each thing, i. e.
the account of its essence, but in a sense there are many,
since the thing itself and the thing itself with an attribute 30
1
ioi7a24-27.
I 2
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io24b METAPHYSICA
are in a sense the same, e. g. Socrates and musical Socrates
(a false account is not the account of anything, except in
a qualified sense). Hence Antisthenes was too simple-
minded when he claimed that nothing could be described
except by the account proper to it, one predicate to one
subject ;from which the conclusion used to be drawn that
there could be no contradiction, and almost that there could
be no error. But it is possible to describe each thing not
35 only by the account of itself, but also by that of something
else. This
maybe done
altogether falsely indeed,but there
is also a way in which it may be done truly ;e.
g. eight
may be described as a double number by the use of the
definition of two.
io25a These things, then, are called false in these senses, but
(3) a false man is one who is ready at and fond of such
accounts, not for any other reason but for their own sake,
and one who is good at impressing such accounts on other
5 people, just as we say things are false, which produce a false
appearance. This is why the proof in the Hippias that the
same man is false and true is misleading. For it assumes
that he is false who can deceive J
(i.e. the man who knows
and is wise) ;and further that he who is willingly bad is
10 better.2 This is a false result of induction for a man who
limps willingly is better than one who does so unwillingly
by*
limping Plato means mimicking a limp ,for if
the man were lame willingly, he would presumably be
worse in this case as in the corresponding case of moral
character.
4
Accident means (i)that which attaches to something 30
and can be truly asserted, but neither of necessity nor
15 usually, e.g. if some one in digging a hole for a plant has
found treasure. This the finding of treasure is for the
man who dug the hole an accident;for neither does the one
come of necessity from the other or after the other, nor, if a
man plants, does he usually find treasure. And a musical man
20
might
be pale ;but since this does not
happen
of necessity
nor usually, we call it an accident. Therefore since there
1
Hippias Minor 365-9.2
Ib. 371-6.
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BOOK A. 30 1025
are attributes and they attach to subjects, and some ofthem
attach to these only in a particular place and at a particular
time, whatever attaches to a subject, but not because it was
this subject, or the time this time, or the place this place,
will be an accident. Therefore, too, there is no definite cause
for an accident, but a chance cause, i. e. an indefinite one.
Going to Aegina was an accident for a man, if he went not 25
in order to get there, but because he was carried out of his
way by a storm or captured by pirates. The accident has
happened or exists, not in virtue of the subject s nature,
however, but of something else ; for the storm was the
cause of his coming to a place for which he was not sailing,
and this was Aegina.4 Accident has also (2)
another meaning, i. e. all that 30
attaches to each thing in virtue of itself but is not in its
essence, as having its angles equal to two right angles
attaches to the triangle. And accidents of this sort may be
eternal, but no accident of the other sort is. This is
explained elsewhere.1
1 An. Post. i. 75a18-22, 39-41, ;6
b 11-16.
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BOOK E
i025b WE are seeking the principles and the causes of the I
things that are, and obviously of them qzta being. For,
while there is a cause of health and of good condition, and
the objects of mathematics have first principles and
5 elements and causes, and in
general every
science which is
ratiocinative or at all involves reasoning deals with causes
and principles, more or less precise, all these sciences mark
off some particular being some genus, and inquire into
io this, but not into being simply nor qiia being, nor do they
offer any discussion of the essence of the things of which
they treat;but starting from the essence some making it
plain to the senses, others assuming it as a hypothesis
they then demonstrate, more or less cogently, the essential
attributes of the genus with which they deal. It is obvious,
therefore, that such an induction yields no demonstration of
15 substance or of the essence, but some other way of exhibit
ing it. And similarly the sciences omit the question whether
the genus with which they deal exists or does not exist,
because it belongs to the same kind of thinking to show
what it is and that it is.
And since natural science, like other sciences, is in fact
about one class of being, i.e. to that sort of substance
30 which has the principle of its movement and rest present in
itself, evidently it is neither practical nor productive. For
in the case ofthings
made theprinciple
is in the maker it
is either reason or art or some faculty, while in the case of
things done it is in the doer viz. will, for that which is
25done and that which is willed are the same. Therefore, if
all thought is either practical or productive or theoretical,
physics must be a theoretical science, but it will theorize
about such being as admits of being moved, and about sub-
stance-as-defined for the most part only as not separable
from matter. Now, we must not fail to notice the mode of
being of the essence and of its definition, for, without this,
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BOOK E. i i025b
inquiry is but idle. Of things defined, i. e. of whats, 3
some are like* snub
,and some like concave . And these
differ because snub is bound up with matter (for what is
snub is a concave nose), while concavity is independentof
perceptible matter. If then all natural things are analogous
to the snub in their nature e. g. nose, eye, face, flesh, bone,ic26
a
and, in general, animal; leaf, root, bark, and, in general,
plant (for none of these can be defined without reference to
movement they always have matter), it is clear how we
must seek and define the what in the case of natural
objects, and also that it belongs to the student of nature to 5
study even soul in a certain sense, i. e. so much of it as is
not independent of matter.
That physics, then, is a theoretical science, is plain from
these considerations. Mathematics also, however, is theo
retical;but whether its objects are immovable and separ
able from matter, is not at present clear; still, it is clear
that some mathematical theorems consider them qua
immovable and qua separable from matter. But if there I0
is something which is eternal and immovable and separable,
clearly the knowledge of it belongs to a theoretical science,
not, however, to physics (for physics deals with certain
movable things) nor to mathematics, but to a science prior
to both. Forphysics
deals withthings
which exist
separately but are not immovable, and some parts of mathematics
deal with things which are immovable but presumably do
not exist separately, but as embodied in matter;
while r 5
the first science deals with things which both exist
separately and are immovable. Now all causes must be
eternal, but especially these;for they are the causes that
operate on so much of the divine as appears to us.
1
Theremust, then, be three theoretical philosophies, mathematics,
physics, and what we may call theology, since it is obvious
that if the divine is present anywhere, it is present in things20
of this sort. And the highest science must deal with the
highest genus. Thus, while the theoretical sciences are
more to be desired than the other sciences, this is more to
be desired than the other theoretical sciences. For one1
i. e. produce the movements of the heavenly bodies.
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io26a METAPHYSICA
might raise the question whether first philosophy is univer
sal, or deals with one genus, i. e. some one kind of being ;
25 for not even the mathematical sciences are all alike in this
respect, geometry and astronomy deal with a certain par
ticular kind of thing, while universal mathematics applies
alike to all. We answer that if there is no substance other
than those which are formed by nature, natural science will
be the first science;but if there is an immovable substance,
3 the science of this must be prior and must be first philo
sophy, and universal in this way, because it is first. And
it will belong to this to consider being qua being both
what it is and the attributes which belong to it qua being.1
But since the unqualified term being has several mean- 2
ings, ofwhich one was seen 2to be the accidental, and another
35 the true( non-being being the false), while besides these
there are the figures of predication (e. g. the what \ quality,
quantity, place, time, and any similar meanings which being
iO26b may have), and again besides all these there is that which
4
is potentially or actually : since4
being has many mean
ings, we must first say regarding the accidental, that there
can be no scientific treatment of it. This is confirmed by
5 the fact that no science practical, productive, or theoretical
troubles itself aboutit.
For on the one hand he whoproduces a house does not produce all the attributes that
come into being along with the house;for these are in
numerable;the house that has been made may quite well
be pleasant for some people, hurtful to some, and useful to
others, and different to put it shortly from all things
that are;
j and the science of building does not aim at pro-
10 ducing any of these attributes. And in the same way the
geometer does not consider the attributes which attach thus
to figures, nor whether *
triangle is different from triangle
whose angles are equal to two right angles . And this
happens naturally enough ;for the accidental is practically
1 With ch. i cf. B. 955b10-13, 997** 15-25, K. 7.
2
Cf. A. 7.3 For the point of the last clause cf. 11. 12, 17, below. The question
as to the identity or difference of various things was popular with the
Sophists.
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BOOK E. 2 I0261
a mere name. And so Plato l was in a sense not wrong in
ranking sophistic as dealing with that which is not. For the 15-
arguments of the sophists deal, we may say, above all with
the accidental; e. g. the question whether musical
and
lettered are different or the same, and whether musical
Coriscus and Coriscus are the same, and whether every
thing which is. but is not eternal, has come to be,with the
paradoxical conclusion that if one who was musical has
come to be lettered, he must also have been lettered and
have come to be musical, and all the other arguments of 20
this sort ; the accidental is obviously akin to non-being.
And this is clear also from arguments such as the following :
things which are in another sense come into being and pass
out of being by a process, but things which are accidentally
do not. But still we must, as far as we can, say further,
regarding the accidental, what its nature is and from what 25
cause it proceeds ;for it will perhaps at the same time
become clear why there is no science of it.
Since, among things which are, some are always in the
same state and are of necessity (not necessity in the sense
of compulsion but that which we assert of things because
they cannot be otherwise), and some are not of necessity
nor always, but for the most part, this is the principle and 3
this the cause of the existence of the accidental;for that
which is neither always nor for the most part, we call acci
dental. For instance, if in the dog-days there is wintry
and cold weather, we say this is an accident, but not if there
is sultry heat, because the latter is always or for the most
part so, but not the former. And it is an accident that 35
a man is pale (for this is neither always nor for the most
part so), but it is not by accident that he is an animal. Andthat the builder produces health is an accident, because it is iO27
a
the nature not of the builder but of the doctor to do this,
but the builder happened to be a doctor. Again, a con
fectioner, aiming at giving pleasure, may make something
wholesome, but not in virtue of the confectioner s art;and
therefore we say it was an accident,and while there is
a sense in which he makes it, in the unqualified sense he1
Cf. Sophistes 237 A, 254 A.
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io27a METAPHYSICA
5 does not. For to other things answer faculties productive
of them, but to accidental results there corresponds no
determinate art nor faculty ;for of things which are or
come to be by accident, the cause also is accidental. There
fore, since not all things either are or come to be of neces
sity and always, but the majority of things areyftr the most
\vpart, the accidental must exist;for instance a pale man is
not always nor for the most part musical, but since this
sometimes happens, it must be accidental (if not, every
thing will be of necessity). The matter, therefore, which
is capable of being otherwise than as it usually is, must be
15 the cause of the accidental. And we must take as our
starting-point the question whether there is nothing that is
neither always nor for the most part. Surely this is im
possible. There is, then, besides these something which is
fortuitous and accidental. But while the usual exists, can
nothing be said to be always, or are there eternal things?
This must be considered later,1 but that there is no science
20 of the accidental is obvious;for all science is either of that
which is always or of that which is for the most part. (For
howrelse is one to learn or to teach another ? The thing
must be determined as occurring either always or for the
most part, e. g. that honey-water is useful for a patient in a
fever is^true for the most part.) But that which is contrary
to the usual law science will be unable to state, i. e. when
the thing does not happen, e. g.4 on the day ofnew moon
;
25 for even that which happens on the day of new moon
happens then either always or for the most part ;but the
accidental is contrary to such laws. We have stated, then,
what the accidental is, and, from what cause it arises, and
that therejs no science which deals with it.
That there are principles and causes which are generable 3
and destructible without ever being in course of being
30 generated or destroyed, is obvious. For otherwise all
things will be of necessity, since that which is being gene
rated or destroyed must have a cause which is not acci
dentally its cause. Will A exist or not ? It will if B
1Cf. A. 6-8.
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BOOK E. 3 io27a
happens ;and if not, not. And B will exist if C happens.
And thus if time is constantly subtracted from a limited
extent of time, one will obviously come to the present.
This man, then, will die by violence, //"he goes out; and 1027
he will do this if he gets thirsty ;and he will get thirsty if
something else happens ;and thus we shall come to that
which is now present, or to some past event. For instance,
he will go out if he gets thirsty ;and he will get thirsty if
he is eating pungent food;and this is either the case or
not;so that he will of necessity die, or of necessity not die. 5
And similarly if one jumps over to past events, the same
account will hold good ;for this I mean the past condition
is already present in something. Everything, therefore,
that will be, will be of necessity ;e. g. it is necessary that he
who lives shall one day die;for already some condition has
come into existence, e. g. the presence of contraries in the
samebody.
But whether he is to die
by
disease or
by
10
violence is not yet determined, but depends on the happen
ing of something else. Clearly then the process goes back
to a certain starting-point, but this no longer points to
something further. This then will be the starting-point
for the fortuitous, and will have nothing else as cause of
its coming to be. But to what sort of starting-point and
what sort of cause we thus refer the fortuitous whether to 15
matter or to the purpose or to the motive power, must be
carefully considered.1
4 Let us dismiss accidental being ;for we have sufficiently
determined its nature. But since that which is in the sense
of being true, or is not in the sense of being false, depends
1 The doctrine of the chapter seems to be as follows. Events in
general occur as the necessary result of a series of causes. E. g. death
is the necessary result of the presence of contrary elements in every
living body. But there are certain events which, while beginninga causal nexus, are not the result of a causal nexus. We can never
say of them, their conditions are being fulfilled, and they are comingto be. At one time they are not, and at another time they are.
Therefore they come to be. But they never are coming to be. Theevents A. seems to be thinking of are those which he would ascribe to
free will, e.g. a man s eating pungent food. Once he does this, hisdeath in some determinate way is certain
;till he does
it, only his
death is certain.
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io27b METAPHYSICA
on combination and separation, and truth and falsity to
gether depend on the allocation of a pair of contradictory20judgements (for the true judgement affirms where the sub
ject and predicate really are combined, and denies where
they are separated, while the false judgement has the opposite ofthis allocation
;it is another question, how it happens
that we think things together or apart ; by together and4
apart I mean thinking them so that there is no succession
2 5 in the thoughts but they become a unity) ;for falsity
and
truth are not in things it is not as if the good were true,
and the bad were in itself false but in thought ;while with
regard to simple concepts and l whats falsity and truth do
not exist even in thought : this being so, we must consider
laterl what has to be discussed with regard to that which is
or is not in this sense. But since the combination and the
3 separation are in thought and not in the things, and that
which is in this sense is a different sort of
l
being from the
things that are in the full sense (for the thought attaches
or removes 2either the subject s what or its having
a certain quality or quantity or something else), that
which is accidentally and that which is in the sense of being
true must be dismissed. For the cause of the former is
indeterminate, and that of the latter is some affection of the
iO28a thought, and both are related to the remaining genus of
being, and do not indicate the existence of any separate
class of being. Therefore let these be dismissed, and let us
consider the causes and the principles of being itself, qua
being. [It was clear in our discussion of the various
5 meanings of terms, that being has several meanings.]3
1 Cf. . 10. 2 Reading in 1. 338 With chs. 2-4 cf. K. io64
bI5~io65
a26.
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BOOKZ
J THERE are several senses in which a thing may be said 10
to be,as we pointed out previously in our book on the
various senses of words;
lfor in one sense the being
meant is4 what a thing is or a
*
this,and in another sense
it means a quality or quantity or one of the other things
that are predicated as these are. While being hasall
these senses, obviously that which *
is primarily is the
what,which indicates the substance of the thing. For T 5
when we say of what quality a thing is, we say that it is
good or bad, not that it is three cubits long or that it is
a man;but when we say what it is, we do not say white
or hot or three cubits long ,but a man or
*
a god .
And all other things are said to be because they are, someof them, quantities of that which is in this primary sense,
others qualities of it, others affections of it, and others some
other determination of it. And so one might even raise 20
the question whether the words to walk,
to be healthy ,
4
to sit imply that each of these things is existent, and
similarly in any other case of this sort;for none of them is
either self-subsistent or capable of being separated from
substance, but rather, if anything, it is that which walks or
sits or is healthy that is an existent thing. Now these are 35
seen to be more real because there is something definite
which underlies them(i.
e. the substance or individual),
which is implied in such a predicate ;for we never use the
word [
goodor
sittingwithout
implyingthis.
Clearlythen it is in virtue of this category that each of the others also
is. Therefore that which is primarily, i.e. not in a qualified
sense but without qualification, must be substance.3o
Now there are several senses in which a thing is said to
be first; yet substance is first in every sense (i) in defini
tion. (2) in order of knowledge, (3)in time. For (3) of the
other categories none can exist independently, but only
1
Cf. A.7.
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io28a METAPHYSICA
35 substance. And (i)in definition also this is first; for in
the definition of each term the definition of its substance
must be present. And (2) we think we know each thing
most fully, when we know what it is, e. g. what man is or
what fire is, rather than when we know its quality, its
io28bquantity, or its place ;
since we know each of these pre
dicates also, only when we know what the quantity or the
quality is.
And indeed the question which was raised of old and is
raised now and always, and is always the subject of doubt,
viz. what being is, is just the question, what is substance ?
For it is this that some lassert to be one, others more than
5one, and that some 2
assert to be limited in number, others;
unlimited. And so we also must consider chiefly and pri
marily and almost exclusively what that is which ts in this
sense.
Substance is thought to belong most obviously to bodies; 2
and so we say that not only animals and plants and their
10parts are substances, but also natural bodies such as fire and
water and earth and everything of the sort, and all things
that are either parts of these or composed of these (either of
parts or of the whole bodies), e.g. the physical universe
and its
parts,stars and
moonand sun. But whether these
alone are substances, or there are also others, or only some
J 5 of these, or others as well, or none of these but only some
other things, are substances, must be considered. Some 4
think the limits of body, i.e. surface, line, point, and unit,
are substances, and more so than body or the solid.
Further, some do not think there is anything substantial
besides sensible things, but others think there are eternal
substances which are more in number and more real;
e. g.
Plato posited two kinds of substance the Forms and the
20 objects of mathematics as well as a third kind, viz. the
substance of sensible bodies. And Speusippus made still
more kinds of substance, beginning with the One. and
assuming principles for each kind of substance, one for
1 The schools of Miletus and Elea.2 The Pythagoreans and Empedocles.3
Anaxagoras and the Atomists.4 The Pythagoreans.
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BOOK Z. 2 io28b
numbers, another for spatial magnitudes, and then another
for the soul;and by going- on in this way he multiplies the
kinds of substance. And some l
say Forms and numbers 25
have the same nature, and the other things come after
them lines and planes until we come to the substance of
the material universe and to sensible bodies.
Regarding these matters, then, we must inquire which of
the common statements are right and which are not right,
and what substances there are, and whether there are or
are not any besides sensible substances, and how sensible
substances exist, and whether there is a substance capable 3
of separate existence (and if so why and how) or no such
substance, apart from sensible substances;and we must first
sketch the nature of substance.
3 The word substance is applied, if not in more senses,
still at least to four main objects ;for both the essence and
the universal and the genus are thought to be the substance
of each thing, and fourthly the substratum. Now the sub- 35
stratum is that of which everything else is predicated, while
it is itself not predicated of anything else. And so we must
first determine the nature of this;for that which underlies 1029*
a thing primarily is thought to be in the truest sense its
substance. And in one sense matter is said to be of the
nature of substratum, in another, shape, and in a third, the
compound of these. (By the matter I mean, for instance,
the bronze, by the shape the pattern of its form, and by the
compound of these the statue, the concrete whole.) There- 5
fore if the form is prior to the matter and more real, it will
be prior also to the compound of both, for the same reason.
We have now outlined the nature ofsubstance, showing
that it is that which is not predicated of a stratum, but of
which all else is predicated. But we must not merely state
the matter thus;
for this is not enough. The statement
itself is obscure, and further, on this view, matter becomes
substance. For if this is not substance, it baffles us to say 10
what, else is. When all else is stripped offevidently nothing but
matter remains. For while the rest are affections, products,
1 The school of Xenocrates.
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io29a METAPHYSICA
and potencies of bodies, length, breadth, and depth are
quantities and not substances (for a quantity is not a sub-
15 stance), but the substance is rather that to which these
belong- primarily. But when length and breadth and depth
are taken away we see nothing left unless there is something
that is bounded by these;so that to those who consider
the question thus matter alone must seem to be substance.
20 By matter I mean that which in itself is neither a particular
thing nor of a certain quantity nor assigned to any other of
the
categories bywrhich
beingis determined. For there is
something of which each of these is predicated, whose
being is different from that of each of the predicates (for
the predicates other than substance are predicated of sub
stance, while substance is predicated of matter). Therefore
the ultimate substratum is of itself neither a particular thing
nor of a particular quantity nor otherwise positively charao
25 terized ; nor yet is it the negations of these, for negations
also will belong to it only by accident.
If we adopt this point of view, then, it follows that matter
is substance. But this is impossible ;for both separability
and thisness are thought to belong chiefly to substance.
And so form and the compound of form and matter would
30 be thought to be substance, rather than matter. The sub
stance compounded of both, i.e. of matter and shape, may
be dismissed;for it is posterior and its nature is obvious.
And matter also is in a sense manifest. But we must
inquire into the third kind of substance;for this is the most
perplexing.
Some of the sensible substances are generally admitted
to besubstances,
so that we must look first
amongthese.
iO2gb
3 For it is an advantage to advance to that which is more
knowable. For learning proceeds for all in this way
through that which is less knowable by nature to that
5which is more knowable
;and just as in conduct our task is
to start from what is good for each and make what is with
out qualification good good for each, so it is our task to
start from what is more knowable to oneself and makewhat^ is knowable by nature knowable to oneself. Now
what is knowable and primary for particular sets of people
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BOOK Z. 3 i029b
is often knowable to a very small extent, and has little or
nothing of reality. But yet one must start from that which 10
is barely knowable but knowable to oneself, and try to know
what is knowable without qualification, passing, as has been
said, by way of those very things which one does know.
4 Since at the startx we distinguished the various marks i
by which we determine substance, and one of these was
thought to be the essence, we must investigate this. And 13
. first let us make some linguistic remarks about it. The
essence of each thingis
whatit is said
to \>tpropterse.
2
For being you is not being musical, since you are not by
your very nature musical. What, then, you are by yourT 5
very nature is your essence.
Nor yet is the whole of this the essence of a thing ;not
that which is propter se as white is to a surface, because
being a surface is not identicalwith being white. But again
the combination of both being a white surface is not
the essence of surface, because surface itself is added.
The formula, therefore, in which the term itself is not
present but its meaning is expressed, this is the formula 20
of the essence of each thing. Therefore if to be a white
surface is to be a smooth surface,3to be white and to be
smooth are one and the same.4
But since there are also compounds answering to the
other categories5
(for there is a substratum for each category,
e. g. for quality, quantity, time, place, and motion), we must 35
inquire whether there is a formula of the essence of each of
them, i. e. whether to these compounds also there belongs
an essence, e. g. to white man .
6 Let the compound be
1
I028b33-6.
2It seems convenient here to translate thus the phrase translated in
A. 18 as;
in virtue of itself.3
Cf. De Sensu 442b
1 1 (on Democritus, whose doctrine, this is).4
i. e. this identification does not give the essence of surface (for
surface is repeated) but it gives the essence of white,since this is
not repeated but replaced by an equivalent.5
i. e. compounds of substance with the other categories.GXfvKos (iv0pu*7ros means a pale as opposed to a dark man, not a white
man as opposed to a negro (cf. H. io44b
25, I. ic-58b
34, K. io68a 17).
But as Aristotle has already in this chapter used Xeu/coi/ in the generalsignificance of white
,I have thought it best to preserve this trans
lation here and in chs. 5 and 6.
045-28
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io29b METAPHYSICA
denoted by cloak . What is the essence of cloak ? But,
it may be said, this also is not & propter se expression. We
reply that there are just two waysin which a predicate may3 fail to be true of a subject propter se, and one of these
results from the addition, and the other from the omission,
of a determinant. One kind of predicate is not propter se
because the term that is being defined is combined with
another determinant, e.g. if in defining the essence of white
one were to state the formula of white man;the other
because in thesubject
another determinant is combined
with that which is expressed in the formula, e. g. if cloak
meant white man,and one were to define cloak as white
;
iO3Oawhite man is white indeed, but its essence is not to be
white.
But is being-a-cloak an essence at all ? Probably not. For
the essence is precisely what something is;but when an attri
bute is asserted of a subject other than itself, the complex is
not precisely what some *
this is, e. g. white man is not
5 precisely what some 4
this is, since thisness belongs only to
substances. 1 Therefore there is an essence only of those
things whose formula is a definition. But we have a defini
tion not where we have a word and a formula identical in
meaning (for in that case all formulae or sets of words
would be definitions;for there will be some name for any
set of words whatever, so that even the Iliad will be
a definition2
),but where there is a formula of something
10primary ;
and primary things are those which do not imply
the predication of one element in them of another element.
Nothing, then, which is not a species of a genus will
have an essence
only specieswill have it, for these are
thought to imply not merely that the subject participates
in the attribute and has it as an affection,3or has it by
accident;but for everything else as well, if it has a name,
15 there will be a formula of its meaning viz. that this
1 The point is that \(v<6v is one thing, avdpu-rros another, while faovand SITTOVI/ are not distinct things but diirow is only a form of G>OV.
Thus avQpnnos XCVKOS is not an individual type and cannot be defined,while (MOV SLTTOW is an individual type and can be defined.
2Sc. of the word Iliad .
3Cf. I037
b14-21 for the interpretation of this.
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BOOK Z. 4 iQ30a
attribute belongs to this subject ;or instead of a simple
formula we shall be able to give a more accurate one;but
there will be no definition nor essence.
Or has definition,like 4
what a thing is, several mean
ings ?* What a thing is in one sense means substance and
the this,in another one or other of the predicates, quan- 2o
tity, quality,and the like. For as is belongs to all things,
not however in the same sense, but to one sort of thing
primarily and to others in a secondary way, so too what
a thing is belongs in the simple sense to substance, but
in a limited sense to the other categories. For even of
a quality we might ask what it is, so that quality also is
a what a thing is \--not in the simple sense, however, but 25
just as, in the case of that which is not, some say,1
empha
sizing the linguistic form, that that which is not is not ts
simply, but ts non-existent;so too with quality.
We must no doubt inquire how weshould
expressour
selves on each point, but certainly not more than how the
facts actually stand. And so now also, since it is evident what
language we use, essence will belong, just as what a thing
is does, primarily and in the simple sense to substance,
and in a secondary way to the other categories also, not 30
essence in the simple sense, but the essence of a quality or
of a quantity. For it must be either by an equivocation
that we say these are, or by adding to and taking from the
meaning of*
are (in the way in which that which is not
known may be said to be known 2
),the truth being that
we use the word neither ambiguously nor in the same
sense, but just as we apply the word medical by virtue of 35
a reference to one and the same thing, not meaning one
and the same thing, nor yet speaking ambiguously ;for iO3Ob
a patient and an operation and an instrument are called
medical neither by an ambiguity nor with a single meaning,
but with reference to a common end. But it does not
matter at all in which of the two ways one likes to describe
the facts;this is evident, that definition and essence in the 5
primary and simple sense belong to substances. Still they
belong to other things as well, only not in the primary1
Cf. PI. Soph. 237, 256 ff.2
i. e. it is known to be unknown.
K 2
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io3ob METAPHYSICA
sense. For if we suppose this it does not follow that there
is a definition of every word which means the same as any
formula;
it must mean the same as a particular kind of
formula;and this condition is satisfied if it is a formula of
something which is one, not by continuity like the Iliad or
10 the things that are one by being bound together, but in one
of the main senses of * one,which answer to the senses of
4
is;now *
that which is in one sense denotes a this,in
another a quantity, in another a quality. And so there can
be a formula or definition even ofwhite man,but not in the
sense in which there is a definition either of white or of
a substance.
It is a difficult question, if one denies that a formula with 5
15 an added determinant xis a definition, whether any of the
terms that are not simple but coupled will be definable.
For we must explain them by adding a determinant. E. g.
there is the nose, and concavity, and snubness, which is
compounded out of the two by the presence of the one in
the other, and it is not by accident that the nose has the
attribute either of concavity or of snubness, but in virtue of
20 its nature;nor do they attach to it as whiteness does to
Callias, or to man (because Callias, who happens to be
a man, is white), but as male*
attaches to animal and4
equal to quantity, and as all so-called4
attributes propter
se attach to their subjects.2 And such attributes are those
in which is involved either \hzformula or the name of the
subject of the particular attribute, and which cannot be ex-
25 plained without this;
e. g. white can be explained apart
fromman,
but not female
apart
from animal. Therefore
there is either no essence and definition of any of these
things, or if there is, it is in another sense, as we have said.3
But there is also a second difficulty about them. For if
snub nose and concave nose are the same thing, snub and
30 concave will be the same thing ;but if snub and concave
are not the same (because it is impossible to speak of snub-
1Cf. io29
b30.
2 In the sense of <a& avro explained in An. Post. i. 73* 37-b3-
3 a ^
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BOOK Z. 5 io3ob
ness apart from the thing of which it is an attribute propter
se, for snubness is concavity-in-a-nose), either it is im
possible to say snub nose or the same thing will have
been said twice, concave-nose nose ; for snub nose will be
concave- nose nose. And so it is absurd that such things
should have an essence;
if they have, there will be an 35
infinite regress ;for in snub-nose nose yet another
* nose
will be involved.
Clearly, then, only substance is definable. For if the iO3ia
other categories also are definable, it must be by addition
of a determinant, e. g. the qualitative is defined thus, and so
is the odd, for it cannot be defined apart from number;nor
can female be defined apart from animal. (When I say*
by
addition I mean the expressions in which it turns out that
we are saying the same thing twice, as in these instances.)
And if this is true, coupled terms also, like odd number,5
will not be definable (but this escapes our notice because
our formulae are not accurate). But if these also are de
finable, either it is in some other way or, as we said,1
definition and essence must be said to have more than one
sense. Therefore in one sense nothing will have a defini- 10
tion and nothing will have an essence, except substances,
but in another sense other things will have them. Clearly,
then, definition is the formula of the essence, and essence
belongs to substances either alone or chiefly and primarily
and in the unqualified sense.
6 We must inquire whether each thing and its essence are 15
the same or different. This is of some use for the inquiry
concerning substance;for each thing is thought to be not
different from its substance, and the essence is said to be
the substance of each thing.
Now in the case of accidental unities the two would be
generally thought to be different, e.g. white man would 20
be thought to be different from the essence of white man.
For if they are the same, the essence of man and that of
white man are also the same;for a man and a white man
are the same thing, as people say, so that the essence of
1
1030ai;-
bi3.
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io3ia METAPHYSICA
white man and that of man would be also the same. But
perhaps it does not follow that the essence of accidental
unities should be the same as that of the simple terms. For
the extreme terms are not in the same way identical with the
25 middle term. But perhaps this might be thought, to follow,
that the extreme terms, the accidents, should turn out to
be the same, e. g. the essence of white and that of musical;
but this is not actually thought to be the case.1
But in the case of so-called self-subsistent things, is a
thing necessarily
the same as its essence ? E.g.
if there are
some substances which have no other substances nor entities
3 prior to them substances such as some assert the Ideas to
be ? If the essence of good is to be different from good-
itself, and the essence of animal from animal-itself, and the
iO3ibessence of being from being-itself, there will, firstly,
be
other substances and entities and Ideas besides those which
are asserted, and, secondly, these others will be prior
substances, if essence is substance. And if the posterior
substances and the prior are severed from each other, (a)
there will be no knowledge of the former,2 and
(/?)the
5 latter3
will have no being. (By*
severed I mean, if the
good-itself has not the essence of good, and the latter has
not the property of being good.) For (a) there is know-
1 The argument used in 11. 21-4 is :
If essence of white man = white man,then since white man = man,and man = essence of man,. . essence of white man = essence of man.
This is absurd, and Aristotle infers that essence of white man does
not = white man.
He next (11. 24-5) hints that this reductio ad absurdum fails because,
while white man is (on the hypothesis under discussion) absolutelyidentical with the essence of white man, as well as man with the essence
of man, white man is identical with man only per accidens. But, he
urges (11. 25-8), it might at least seem to follow from the identification
of an accidental unity with its essence that the accidental extremes,essence of white and essence of musical, are identical :
-
Musical man = essence of musical man.
Man = musical man.
White man = man.
Essence of white man = white man.
. .essence of white man = essence of musical man.. . essence of white = essence of musical.
Which is absurd.2 The Ideas or things-themselves.
3 The essences.
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BOOK Z. 6 io3ib
ledge of each thing only when we know its essence. And
(/3)the case is the same for other things as for the good ;
so that if the essence of good is not good, neither is the
essence of reality real, nor the essence of unity one. Andall essences alike exist or none of them does
;so that if 10
the essence of reality is not real, neither is any ofthe others.
Again, that to which the essence of good does not belonglis
not good. The good, then, must be one with the essence of
good, and the beautiful with the essence of beauty, and so
with all things which do not depend on something else but
are self-subsistent and primary. For it is enough if they
are this, even ifthey are not Forms;or rather, perhaps, even
if they are Forms. (At the same time it is clear that if 15
there are Ideas such as some people say there are, it will
not be substratum that is substance;for these must be sub
stances, but not predicable of a substratum;for if they were
they would exist only by being participated in.2
)
Each thing itself, then, and its essence are one and the
same in no merely accidental way, as is evident both
from the preceding arguments and because to know each 20
thing, at least, is just to know its essence, so that even by
the exhibition of instances it becomes clear that both must
be one.
(But of an accidental term, e. g. the musical or*
the
white,since it has two meanings, it is not true to say that
it itself is identical with its essence;for both that to which
the accidental quality belongs, and the accidental quality,
are white, so that in a sense the accident and its essence are 2 5
the same, and in a sense they are not;for the essence of
white is not the same as the man 3 or the white man, but it
is thesame
asthe
attributewhite.)
The absurdity of the separation would appear also if one
were to assign a name to each of the essences;for there
would be yet another essence besides the original one, e. g. to 3
the essence of horse there will belong a second essence.4
1i.e. the Idea of good (1. 5).
2i. e. as immanent in particulars.
sSc. who is white.
4Sc. and so ad
infinitum.As an infinite
processis
absurd, whytake the first step that commits you to it why say that the essence of
horse is separate from the horse ?
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io3ib METAPHYSICA
Yet why should not some things be their essences from the
start, since essence is substance ? But indeed not only are
a thing and its essence one, but the formula of them is also
iO32
a
the same, as is clear even from what has been said ; for it is
not by accident that the essence of one, and the one, are
one. Further, if they are to be different, the process will
go on to infinity; for we shall have (i) the essence of one.
and (2) the one, so that to terms of the former kind the
same argument will be applicable.1
5 Clearly, then, each primary and self-subsistent thing is
one and the same as its essence. The sophistical objections
to this position, and the question whether Socrates and to
be Socrates are the same thing, are obviously answered by
the same solution;for there is no difference either in the
standpoint from which the question would be asked, or in
10 that from which one could answer it successfully. We have
explained, then,
in what sense eachthing
is the same as its
essence and in what sense it is not.
Of things that come to be, some come to be by nature, 7
some by art, some spontaneously. Now everything that
comes to be comes to be by the agency of something and
from something and comes to be something. And the
somethingwhich I
sayit comes to be
maybe found in
anycategory ;
it may come to be either a this or of some size
or of some quality or somewhere.
15 Now natural comings to be are the comings to be of those
things which come to be by nature;and that out of which
they come to be is what we call matter;and that by which
they come to be is something which exists naturally ;and
the something which they come to be is a man or a plant or
one of the things of this kind, which we say are substances
20 if anything is all things produced either by nature or by
art have matter;for each of them is capable both of being
and of not being, and this capacity is the matter in each
and, in general, both that from which they are produced is
nature, and the type according to which they are produced
1i. e. if the essence of one is different from the one, the essence of
the essence of one is different from the essence Qf one.
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BOOK Z. 7 io32a
is nature (for that which is produced, e. g. a plant or an
animal, has a nature), and so is that by which they are pro
duced the so-called formal nature, which is specifically
the same (though this is in another individual) ; for manbegets man.
Thus, then, are natural products produced ;all other 25
productions are called makings . And all makings pro
ceed either from art or from a faculty or from thought.1
Some of them happen also spontaneously or by luck 2
just
as natural products sometimes do;for there also the same 30
things sometimes are produced without seed as well as from
seed. Concerning these cases, then, we must inquire later,3
but from art proceed the things of which the form is in the
soul of the artist. (By form I mean the essence of each iO32b
thing and its primary substance.) For even contraries have
in a sense the same form;for the substance of a privation
is the opposite substance, e. g. health is the substance of
disease (for disease is the absence of health) ;and health is 5
the formula in the soul or the knowledge of it. The healthy
subject is produced as the result of the following train
of thought : since this is health, if the subject is to be
healthy this must first be present, e. g. a uniform state of
body, and if this is to be present, there must be heat;and the
physician goes on thinkingthus until he reduces the matter
to a final something which he himself can produce. Then
the process from this point onward, i. e. the process towards 10
health, is called a*
making . Therefore it follows that in
a sense health comes from health and house from house,
that with matter from that without matter;for the medical
art and the building art are the form of health and of the
house, and when I speak of substance without matter I meanthe essence.
Of the productions or processes one part is called think-I5
ing and the other making, that which proceeds from the
starting-point and the form is thinking, and that which pro
ceeds from the final step of the thinking is making. And
*
Cf. E. I025b22.
For the theory of these cf. Phys. ii. 5, 6.
3Cf.
b23-30,
a b
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io32b METAPHYSICA
each of the other, intermediate, things is produced in the
same way. I mean, for instance, if the subject is to be
healthy his bodily state must be made uniform. What
then does being made uniform imply ? This or that. And20 this depends on his being made warm. What does this
imply ? Something else. And this something is present
potentially ;and what is present potentially is already in
the physician s power.
The active principle then and the starting-point for the
process of becoming healthy is, if it happens by art, the
form in the soul, and if spontaneously, it is that, whatever
it is, which starts the making,1for the man who makes by
25 art, as in healing the starting-point is perhaps the produc
tion ofwarmth (and this the physician produces by rubbing).
Warmth in the body, then, is either a part of health or is
followed (either directly or through several intermediate
steps) by something similar which is a part of health;
andthis, viz. that which produces the part of health, is the
limiting-point,2 and so too with a house (the stones are
the limiting-point here) and in all other cases.
30 Therefore, as the saying goes, it is impossible that any
thing should be produced if there were nothing existing
before. Obviously then some part of the result will pre
exist of necessity ;for the matter is a part ; for this is
present in the process and it is this that becomes some-
i033a
thing. But is the matter an element even in \hzformula ?
We certainly describe in both ways3 what brazen circles
are;we describe both the matter by saying it is brass, and
the form by saying that it is such and such a figure ;and
figure is the proximate genus in which it is placed.The
brazen circle, then, has its matter in itsformula.
5 As for that out of which as matter they are produced,
some things are said, when they have been produced, to be
not that but thaten;
e. g.the statue is not gold but
1Sc. not the thinking, cf. 11. 15-17.
2i. e. the minimum necessary basis.
3
From the proportion established, warmth:
health::
stones:
house,and from the next paragraph, it would appear that warmth is treated
as the matter which when specialized in a particular way becomes
health.
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BOOK Z. 7 i033a
golden.1 And a healthy man is not said to be that from which
he has come. The reason is that though a thing comes both
from its privation and from its substratum, which we call its
matter (e. g. what becomes healthy is both a man and an 10
invalid), it is said to come rather from its privation (e. g. it
is from an invalid rather than from a man that a healthy
subject is produced). And so the healthy subject is not
said to be an invalid, but to be a man, and the man is said
to be healthy. But as for the things whose privation is
obscure and nameless, e. g. in brass the privation of a par
ticular shape or in bricks and timber the privation of
arrangement as a house, the thing is thought to be pro- 15
duced front these materials, as in the former case the
healthy man is produced from an invalid. And so, as
there also a thing is not said to be that from which it comes,
here the statue is not said to be wood but is said by a verbal
changeto be wooden 2
,not brass but brazen, not
gold
but
goldenJ
,and the house is said to be not bricks but bricken
(though we should not say without qualification,if we 20
looked at the matter carefully, even that a statue is pro
duced from wood or a house from bricks, because coming to
be implies change in that from which a thing comes to be,
and not permanence). It is for this reason, then, that we
use this way of speaking.
8 Since anything which is produced is produced by some
thing (and this I call the starting-point of the production),
and from something (and let this be taken to be not the priva- 25
tion but the matter;
for the meaning we attach to this
has alreadya been explained), and since something is pro
duced(and
this is either a
sphere
or a circle or whatever
else it may chance to be), just as we do not make the sub
stratum (the brass), so we do not make the sphere, except
incidentally, because the brazen sphere is a sphere and we
make the former. For to make a this is to make a this 30
out of the substratum in the full sense of the word.4
(Imean
1Aristotle uses the example of stone, but unfortunately we do not
say stonen ,
2
Omitting 01 uXoi> in 1. 1 8.3
Cf. 1032* 17.4
i. e. including form as well as matter (cf. lO29a3).
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io33a METAPHYSICA
that to make the brass round is not to make the round or
the sphere, but something else, i. e. to produce this form in
something different from itself. For if we make the form,
we must make it out of something else;for this was
i033bassumed. 1
E.g. we make a brazen sphere ;and that in the
sense that out of this, which is brass, we make this other,
which is a sphere.) If, then, we also make the substratum
itself, clearly we shall make it in the same way, and thepro-
5 cesses ofmaking will regress to infinity. Obviously then the
formalso,
2or whatever we
oughtto call the
shape presentin the sensible thing, is not produced, nor is there any production of
it, nor is the essence produced ;for this is that
which is made to be in something else either by art or bynature or by some faculty. But that there is a brazen sphere,
this we make. For we make it out of brass and the sphere ;
10 we bring the form into this particular matter, and the result
is a brazen sphere. But if the essence of sphere in general
is to be produced, something must be produced out of
something. For the product will always have to be
divisible, and one part must be this and another that;
I mean the one must be matter and the other form. If,
then, a sphere is the figure whose circumference is at all
points equidistant from the centre, part of this will be
J 5 the medium in which the thing made will be, and part
will be in that medium, and the whole will be the
thing produced, which corresponds to the brazen sphere.
It is obvious, then, from what has been said, that that
which is spoken of as form or substance is not produced,
but the concrete thing which gets its name from this is
produced,and that in
everything whichis
generatedmatter
is present, and one part of the thing is matter and the
other form.
Is there, then, a sphere apart from the individual spheres
20 or a house apart from the bricks ? Rather we may say
that no this would ever have been coming to be, if this
had been so, but that the form means the such,and is
not a this a definite thing ; but the artist makes, or the
1 a25.
2Sc. as well as the matter.
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BOOK Z. 8 i033b
father begets, a such out of as
this;and when it has
been begotten, it is a*
this such V And the whole this,
Callias or Socrates, is analogous to this brazen sphere ,
but man and animal to brazen sphere in general. Obvi- 2 5
ously, then, the cause which consists of the Forms (taken in
the sense in which some maintain the existence of the
Forms, i. e. if they are something apart from the individuals)
is useless, at least with regard to comings-to-be and to
substances;and the Forms need not, for this reason at
least, be self-subsistent substances. In some cases indeed
it is even obvious that the begetter is of the same kind as 30
the begotten (not, however, the same nor one in number,
but in form), i.e. in the case of natural products (for
man begets man), unless something happens contrary to
nature, e. g. the production of a mule by a horse. (And
even these cases are similar;for that which would be found
to be common to horse andass,
the
genusnext above
them,has not received a name, but it would doubtless be both, 1034
a
in fact something like a mule.) Obviously, therefore, it is
quite unnecessary to set up a Form as a pattern (for we
should have looked for Forms in these cases if in any ;for
these are substances if anything is so) ;the begetter is
adequate to the making of the product and to the causing
of the form in the matter. And when we have the whole, 5
such and such a form in this flesh and in these bones, this
is Callias or Socrates;and they are different in virtue of
their matter (for that is different),but the same in form
;for
their form is indivisible.
9 The question might be raised, why some things are pro
duced spontaneously as well as by art, e. g. health, whileothers are not, e. g. a house. The reason is that in some i0
cases the matter which governs the production in the
making and producing of any work of art, and in which
a part of the product is present, some matter is such as to
be set in motion by itself and some is not of this nature,
and of the former kind some can move itself in the particular
1i. e. the artist, or the father, turns a mere piece of matter into
a qualified piece of matter.
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io34a METAPHYSICA
way required, while other matter is incapable of this;
for many things can be set in motion by themselves but not
J 5 in some particular way, e.g. that of dancing. The things,
then, whose matter is of this sort, e. g. stones, cannot be
moved in the particular way required,1
except by some
thing else, but in another way they can move themselves
and so it is with fire. Therefore some things will not exist
apart from some one who has the art of making them,
while others will;for motion will be started by these things
20 which have not the art but can themselves be movedby
other things which have not the art or with a motion starting
from a part of the product.2
And it is clear also from what has been said that in a sense
every product of art is produced from a thing which
shares its name (as natural products are produced), or
from a part of itself which shares its name(e. g. the house
is produced from a house, q^ta produced by reason ; for the
art of building is the form of the house), or from some
thing which contains a part of it, if we exclude things
25 produced by accident;for the cause of the thing s producing
the product directlyper se is a part of the product. The
heat in the movement 3caused heat in the body, and this is
either health, or a part of health, or is followed by a part of
health or by health itself. And so it is said to cause health,
because it causes that to which health attaches as a con
sequence.
30 Therefore, as in syllogisms, substance 4is the starting-
point of everything. It is from what a thing is that
syllogisms start;and from it also we now find processes of
productionto start.
5
Things which are formed by nature are in the same case
as these products of art. For the seed is productive in the
same way as the things that work by art;
for it has the
form potentially, and that from which the seed comes has
iO34bin a sense the same name as the offspring only in a sense,
1Sc. for building.
2 i. e. an element of it pre-existing in the things themselves (cf.
3Sc. of the rubber s hand.
4i. e. essence.
5Cf. TO eldos, 1. 24.
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BOOK Z. 9 i034b
for we must not expect parent and offspring always to
have exactly the same name, as in the production of
1 human being from human being ;for a woman also
can be produced by a man unless the offspring be an
imperfect form;which is the reason why the parent of
a mule is not a mule. 1 The natural things which (like
the artificial objects previously considered2
)can be produced 5
spontaneously are those whose matter can be moved even
by itself in the way in which the seed usually moves it;
those things which have not such matter cannot be pro
duced except from the parent animals themselves.
But not only regarding substance does our argument
prove that its form does not come to be, but the argument
applies to all the primary classes alike, i. e. quantity, quality,
and the other categories. For as the brazen sphere comes I0
to be, but not the sphere nor the brass, and so too in the
caseof
brassitself,
if it
comesto
be,it is its concrete
unitythat comes to be (for the matter and the form must always
exist before), so is it both in the case of substance and in
that of quality and quantity and the other categories like
wise;for the quality does not come to be, but the wood ot
that quality, and the quantity does not come to be, but the 15
wood or the animal of that size. But we may learn from
these instances a peculiarity of substance, that there mustexist beforehand in complete reality another substance
which produces it, e. g. an animal if an animal is produced ;
but it is not necessary that a quality or quantity should
pre-exist otherwise than potentially.
10 Since a definition is a formula, and every formula has 20
parts,and as the formula is to the
thing,so is the
partof
the formula to the part of the thing, the question is already
being asked whether the formula of the parts must be
present in the formula of the whole or not. For in some
cases the formulae of the parts are seen to be present, and
in some not. The formula of the circle does not include
that of the segments, but that of the syllable includes that 35
of the letters ; yet the circle is divided into segments as the
1Cf. 1033*33.
2
cf.*9-3 2.
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io34b METAPHYSICA
syllable is into letters. And further if the parts are prior to
the whole, and the acute angle is a part of the right angle
and the finger a part of the animal, the acute angle will be
3o prior to the right angle and the finger to the man. Butthe latter are thought to be prior ;
for in formula the parts
are explained by reference to them, and in respect also of
the power of existing apart from each other the wholes are
prior to the parts.
Perhaps we should rather say that4
part is used in
several senses. One of these isl
that which measures
another thing in respect of quantity . But let this sense be
set aside;
let us inquire about the parts of which substance
IO35aconsists. If then matter is one thing, form another, the
compound of these a third, and both the matter and the
form and the compound are substance, even the matter is in
a sense called part of a thing, while in a sense it is not, but
onlythe elements of which the formula of the form consists.
E.g. of concavity flesh (for this is the matter in which it is
5 produced) is not a part, but of snubness it is a part ;and
the bronze is a part of the concrete statue, but not of the
statue when this is spoken of in the sense of the form. (For
the form, or the thing as having form, should be said to be
the thing, but the material element by itself must never be
said to be so.) And so the formula of the circle does not
10 include that of the segments, but the formula of the syllable
includes that of the letters;for the letters are parts of the
formula of the form, and not matter, but the segments are
parts in the sense of matter on which the form supervenes ;
yet they are nearer the form than the bronze is when
roundness is produced in bronze. But in a sense not even
every kind of letter will be present in the formula of the
15 syllable, e. g. particular waxen letters or the letters as move
ments in the air;for in these also we have already some
thing that is part of the syllable only in the sense that it is
its perceptible matter. For even if the line when divided
passes away into its halves, or the man into bones and
muscles and flesh,it does not follow that
theyare
composed of these as parts of their essence, but rather as
20 matter;and these are parts of the concrete thing, but not
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BOOK Z. 10 i035a
also of the form, i. e. of that to which the formula refers;
wherefore also they are not present in the formulae. In
one kind of formula, then, the formula of such parts will
be present, but in another it must not be present, wherethe formula does not refer to the concrete object. For it
is for this reason that some things have as their constituent
principles parts into which they pass away, while some have
not. Those things which are the form and the matter taken 2 5
together, e. g. the snub, or the bronze circle, pass awayinto these materials, and the matter is a part of them
;but
those things which do not involve matter but are without
matter, and whose formulae are formulae of the form only,
do not pass away, either not at all or at any rate not in
this way. Therefore these materials are principles and 30
parts of the concrete things, while of the form they are
neither parts nor principles. And therefore the clay statue
is resolved into clay and the ball into bronze and Callias
into flesh and bones, and again the circle into its segments ;
for there is a sense of circle in which it involves matter.
For circle is used ambiguously, meaning both the circle. iO35b
unqualified, and the individual circle, because there is no
name peculiar to the individuals.
The truth has indeed now been stated, but still let us state
it
yet
moreclearly, taking up
the
question again.The
parts of the formula, into which the formula is divided, are 5
prior to it, either all or some of them. The formula of the
right angle, however, does not include the formula of the
acute, but the formula of the acute includes that of the right
angle ;for he who defines the acute uses the right angle ;
for the acute is less than a right angle . The circle and
the semicircle also are in a like relation;
for the semicircleis defined by the circle
;and so is the finger by the whole 10
body, for a finger is such and such a part of a man .
Therefore the parts which are of the nature of matter, and
into which as its matter a thing is divided, are posterior ;
but those which are of the nature of parts of the formula,
and of the substance according to its formula, are prior,
either all or some of them. And since the soul of animals
(for this is the substance of a living being) is their substance 15
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io35b METAPHYSICA
according to the formula, i. e. the form and the essence of
a body of a certain kind (at least we shall define each part,
if we define it well, not without reference to its function,
and this cannot belong to it without perception 1), so that
the parts of soul are prior, either all or some of them, to
the concrete animal,and so too with each individual
20 animal;and the body and its parts are posterior to this,
the essential substance, and it is not the substance but
the concrete thing that is divided into these parts as its
matter : this being so, to the concrete thing these are in
a sense prior, but in a sense they are not. For they cannot
even exist if severed from the whole;for it is not a finger
in any and every state that is the finger of a living thing, but
25 a dead finger is a finger only in name. Some parts are
neither prior nor posterior to the whole, i. e. those which
are dominant and in which the formula, i. e. the essential
substance,is
immediately present, e. g. perhaps the heart orthe brain
;for it does not matter in the least which of the
two has this quality. But man and horse and terms which
are thus applied to individuals, but universally, are not sub
stance but something composed of this particular formula
30 and this particular matter treated as universal;and as
regards the individual, Socrates already includes in him
ultimate individual matter ; and similarly in all other cases.
* A part may be a part either of the form(i.
e. of the
essence), or of the compound of the form and the matter, or
of the matter itself. But only the parts of the form are
parts of the formula, and the formula is of the universal;
1036* for*
being a circle is the same as the circle, and being
a soul the same as the soul. But when we come to the
concrete thing, e. g. this circle, i. e. one of the individual
circles, whether perceptible or intelligible (I mean by intel
ligible circles the mathematical, and by perceptible circles
5 those ofbronze and of wood), of these there is no definition,
but they are known by the aid of intuitive thinking or of
perception ;and when they pass out of this complete realiza
tion it is not clear whether they exist or not;
but theyare
always stated and recognized by means of the universal for-
1 And therefore not without soul.
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BOOK Z. 10 1036
mula. But matter is unknowable in itself. And some matter
is perceptible and some intelligible, perceptible matter being10
for instance bronze and wood and all matter that is change
able, and intelligible matter being that which is presentin perceptible things not qzia perceptible, i. e. the objects of
mathematics.
We have stated, then, how matters stand with regard to
whole and part, and their priority and posteriority. But
when any one asks whether the right angle and the circle
and the animal are prior, or the things into which they are 15
divided and of which they consist, i.e. the parts,we must meet
the inquiry by saying that the question cannot be answered
simply. For if even bare soul is the animal or 1the
living thing, or the soul of each individual is the individual
itself, and being a circle is the circle, and being a right
angle and the essence of the right angle is the right angle,
then the whole in one sense must be called posterior to the
part in one sense, i. e. to the parts included in the formula
and to the parts of the individual right angle (for both the 20
material right angle which is made of bronze, and that
which is formed by individual lines, are posterior to their
parts) ;while the immaterial right angle is posterior to the
parts included in the formula, but prior to those included
in the particular instance, and the question must not beanswered simply. If, however, the soul is something
different and is not identical with the animal, even so some
parts must, as we have maintained, be called prior and 2 5
others, must not.
II Another question is naturally raised, viz. what sort of
partsbelong
to the form and what sort not to the form, but
to the concrete thing. Yet if this is not plain it is not
possible to define any thing ;for definition is of the universal
and of the form. If then it is not evident what sort of parts
are of the nature of matter and what sort are not, neither 30
will the formula of the thing be evident. In the case of
things which are found to occur in specifically different
materials, as a circle may exist in bronze or stoneor
wood,
1Sc. to put it more widely so as to include the vegetable world.
L 2
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io36a METAPHYSICA
it seems plain that these, the bronze or the stone, are no
part of the essence of the circle, since it is found apart from
35 them. Of things which are not seen to exist apart, there
1036** is no reason why the same may not be true, just as if all
circles that had ever been seen were of bronze;for none
the less the bronze would be no part of the form;but it is
hard to eliminate it in thought. E. g. the form of man is
always found in flesh and bones and parts of this kind;are
5 these then also parts of the form and the formula ? No,
they are matter;but because man is not found also in other
matters we are unable to perform the abstraction.
Since this is thought to be possible, but it is not clear
when it is the case, some peoplel
already raise the question
even in the case of the circle and the triangle, thinking that
it is not right to define these by reference to lines and to
10 the continuous, but that all these are to the circle or the
triangle as flesh and bones are to man, and bronze or stoneto the statue
;and they reduce all things to numbers, and
they say the formula of line is that of two . And of
those who assert the Ideas some 2 make * two the line-itself,
15 and others make it the Form of the line;for in some cases
they say the Form and that of which it is the Form are the
same, e. g. two and the Form of two;but in the case of
line they say this is no longer so.
It follows then that there is one Form for many things
whose form is evidently different (a conclusion which con
fronted the Pythagoreans also) ;and it is possible to make
one thing the Form-itself of all, and to hold that the others
are not Forms;but thus all things will be one.
We havepointed
out, then, that the
question
of defini
tions contains some difficulty, and why this is so. And so
to reduce all things thus to Forms and to eliminate the
matter is useless labour;for some things surely are a par
ticular form in a particular matter, or particular things in
a particular state. And the comparison which Socrates the
younger3 used to make in the case of animal 4
is not
1
Aristotle is thinking of Pythagoreans.2 This probably includes Plato himself.
3Cf. PI. Theaet. 147 D ; Soph. 218 B
;Pol. 257 C
; Epp. 358 D.
4Cf.
a34~
b7-
20
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BOOK Z. ii ios6b
sound;for it leads away from the truth, and makes one
suppose that man can possibly exist without his parts, as
the circle can without the bronze. But the case is not
similar ; for an animal is something perceptible, and it is
not possible to define it without reference to movement
nor, therefore, without reference to the parts being in
a certain state. For it is not a hand in any and every 30
state that is a part of man, but only when it can fulfil
its work, and therefore only when it is alive;
if it is not
alive it is not a part.
Regarding the objects of mathematics, why are the
formulae of the parts not parts of the formulae of the
wholes;
e. g. why are not the semicircles included in
the formula of the circle ? It cannot be said,l
because
these parts are perceptible things ;for they are not. But
perhaps this makes no difference;
for even some things 35
which are notperceptible
must have matter;indeed there
1037**is some matter in everything which is not an essence and
a bare form but a*
this . The semicircles, then, will not
be parts of the universal circle, but will be parts of the
individual circles, as has been said before l
;for while one
kind of matter is perceptible, there is another which is
intelligible.
It is clear also that the soul is the primary substance and 5
the body is matter, and man or animal is the compound of
both taken universally ;and Socrates or Coriscus
,if
even the soul of Socrates may be called Socrates,2 has two
meanings (for some mean by such a term the soul, and
others mean the concrete thing), but if Socrates or4
Coriscus means simply this particular soul and this par
ticular body, the individual is analogous to the universal in
its composition.3
Whether thereis, apart from the matter of such sub- 10
stances, another kind of matter, and one should look for
some substance other than these, e. g. numbers or some
thing of the sort, must be considered later.4 For it is for
1
1035* 3o-b 3. 2 Cf. I036a 16-17, H - i43b 2-4.3
i.e. as man = soul -f body, Socrates = this soul + this body.4
Cf. M, N.
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i037a METAPHYSICA
the sake of this that we are trying- to determine the nature
of perceptible substances as well, since in a sense the inquiry15 about perceptible substances is the work of physics, i. e. ot
second philosophy ;for the physicist must come to know
not only about the matter, but also about the substance ex
pressed in the formula, and even more than about the other.
And in the case of definitions, how the elements in the
formula are parts of the definition, and why the definition
is one formula (for clearly the thing is one, but in virtue of
20 what is the
thing one, althoughit has
parts ?),
this must
be considered later.1
What the essence is and in what sense it is independent,
has been stated universally in a way which is true of every
case,2 and also why the formula of the essence of some
things contains the parts of the thing defined, while that of
others does not. And we have stated that in the formula
25 of the substance the material parts will not be present (for
they are not even parts of the substance in that sense, but
of the concrete substance;but of this there is in a sense
a formula, and in a sense there is not;
for there is no
formula of it with its matter, for this is indefinite, but there
is a formula of it with reference to its primary substance
e. g.in the case of man the formula of the soul
,for the
substance is the indwelling form, from which and the
matter the so-called concrete substance is derived;
3e. g.
30 concavity is a form of this sort, for from this and the nose
arise snub nose and snubness) ;
but in the concrete
substance, e. g. a snub nose or Callias, the matter also will
be present.4 And we have stated that the essence and the
iO37
b
thingitself are in some cases the same
;i. e. in the case of
primary substances, e. g. curvature and the essence of curva
ture, if this is primary. (By a*
primary substance I mean
one which does not imply the presence of something in
something else, i. e. in something that underlies it which
acts as matter.) But things which are of the nature of
matter, or of wholes that include matter, are not the same
5 as their essences, nor are accidental unities like that of
1Cf. z. 12, H. 6.
2 Ch. 4.& Chs. 10, ii.
4 Ch. 5.
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BOOK Z. ii io37b
Socrates and *
musical;
for these are the same only by
accident.1
12 Now let us treat first of definition, in so far as we have
not treated of it in the Analytics2
;for the problem stated
in them 3is useful for our inquiries concerning substance.
I mean this problem : wherein can consist the unity of 10
that, the formula of which we call a definition, as for
instance, in the case of man,*
two-footed animal;for let
this be the formula of man. Why, then, is this one, and
not many, viz.
4
animal and*
two-footed ? For in thecase of man and *
pale there is a plurality when one term 15
does not belong to the other, but a unity when it does
belong and the subject, man, has a certain attribute;for
then a unity is produced and we have the pale man . In
the present case, on the other hand,4 one does not share in
the other;the genus is not thought to share in its differ
entiae (for then the same thing would share in contraries ;
for the differentiae by which the genus is divided are con- 20
trary). And even if the genus does share in them, the
same argument applies, since the differentiae present in
man are many, e. g. endowed with feet, two-footed, feather-
less. Why are these one and not many? Not because
they are present in one thing ;for on this principle a unity
can be made out of all the attributes ofa thing. But surely
all the attributes in the definition must be one;
for the 25
definition is a single formula and a formula of substance, so
that it must be a formula of some one thing ;for substance
means a one and a this,as we maintain.
We must first inquire about definitions reached by the
method of divisions. There is
nothingin the definition
except the first-named genus and the differentiae. The 30
other genera are the first genus and along with this the
differentiae that are taken with it, e.g.
the first may be
1
animal,the next
* animal which is two-footed,and again
1
animal which is two-footed and featherless,and similarly
if the definition includes more terms. And in general it iO38a
1
Ch. 6.2
Cf. An. Post. ii. 3-10, 13.3
Cf. ib. 97*29.4That of
*
animal and two-footed .
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io38a METAPHYSICA
makes no difference whether it includes many or few
terms, nor, therefore, whether it includes few or simply
two;and of the two the one is differentia and the other
genus; e. g. in
*
two-footed animal4
animal is genus, andthe other is differentia.
5 If then the genus absolutely does not exist apart from
the species-of-a-genus, or if it exists but exists as matter
(for the voice is genus and matter, but its differentiae make
the species, i. e. the letters, out of it), clearly the definition
is the formula which comprises the differentiae.
But it is also necessary that the division be by the differentia
ofthe differentia ;e. g. endowed with feet is a differentia
10 of animal; again the differentia of animal endowed with
feet must be of it qua endowed with feet. Therefore we
must not say, if we are to speak rightly, that of that which
is endowed with feet one part has feathers and one is
featherless (if we do this we do it through incapacity) ;we
must divide it only into cloven-footed and not-cloven;for
these are differentiae in the foot;
cloven-footedness is
15 a form of footedness. And the process wants always to goon so till it reaches the species that contain no differences.
And then there will be as many kinds of foot as there are
differentiae, and the kinds of animals endowed with feet
will be equal in number to the differentiae. If then this is
so, clearly the last differentia will be the substance of the
20 thing and its definition, since it is not right to state the
same things more than once in our definitions;
for it is
superfluous. And this does happen ;for when we say
1 animal endowed with feet and two-footed we have said
nothing other than4
animal having feet, having two feet;
and if we divide this by the proper division, we shall be
saying the same thing more than once as many times as
there are differentiae.
35 If then a differentia of a differentia be taken at each step,
one differentia the last will be the form and the sub
stance;but if we divide according to accidental qualities,
e. g. if we were to divide that which is endowed with feet
into the white and the black, there will be as many differ
entiae as there are cuts. Therefore it is plain that the
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BOOK Z. 12 ioa8a
definition is the formula which contains the differentiae, or,
according to the right method, the last of these. This 30
would be evident, if we were to change the order of such
definitions, e. g. of that of man, saying animal which is
two-footed and endowed with feet;
for endowed with
feet is superfluous when*
two-footed has been said. But
there is no order in the substance;for how are we to think
the one element posterior and the other prior ? Regarding
the definitions, then, which are reached by the method of
divisions, let this suffice as our first attempt at stating their 3s
nature.
13 Let us return to the subject of our inquiry, which is iO38b
substance. As the substratum and the essence and the
compound of these are called substance, so also is the
universal. About two of these we have spoken ;both about
the essence l and about the substratum,2 of which we have
said 3 that it underlies in two senses, either being a4 this 5
which is the way in which an animal underlies its attri
butes or as the matter underlies the complete reality.
The universal also is thought by some to be in the fullest
sense a cause, and a principle ;therefore let us attack the
discussion of this point also. For it seems impossible that
any universal term should be the name of a substance. For
firstly the substance of each thing is that which is peculiar
to it, which does not belong to anything else;
but the 10
universal is common, since that is called universal which is
such as to belong to more than one thing. Of which indi
vidual then will this be the substance ? Either of all or of
none;but it cannot be the substance of all. And if it is to
be thesubstance of one,
this
onewill
bethe
othersalso
;
for things whose substance is one and whose essence is one
are themselves also one.
Further, substance means that which is not predicable of 15
a subject, but the universal is predicable of some subject
always.
But perhaps the universal, while it cannot be substance
in the way in which the essence is so, can be present in this ;
1Chs. 4-6, 10-12.
2Ch. 3.
3
io29a2-3, 23-4.
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ios8b METAPHYSICA
e. g.*
animal can be present in man and horse . Then
clearly it is1 a formula of the essence. And it makes
no difference even if it is2 not a formula of everything that
20 is in the substance ; for none the less the universal will
be the substance of something, as* man is the substance of
the individual man in whom it is present, so that the same
result will follow once more;
for the universal, e. g.4 animal
,will be the substance of that in which it is present
as something peculiar to it. And further it is impossible
and absurd that the this,
i. e. the substance, if it consists
25 of parts, should not consist of substances nor of what is
a this,but of quality ;
for that which is not substance,
i. e. the quality, will then be prior to substance and to the
4
this . Which is impossible ;for neither in formula nor
in time nor in coming to be can the modifications be
prior to the substance;for then they will also be separ
able fromit.
Further, Socrates will contain a substance
present in a substance 3,so that this will be the substance
30 of two things. And in general it follows, if man and
such things are substance, that none of the elements in
their formulae is the substance of anything, nor does it
exist apart from the species or in anything else;
I mean,
for instance, that no animal exists apart from the parti
cular kinds of animal, nor does any other of the elements
present in formulae exist apart.
If, then, we view the matter from these standpoints, it is
35 plain that no universal attribute is a substance, and this is
plain also from the fact that no common predicate indicates
iO39a a this
,but rather a such . If not, many difficulties
follow and especially the third man .
4
The conclusion is evident also from the following con
sideration. A substance cannot consist of substances present
in it in complete reality ;for things that are thus in com-
5 plete reality two are never in complete reality one, though
if they are potentially two, they can be one (e.g. the
double line consists of two halves potentially ;for the
1
Reading in 1. 19 m .
2
Reading in 1.
3
Reading in 1. 29 ovaia ova-ia.*
Cf. A. 99Ob
17.
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BOOK Z. 13 1039
complete realization of the halves divides them from one
another) ;therefore if the substance is one, it will not con
sist of substances present in it and present in this way,
which Democritus describes rightly ; he says one thing can
not be made out of two nor two out ofone;for he identifies 10
substances with his indivisible magnitudes. It is clear there
fore that the same will hold good of number, if number is
a synthesis of units, as is said by some 1;for two is either
not one, or there is no unit present in it in complete
reality.
But our result involves a difficulty.If no substance can 15
consist of universals because a universal indicates a such,
not a this,and if no substance can be composed of
substances existing in complete reality, every substance
would be incomposite, so that there would not even be
a formula of any substance. But it is thottght by all and
wasstated
long ago
2
thatit is
either only, or primarily,substance that can be defined
; yet now it seems that not 20
even substance can. There cannot, then, be a definition of
anything ;or in a sense there can be, and in a sense there
cannot. And what we are saying will be plainer from what
follows.3
14 It is clear also from these
very
facts whatconsequenceconfronts those who say the Ideas are substances capable
of separate existence, and at the same time make the Form 2 5
consist of the genus and the differentiae. For if the Forms
exist and animal is present in* man and *
horse,
it is
either one and the same in number, or different. (In
formula it is clearly one;for he who states the formula will
go through the same formula in either case.) If then there 30
is a man-in-himself who is a this and exists apart, the
parts also of which he consists, e. g.* animal and two-
footed,must indicate thises
,and be capable of separate
existence, and substances;therefore animal
,as well as
man,must be of this sort.
Now(i)
if the animal in the horse and in man is
1Thales is said to have defined number as a system of units .
2Cf. 1031*11-14.
3Cf. Z. 15, H. 6.
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i039a METAPHYSICA
one and the same, as you are with yourself, (a) how will the
one in things that exist apart be one, and how will this
animal escape being- divided even from itself?
Further, (6) if it is to share in two-footed and*
many-footed
,an impossible conclusion follows
;for contrary
attributes will belong at the same time to it although it is
one and a this . If it is not to share in them, what is the
relation implied when one says the animal is two-footed or
5 possessed of feet ? But perhaps the two things are put
together and are*
in contact,or are mixed . Yet all
these expressions are absurd.
But (2) suppose the Form to be different in each species.
Then there will be practically an infinite number of things
whose substance isi animal
;for it is not by accident that
* man has animal for one of its elements. Further, many
things will be animal-itself . For(i)
the animal in each
10 species will be the substance of the species;
for it is after
nothing else that the species is called;if it were, that other
would be an element in man,
i. e. would be the genus of
man. And further, (ii)all the elements of which man is
composed will be Ideas. None of them, then, will be the
Idea of one thing and the substance of another; this is
impossible. The animal, then, present in each species of
animals will be animal-itself. Further, from what is this
4
animal in each species derived, and how will it be derived
15 from animal-itself ? Or how can this animal,whose
essence is simply animality, exist apart from animal-itself?
Further, (3)in the case of sensible things both these con
sequences and others still more absurd follow. If, then,
these consequences are impossible, clearly there are not
Forms of sensible things in the sense in which some maintain
their existence.
20 Since substance is of two kinds, the concrete thing and 15
the formula(I mean that one kind of substance is the for
mula taken with the matter, while another kind is the
formulain
its generality), substances in the former senseare capable of destruction (for they are capable also of
generation), but there is no destruction of the formula in
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BOOK Z. 15 io39b
the sense that it is ever in course of being destroyed (for
there is no generation of it either;the being of house is
not generated, but only the being of this house), but with- 25
out generation and destruction formulae are and are not ;
for it has been shown lthat no one begets nor makes
these. For this reason, also, there is neither definition
of nor demonstration about sensible individual substances,
because they have matter whose nature is such that they
are capable both of being and of not being ;for which 30
reason all the individual instances of them are destructible.
If then demonstration is of necessary truths and definition
is a scientific process, and if, just as knowledge cannot be
sometimes knowledge and sometimes ignorance, but the
state which varies thus is opinion, so too demonstration and
definition cannot vary thus, but it is opinion that deals with
that which can be otherwise than as it is, clearly there can 1040**
neither be definition of nor demonstration about sensible
individuals. For perishing things are obscure to those who
have the relevant knowledge, when they have passed from
our perception ;and though the formulae remain in the
soul unchanged, there will no longer be either definition or
demonstration. And so when one of the definition- 5
mongers defines any individual, he must recognize that his
definition may always be overthrown ; for it is not possible
to define such things.
Nor is it possible to define any Idea. For the Idea is,
as its supporters say, an individual, and can exist apart ;
and the formula must consist of words;and he who defines 10
must not invent a word (for it would be unknown), but the
established words are common to all the members of a
class;these then must apply to something besides the thing
defined;
e. g. if one were defining you, he would say an
animal which is lean or pale ,or something else which
will apply also to some one other than you. If any one
were to say that perhaps all the attributes taken apart may
belong to many subjects, but together they belong only to
this one, we must reply first that they belong also to both 15
the elements;
e. g,l
two-footed animal belongs to animal
1Ch. 8.
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i040a METAPHYSICA
and to the two-footed. (And in the case ofeternal entities1
this is even necessary, since the elements are prior to and
parts of the compound ; nay more, they can also exist
apart, if*
man can exist apart. For either neither or both20 can. If, then, neither can, the genus will not exist apart
from the various species ;but if it does, the differentia will
also.) Secondly, we must reply that animal and two-
footed are prior in being to*
two-footed animal;
and
things which are prior to others are not destroyed when
the others are.
Again, if the Ideas consist of Ideas (as they must, since
elements are simpler than the compound), it will be further
necessary that the elements also of which the Idea consists,
e. g. animal and two-footed,should be predicated of
25 many subjects. If not, how will they come to be known ?
For there will then be an Idea which cannot be predicated
ofmoresubjects
than one. But this is notthought possible
every Idea is thought to be capable of being shared.
As has been said,2
then, the impossibility of defining
individuals escapes notice in the case of eternal things,
especially those which are unique, like the sun or the moon.
30 For people err not only by adding attributes whose removal
the sun would survive, e. g. going round the earth or
night-hidden (for from their view it follows that if it
stands still or is visible,3
it will no longer be the sun;but
it is strange if this is so;for the sun means a certain
sitbstance] ;but also by the mention ofattributes which can
belong to another subject ;e. g. if another thing with the
stated attributes comes into existence, clearly it will be
iO4oba sun
;the formula therefore is general. But the sun was
supposed to be an individual, like Cleon or Socrates. After
all, why does not one of the supporters ofthe Ideas produce
a definition of an Idea ? It would become clear, if they
tried, that what has now been said is true.
5 Evidently even of the things that are thought to be sub- 16
stances, most are only potencies, both the parts ofanimals
(fornone of them exists separately ;
and when they are
1i. e. the Ideas.
2Cf. 1. 17.
3Sc. at night.
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BOOK Z. 16 i040b
separated, then too they exist, all of them, merely as matter)
and earth and fire and air;for none of them is a unity, but
as it were a mere heap, till they are worked up and some
unity is made out of them. One might most readily suppose 10
the parts of living1
things and the parts of the soul nearly
related to them to turn out to be both, i.e. existent in com
plete reality as well as in potency, because they have sources
of movement in something in their joints ;for which reason
some animals live when divided. Yet all the parts must
exist only potentially, when they are one and continuous by
nature, not by force or by growing into one, for such a 15
phenomenon is an abnormality.
Since the term unity is used like the term being ,and
the substance of that which is one is one, and things whose
substance is numerically one are numerically one, evidently
neither unity nor being can be the substance of things, just
as
beingan element or a
principle
cannot be the substance,
but we ask what, then, the principle is, that we may reduce 20
the thing to something more knowable. Now of these
concepts being and unity are more substantial than
principle or element or cause,but not even the
former are substance, since in general nothing that is com
mon is substance;for substance does not belong to anything
but to itself and to that which has it, of which it is the
substance. Further, that which is one cannot be in many 25
places at the same time, but that which is common is present
in many places at the same time;so that clearly no universal
exists apart from its individuals.
But those who say the Forms exist, in one respect are
right, in giving the Forms separate existence, if they are
substances ; but in another respect they are not right,
because they say the one over many is a Form. The reason30
for their doing this is that they cannot declare what are the
substances of this sort, the imperishable substances which
exist apart from the individual and sensible substances.
They make them, then, the same in kind as the perishable
things (for this kind of substance we know) man-himself
and horse-itself, adding to the sensible things the word
itself. Yet even if we had not seen the stars, none the io4ia
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io4ia METAPHYSICA
less, I suppose, would they have been eternal substances
apart from those which we knew;so that now also if we
do not know what non-sensible substances there are, yet it
is doubtless necessary that there should be some. Clearly,
then, no universal term is the name of a substance, and no
5 substance is composed of substances.
Let us state what, i. e. what kind of thing, substance 17
should be said to be, taking once more another starting-
point ;for perhaps from this we shall get a clear view also
ofthat substance which exists apart from sensible substances.
Since, then, substance is a principle and a cause, let us pur-
10 sue it from this starting-point. The why is always sought
in this form why does one thing attach to some other ?
For to inquire why the musical man is a musical man, is
either to inquire as we have said why the man is musical,
or it is something else. Now why a thing is itself is
15 a meaningless inquiry (for (to give meaning to the question
why )the fact or the existence of the thing must already
be evident e. g. that the moon is eclipsed but the fact
that a thing is itself is the single reason and the single
cause to be given in answer to all such questions as whythe man is man, or the musician musical \
lunless one were
to answer because each
thing
is
inseparable
from itself,
and its being one just meant this; this, however, is com
mon to all things and is a short and easy way with the
20question). But we can inquire why man is an animal of
such and such a nature. This, then, is plain, that we are not
inquiring why he who is a man is a man. We are inquiring,
then, why something is predicable of something (that it is
predicable must be clear ; for if not, the inquiry is an
inquiry into nothing). E. g. why does it thunder ? This
is the same as why is sound produced in the clouds ?
2 5 Thus the inquiry is about the predication of one thing of
another. And why are these things, i. e. bricks and stones,
a house ? Plainly we are seeking the cause. And this is
the essence (to speak abstractly), which in some cases is the
1Sc. and therefore in this case, when the fact is known, there is no
question as to the why .
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BOOK Z. 17 i04ia
end, e. g. perhaps in the case of a house or a bed, and in
some cases is the first mover;for this also is a cause. But 3
while the efficient cause is sought in the case of genesis
and destruction, the final cause is
sought
in the case of being
also.
The object of the inquiry is most easily overlooked where
one term is not expressly predicated of another(e. g. when
we inquire* what man is
),because we do not distinguish and iO4i
b
do not say definitely that certain elements make up a certain
whole. But we must articulate our meaning before we
begin to inquire; if not, the inquiry is on the border-line
between being a search for something and a search for
nothing. Since we must have the existence of the thing as
something given, clearly the question is why the matter is
some definite thing ;e. g. why are these materials a house ?
Because thatwhich was the essence ofa house is present. And 5
why is this individual thing, or this body having this form, a
man ? Therefore what we seek is the cause, i. e. the form, byreason of which the matter is some definite thing ;
and this
is the substance of the thing. Evidently, then, in the case
of simple terms no inquiry nor teaching is possible ;our 10
attitude towards such things is other than that of inquiry.
Since * that which is compounded out of something so
that the whole is one, not like2a heap but like a syllable,
now the syllable is not its elements, ba is not the same as b
and , nor is flesh fire and earth (for when these are separated
the wholes, i. e. the flesh and the syllable, no longer exist,
but the elements of the syllable exist, and so do fire and 15
earth) ;the syllable, then, is something not only its ele
ments (the vowel and the consonant) but also something
else,and the flesh is not
onlyfire and earth or the hot and
the cold, but also something else : if, then, that something
must itself be either an element or composed of elements,
(i) if it is an element the same argument will again apply ;ao
for flesh will consist of this and fire and earth and some
thing still further, so that the process will go on to infinity.
1Not even the protasis of the sentence beginning io4i
b n is ever
completed;
theparenthesis beginning 17
Se<7iAXa/3^,
1.
12,is so
longthat the original construction is forgotten.2
Omitting ai/ in 1. 12.
645-28 M
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i04ib METAPHYSICA
But(2)
if it is a compound, clearly it will be a compoundnot of one but of more than one (or else that one will be
the thing itself), so that again in this case we can use the
same argument as in the case of flesh or of the syllable.
35 But it would seem that this*
other is something, and not
an element, and that it is the cause which makes this thing
flesh and that a syllable. And similarly in all other cases.
And this is the sitbstance of each thing (for this is the
primary cause of its being) ;and since, while some things
are not substances, as many as are substances are formed
inaccordance with
a nature of their
ownand
byaprocess
3 of nature, their substance would seem to be this kind of
nature V which is not an element but a principle. An
element, on the other hand, is that into which a thing is
divided and which is present in it as matter;
e. g. a and b
are the elements of the syllable.
1
Sc. the formal cause. Cf. A. ioi4b36 in contrast with ib. 27.
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BOOK H
I WE must reckon up the results arising from what has been 1042*
said, and compute the sum of them, and put the finishing
touch to our inquiry. We have said that the causes, princi- 5
pies,and elements ofsubstances are the object ofour search.
1
And some substances are recognized by every one, but some
have been advocated by particular schools. Those gener
ally recognized are the natural substances, i.e. fire, earth,
water, air, &c., the simple bodies; secondly, plants and
their parts, and animals and the parts of animals;and 10
finally the physical universe and its parts ;while some
particular schools say that Forms and the objects of mathe
matics are substances.2 But there are arguments which
lead to the conclusion that there are other substances, the
essence and the substratum. Again, in another way the
genus seems more substantial than the various species, and
the universal than the particulars.3 And with the universal 15
and the genus the Ideas are connected;
it is in virtue of the
same argument that they are thought to be substances.
And since the essence is substance, and the definition is
a formula of theessence,
for this reason we have discussed
definition and essential predication.4 Since the definition
is a formula, and a formula has parts, we had to consider
also with respect to the notion of part ,what are parts of 20
the substance and what are not, and whether the parts of the
substance are also parts of the definition.5
Further, too,
neither the universal nor the genus is a substance;
6 we
must inquire later into the Ideas and the objects of mathematics
;
7for some say these are substances as well as the
sensible substances.
But now let us resume the discussion of the generally
recognized substances. These are the sensible substances, 25
and sensible substances all have matter. The substratum is
1
Cf. z. i.
2
Cf. z. 2.
3
Cf. Z. 3. io28b
33-6.4Cf. Z. 4-6, 12, 15.
6Cf. Z. 10, ii.
6Cf. Z. 13, 14, 16. I04o
bi6-i04i
a5.
7Cf. M and N.
M 2
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io4 2a METAPHYSICA
substance, and this is in one sense the matter (and by matter
I mean that which, not being- a this actually, is potentially
a*
this),and in another sense the formula or shape (that
which being athis
can be separately formulated),and
30 thirdly the complex of these two, which alone is generated
and destroyed, and is, without qualification, capable of
separate existence;
for of substances completely expres
sible in a formula some are separable and some are not.
But clearly matter also is substance;for in all the oppo
site changes that occur there is something which underlies
the changes, e. g. in respect of place that which is now here
35 and again elsewhere, and in respect of increase that which
is now of one size and again less or greater,and in respect
of alteration that which is now healthy and again diseased;
iO42b and similarly in respect of substance there is something that
is now being generated and again being destroyed, and
nowr lunderlies the process as a
l
this and again2
underlies
it in respect of a privation of positive character. And in this
change the others are involved. But in either one or two
5 of the others this is not involved;for it is not necessary if
a thing has matter for change of place that it should also
have matter for generation and destruction.
The difference between becoming in the full sense and
becoming in a qualified sense has been stated in our physicalworks.
3
Since the substance which exists as underlying and 2
as matter is generally recognized, and this is that which
10 exists potentially, it remains for us to say what is the sub
stance, in the sense of actuality, of sensible things. Demo-
critus seems to think there are three kinds of difference
between things ;the underlying body, the matter, is one
and the same, but they differ either in rhythm, i. e. shape,
or in turning, i. e. position, or in inter-contact, i. e. order.4
15 But evidently there are many differences;
for instance,
some things are characterized by the mode of composition
1 Sc. in the case of destruction. 2 Sc. in the case of generation.8
Cf. Phys. 22 Sa12-20, De Gen. et Corr. 317* 17-31.
4Cf. A. 98s
b13-19.
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BOOK H. a i042b
of their matter, e. g. the things formed by blending, such as
honey-water ;and others by being bound together, e. g.
a bundle;and others by being glued together, e. g. a book
;
and others by being nailed together, e. g. a casket;
andothers in more than one of these ways ;
and others by
position, e. g. threshold and lintel (for these differ by being
placed in a certain way) ;and others by time, e. g. dinner 2o
and breakfast;and others by place, e. g. the winds
;and
others by the affections proper to sensible things, e. g. hard
ness and softness, density and rarity, dryness and wetness;
and some things by some of these qualities, others by them
all, and in general some by excess and some by defect.
Clearly, then, the word is has just as many meanings ; 25
a thing is a threshold because it lies in such and such a posi
tion, and its being means its lying in that position, while
being ice means having been solidified in such and such
a way. And the being of some things will be defined by
all these qualities, because some parts of them are mixed,
others are blended, others are bound together, others are 3
solidified, and others use the other differentiae;
e. g. the
hand or the foot requires such complex definition. Wemust grasp, then, the kinds of differentiae (for these will
be the principles of the being of things), e.g. the things
characterized bythe
more andthe
less, or by the denseand the rare, and by other such qualities ;
for all these are
forms of excess and defect. And anything that is charac- 35
terized by shape or by smoothness and roughness is
characterized by the straight and the curved. And for
other things their being will mean their being mixed, and 1043**
their not being will mean the opposite.
It is clear, then, from these facts that, since its substance is
the cause of each thing s being, we must seek in these
differentiae what is the cause of the being of each of these
things. Now none of these differentiae is substance, even
when coupled with matter, yet it is what is analogous to sub
stance in each case;and as in substances that which is 5
predicated of the matter is the actuality itself, in all other
definitions also it is what most resembles fullactuality.
E. g. if we had to define a threshold, we should say wood
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io43a METAPHYSICA
or stone in such and such a position ,and a house we should
define as*
bricks and timbers in such and such a position (or
a purpose may exist as well in some cases), and if we had to
define ice we should say water frozen or solidified in such10 and such a way ,
and harmony is such and such a blending
of high and low;and similarly in all other cases.
Obviously, then, the actuality or the formula is different
when the matter is different;for in some cases it is the
composition, in others the mixing, and in others some other
of the attributes we have named. And so, of the people
who go in for defining, those who define a house as stones,
15 bricks, and timbers are speaking of the potential house, for
these are the matter;but those who propose
1 a receptacle
to shelter chattels and living beings ,or something of the
sort, speak of the actuality. Those who combine both of
these speak of the third kind of substance, which is com
posed
of matter and form (for the formula that
gives
the
differentiae seems to be an account of the form or actuality,
20 while that which gives the components is rather an account
of the matter); and the same is true of the kind of defi
nitions which Archytas used to accept ; they are accounts
of the combined form and matter. E.g. what is still weather ?
Absence ofmotion in a large expanse of air; air is the matter,
and absence of motion is the actuality and substance. What25 is a calm ? Smoothness of sea
;the material substratum is
the sea, and the actuality or shape is smoothness. It is
obvious then, from what has been said, what sensible sub
stance is and how it exists one kind of it as matter, another
as form or actuality, while the third kind is that which is
composed of these two.
We must not fail to notice that sometimes it is not clear 3
30 whether a name means the composite substance, or the
actuality or form, e.g. whether house is a sign for the
composite thing, a covering consisting of bricks and stones
laid thus and thus \ or for the actuality or form, a covering ,
and whether a line is twoness in
length
or twoness,and
35 whether an animal is a soul in a body or a soul;for
1
Reading in 1. 17
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BOOK H. 3 i043a
soul is the substance or actuality of some body.* Animal
might even be applied to both, not as something definable
by one formula, but as related to a single thing. But
this question,
1
while important for another purpose,is
of no importance for the inquiry into sensible substance;
for the essence certainly attaches to the form and the actu- iO43b
ality. For soul and *
to be soul are the same, but to be
man and man are not the same, unless even the bare soul
is to be called man;and thus on one interpretation the thing
is the same as its essence, and on another it is not.
If we examine2
we find that the syllable does not consist 5
of the letters +juxtaposition, nor is the house bricks +juxta
position. And this is right ;for the juxtaposition or
mixing does not consist of those things of which it is the
juxtaposition or mixing. And the same is true in all other
cases; e.g. if the threshold is characterized by its posi
tion, the position is not constituted by the threshold, but
rather the latter is constituted by the former. Nor is man 10
animal + biped, but there must be something besides these,
if these are matter, something which is neither an element
in the whole nor a compound, but is the substance;but this
people eliminate, and state only the matter. If, then, this is
the cause of the thing s being, and if the cause of its being is
its substance,3
they
will not bestating
the substance itself.
(This, then, must either be eternal or it must be destruc-15
tible without being ever in course of being destroyed, and
must have come to be without ever being in course of
coming to be. But it has been proved and explained else
where 4that no one makes or begets the form, but it is the
individual that is made, i. e. the complex of form and
matter that is generated. Whether the substances ofdestructible things can exist apart, is not yet at all clear
;
except that obviously this is impossible in some cases in 20
the case of things which cannot exist apart from the in
dividual instances, e. g. house or utensil. Perhaps, indeed,
neither these things themselves, nor any of the other things
1Sc. whether the name means the form or the concrete
thing.2Aristotle returns to the subject discussed in ch. 2.
3Cf. A. 1017^14-15.
*Cf. Z. 8.
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io43b METAPHYSICA
which are not formed by nature, are substances at all;
for
one might say that the nature in natural objects is the only
substance to be found in destructible things.)
Therefore thedifficulty which used to be raised by the
school ofAntisthenes and other such uneducated people has
25 a certain timeliness. They said that the*
what cannot be
defined (for the definition so called is a long rigmarolel
)
but of what sort a thing, e. g. silver, is, they thought it
possible actually to explain, not saying what it is, but that
it is like tin. Therefore one kind of substance can be
defined and formulated, i. e. the composite kind, whether it
30 be perceptible orintelligible ;
but the primary parts of
which this consists cannot be defined, since a defmitory
formula predicates something of something, and one part
of the definition must play the part of matter and the other
that of form.
It is also obvious that, if substances are in a sense
numbers, they are so in this sense and not, as some say,2
as numbers of units. For a definition is a sort of number;
35 for (i) it is divisible, and into indivisible parts (for defini-
tory formulae are notinfinite"),
and number also is of this
nature. And (2) as, when one of the parts of which
a number consists has been taken from or added to the
number,it
is no longer the same number, but a different
one, even if it is the very smallest part that has been taken
ic>44
a
away or added, so the definition and the essence will no
longer remain when anything has been taken away or
added. And(3)
the number must be something in virtue
of which it is one, and this these thinkers cannot state,
what makes it one, if it is one (for either it is not one but a
sort of heap, or if it is, we ought to say what it is that
5 makes one out of many) ;and the definition is one, but
similarly they cannot say what makes it one. And this is
a natural result;
for the same reason is applicable, and
substance is one in the sense which we have explained, and
not, as some say, by being a sort of unit or point ;each is
1Sc. and therefore cannot give the essence, which is simple. For
the contemptuous meaning of paKpos \6yos cf. N.ic>9i
a7.
2 The Pythagoreans and Platonists (cf. M. 6, 7),8
Reading in 1. 35 arreipoi. &rreipos is a misprint.
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BOOK H. 3 1044*
a complete reality and a definite nature. And (4) as
number does not admit of the more and the less, neither does 10
substance, in the sense of form, but if any substance does, it
is only the substance which involves matter. Let this, then,suffice for an account of the generation and destruction of
so-called substances in what sense it is possible and in
what sense impossible and of the reduction of things to
number.
4 Regarding material substance we must not forget that 15
even if all
thingscome from the same first cause 1
or have
the same things for their first causes, and if the same
matter serves as starting-point for their generation, yet
there is a matter proper to each, e. g. for phlegm the sweet
or the fat, and for bile the bitter, or something else; though
perhaps these come from the same original matter. And 20
there come to be several matters for the same thing, when
the one matter is matter for the other ; e. g. phlegm comesfrom the fat and from the sweet, if the fat comes from the
sweet;and it comes from bile by analysis of the bile into
its ultimate matter. For one thing comes from another
in two senses, either because it will be found at a later
stage, or because it is produced if the other is analysed into
its original constituents. When the matter is one, different35
things may be produced owing to difference in the moving
cause;
e. g. from wood may be made both a chest and a bed.
But some different things must have their matter different;
e. g. a saw could not be made of wood, nor is this in the
power of the moving cause;for it could not make a saw of
wool or of wood. But if, as a matter of fact, the same thing
can be made of different material, clearly the art, i. e. the 30
moving principle, is the same;for if both the matter and
the moving cause were different, the product would be so
too.
When one inquires into the cause of something, one
should, sincel
causes are spoken of in several senses, state
all the possible causes. E. g. what is the material cause of
man ? Shall
we say the menstrual fluid?
Whatis
the 35
1
Sc. material cause.
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io44a METAPHYSICA
moving cause ? Shall we say the seed ? The formal cause ?
His essence. The final cause ? His end. But perhaps the
iO44blatter two are the same. It is the proximate causes we must
state. Whatis the
material cause?
We must namenot
fire or earth, but the matter peculiar to the thing.
Regarding the substances that are natural and generable,
if the causes are really these and of this number and we
5 have to learn the causes, we must inquire thus, if we are to
inquire rightly. But in the case of natural but eternal
substances another account must be given. For perhaps
some have no matter, or not matter of this sort but only
such as can be moved in respect of place. Nor does matter
belong to those things which exist by nature but are not
substances;their substratum is the substance. E. g. what
ic is the cause of eclipse ? What is its matter ? There is none;
the moon is that which suffers eclipse.1 What is the
moving cause which extinguished the light ? The earth.
The final cause perhaps does not exist. The formal principle
is the definitory formula, but this is obscure if it does not
include the cause.2
E. g. what is eclipse ? Deprivation of
light.But if we add 4
by the earth s coming in between ,
15 this is the formula which includes the cause. In the case
of sleep it is not clear what it is that proximately has this
affection. Shall we say that it is the animal?
Yes, butthe
animal in virtue of what, i. e. what is the proximate subject ?
The heart or some other part. Next, by what is it produced?
Next, what is the affection that of the proximate subject,
not of the whole animal ? Shall we say that it is immobility
of such and such a kind ? Yes, but to what process in the
20 proximate subject is this due ?
Since some things are and are not, without coming to be 5
and ceasing to be, e. g. points, if they can be said to be, and
in general forms (for it is not white that comes to be, but
the wood comes to be white, if everything that comes to be
comes from something and comes to be something), not all
25 contraries can come from one another, but it is in different
1i. e. the substratum of a substance is bare matter, but the sub
stratum of an attribute is a determinate substance such as the moon.2Sc. the efficient cause.
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BOOK H. 5 i044b
senses that a pale man comes from a dark man, and pale
comes from dark. Nor has everything matter, but only
those things which come to be and change into one an
other. Those things which, without ever being in courseof changing, are or are not, have no matter.
There is difficulty in the question how the matter of each
thing is related to its contrary states. E. g. if the body is 30
potentially healthy, and disease is contrary to health, is it
potentially both healthy and diseased ? And is water poten
tially wine and vinegar ? We answer that it is the matter
of one in virtue of its positive state and its form, and of the
other in virtue of the privation of its positive state and the
corruption of it contrary to its nature. It is also hard to
say why wine is not said to be the matter of vinegar nor
potentially vinegar (though vinegar is produced fromit), 35
and why a living man is not said to be potentially dead.
In fact they are not, but the corruptions in question are
accidental, and it is the matter of the animal that is itself 104 5a
in virtue of its corruption the potency and matter of a corpse,
and it is water that is the matter of vinegar. For the corpse
comes from the animal, and vinegar from wine, as night
from day. And all the things which change thus into one
another must go back to their matter;
e. g. if from a corpse
is
producedan
animal,the
corpsefirst
goesback to its
matter, and only then becomes an animal;and vinegar first 5
goes back to water, and only then becomes wine.
6 To return to the difficulty which has been stated1with
respect both to definitions and to numbers, what is the
cause of their unity ? In the case of all things which have
several parts and in which the totality is not, as it were,
a mere heap, but the whole is something besides the parts,
there is a cause;for even in bodies contact is the cause of 10
unity in some cases, and in others viscosity or some other
such quality. And a definition is a set of words which is
one not by being connected together, like the Iliad, but by
dealing with one object. What, then, is it that makes man
one; why is he one and not many, e.g. animal + biped,
1Cf. Z. 12, H. io44
a 2-6.
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io45a METAPHYSICA
15 especially if there are, as some say, an animal-itself and
a biped-itself ? Why are not those Forms themselves the
man, so that men would exist by participation not in man,
nor in one Form, but in two, animal and biped, and in
general man would be not one but more than one thing,
animal and biped ?
20Clearly, then, if people proceed thus in their usual manner
of definition and speech, they cannot explain and solve the
difficulty. But if, as we say, one element is matter and an
other is form, and one is potentially and the other actually,
25 the question will no longer be thought a difficulty. For
this difficulty is the same as would arise if round bronze
were the definition of cloak;
lfor this word would be
a sign of the defmitory formula, so that the question is,
what is the cause of the unity of round and bronze ?
The difficulty disappears, because the one is matter, the
30other form.
What, then,causes this that which was
potentially to be actually except, in the case of things which
are generated, the agent ? For there is no other cause of
the potential sphere s becoming actually a sphere, but this
was the essence of either.2 Of matter some is intelligible,
some perceptible, and in a formula there is always an
35 element of matter as well as one of actuality ;e. g. the
circle is a plane figure.
3
But of the things which have no
matter, either intelligible or perceptible, each is by its
iO45b nature essentially a kind of unity, as it is essentially a kind
of being individual substance, quality, or quantity (and so
neither existent nor one is present in their defini
tions), and the essence of each of them is by its very nature
a kind of unity as it is a kind of being and so none of
these has any reason outside itself for being one, nor for
5 being a kind of being ;for each is by its nature a kind
of being and a kind of unity, not as being in the genus
being or one nor in the sense that being and unity
can exist apart from particulars.
1Cf. Z. I029
b28, de Int. i8a 19.
2i. e. it was the essence of the
potential
ball to become an actual
ball, and of the actual ball to be produced from a potential ball.
3Aristotle does not give the whole definition, but only the genus, or
material element.
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BOOK H. 6 i045b
Owing to the difficulty about unity some speak of par
ticipation ,and raise the question, what is the cause of
participation and what is it to participate ;and others speak
of communion , as Lycophron says knowledge is a com- 10
munion of knowing with the soul;and others say life is
a composition or connexion of soul with body. Yet
the same account applies to all cases;for being healthy, too,
will on this showing be either a communion or a con
nexion or a composition of soul and health, and the fact
that the bronze is a triangle will be a composition of
bronze and triangle, and the fact that a thing is white will 15
be a*
composition of surface and whiteness. The reason
is that people look for a unifying formula, and a difference,
between potency and complete reality. But, as has been
said,1the proximate matter and the form are one and the
same thing, the one potentially, and the other actually.
Therefore it is like asking what in general is the cause of
unity and of a thing s being one;for each thing is a unity,
20
and the potential and the actual are somehow one. There
fore there is no other cause here unless there is something
which caused the movement from potency into actuality.
And all things which have no matter are without qualifi
cation essentially unities.
1Cf.
a23-33.
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BOOK
WE have treated l of that which is primarily and to which i
all the other categories of being are referred i. e. of sub
stance. For it is in virtue of the concept of substance that
30 the others also are said to be quantity and quality and the
like;for all will be found to involve the concept of sub
stance, as we said in the first part of our work.2 And since
being is in one way divided into individual thing, quality,
and quantity, and is in another way distinguished in respect
of potency and complete reality, and of function, let us now
35 add a discussion of potency and complete reality. And first
let us explain potency in the strictest sense, which is, hovv-
I046aever, not the most useful for our present purpose. For
potency and actuality extend beyond the cases that involve
a reference to motion. But when we have spoken of this
first kind, we shall in our discussions of actuality3
explain
the other kinds of potency as well.
We have pointed out elsewhere 4that potency and the
5 word can have several senses. Of these we may neglectall the potencies that are so called by an equivocation.
For some are called so by analogy, as in geometry we say
one thing is or is not a4
power of another by virtue of the
presence or absence of some relation between them. But
all potencies that conform to the same type are originative
10 sources of some kind, and are called potencies in reference
to one primary kind of potency, which is an originative
source of change in another thing or in the thing itself qua
other. For one kind is a potency of being acted on, i. e.
the originative source, in the very thing acted on, of its
being passively changed by another thing or by itself qua
other; and another kind is a state of insusceptibility to
changefor the worse and to destruction by another thing
1Cf. ZH.
2Cf. z. i.
3Cf. 0. 1048* 27-
b6.
4Cf. A. 12.
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BOOK 0. i i046a
or by the thing itself qua other by virtue ot an originative
source of change. In all these definitions is implied the 15
formula of potency in the primary sense. And again these
so-called
potencies
are
potencies
either of
merely acting
or
being acted on, or of acting or being acted on well, so that
even in the formulae of the latter the formulae of the prior
kinds of potency are somehow implied.
Obviously, then, in a sense the potency of acting and of
being acted on is one (for a thing may be capable either 20
because it can itself be acted on or because something else
can be acted on by it), but in a sense the potencies aredifferent. For the one is in the thing acted on
;it is because
it contains a certain originative source, and because even
the matter is an originative source, that the thing acted on is
acted on, and one thing by one, another by another;for that
which is oily can be burnt, and that which yields in a par
ticular way can be crushed;
J and similarly in all other cases. 25
But the other potency is in the agent, e. g. heat and the art of
building are present, one in that which can produce heat
and the other in the man who can build. And so, in so far
as a thing is an organic unity, it cannot be acted on by
itself; for it is one and not two different things. And1
impotence and impotent stand for the privation which
is contrary to potency of this sort, so that every potency 3
belongs to the same subject and refers to the same process
as a corresponding impotence. Privation has several senses;
for it means (i) that which has not a certain quality and (2)
that which might naturally have it but has not it, either
(a)in general or
(b) when it might naturally have it, and
either (a) in some particular way, e. g. when it has not it
completely,or
(/?)
when it has not it at all.
Andin certain
cases if things which naturally have a quality lose it by 35
violence, we say they have suffered privation.
2 Since some such originative sources are present in soul
less things, and others in things possessed of soul, and in
soul, and in the rational part of the soul, clearly some iO46b
1i. e. the event would not happen ifthe passive factor were different.
What is oily cannot necessarily be crushed, nor what is yielding burnt.
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i046b METAPHYSICA
potencies will be non-rational and some will be accom
panied by a rational formula. This is why all arts, i.e. all
productive forms of knowledge, are potencies ; they are
originativesources of
changein another
thingor in the
artist himself considered as other.
And each of those which are accompanied by a rational
5 formula is alike capable of contrary effects, but one non-
rational power produces one effect;
e. g. the hot is capable
only of heating, but the medical art can produce botli
disease and health. The reason is that science is a rational
formula, and the same rational formula explains a thing andits privation, only not in the same way ;
and in a sense it
applies to both, but in a sense it applies rather to the
10 positive fact. Therefore such sciences must deal with
contraries, but with one in virtue of their own nature and
with the other not in virtue of their nature;for the rational
formula applies to one object in virtue of that object s
nature, and to the other, in a sense, accidentally. For it is
by denial and removal that it exhibits the contrary; for the
contrary is the primary privation, and this is the removal
15 of the positive term. Now since contraries do not occur
in the same thing, but science is a potency which depends
on the possession of a rational formula, and the soul
possesses an originative source of movement;
therefore,while the wholesome produces only health and the calorific
only heat and the frigorific only cold, the scientific man
20 produces both the contrary effects. For the rational for
mula is one which applies to both, though not in the same
way, and it is in a soul which possesses an originative
source of movement;
so that the soul will start both
processes from the same originative source, having linked
them up with the same thing.1 And so the things whose
potency is according to a rational formula act contrariwise
to the things whose potency is non-rational;
for the
products of the former are included under one originative
source, the rational formula.
25 It is obvious also that the potency ofmerely doing a thing
or having it done to one is implied in that of doing it or
1i. e. with the rational formula.
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BOOK 0. 2 i046b
having it done well, but the latter is not always implied in
the former : for he who does a thing well must also do it,
but he who does it merely need not also do it well.
3 There are some who say, as the Megaric school does, that
a thing* can act only when it is acting, and when it is not
acting it cannot act, e.g. that he who is not building can-30
not build, but only he who is building, when he is building ;
and so in all other cases. It is not hard to see the absurdi
ties that attend this view.
For it is clear that on this view a man will not be a
builder unless he is building (for to be a builder is to be
able to build), and so with the other arts. If, then, it is 35
impossible to have such arts if one has not at some time
learnt and acquired them, and it is then impossible not to
have them if one has not sometime lost them (either by for- 1047*
getfulness or by some accident or by time;for it cannot be
by the destruction of the object^ for that lasts for ever), a
man will not have the art when he has ceased to use it, and
yet he may immediately build again ;how then will he have
got the art ?2 And similarly with regard to lifeless things ;
nothing will be either cold or hot or sweet or perceptible 5
at all if people are not perceiving it;so that the upholders
of this view will have to maintain the doctrine of Pro
tagoras.
3
But, indeed, nothingwill even have
perceptionif
it is not perceiving, i.e. exercising its perception. If, then,
that is blind which has not sight though it would naturally
have it, when it would naturally have it and when it still
exists, the same people wall be blind many times in the day
and deaf too.
Again, if that which is deprived of potency is incapable, 10
that which is not happening will be incapable of happen
ing ;but he who says of that which is incapable of happen
ing either that it is or that it will be will say what is untrue;
for this is what incapacity meant. Therefore these views
1 The object of knowledge is always a form, which is eternal. Thematter which makes things perishable is no object for knowledge.
2 The protasis here states facts, the apodosis states a conclusion
which follows from the Megaric theory, and the final question states
a difficulty which follows from the apodosis.3
Cf. r. 5, 6.
645-28 N
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io47a METAPHYSICA
15 do away with both movement and becoming. For that
which stands will always stand, and that which sits will
always sit, since if it is sitting it will not get up ;for that
which,as
weare
told,cannot
get upwill be
incapableot
getting up. But we cannot say this, so that evidently
potency and actuality are different (but these views make
potency and actuality the same, and so it is no small thing
20 they are seeking to annihilate), so that it is possible that a
thing may be capable of being and not be, and capable ot
not being and yet be, and similarly with the other kinds of
predicate ; it may be capable of walking and yet not walk,
or capable of not walking and yet walk. And a thing is
capable of doing something if there will be nothing im-
25 possible in its having the actuality of that of which it is
said to have the capacity. I mean, for instance, if a thing is
capable of sitting and it is open to it to sit, there will be
nothing impossible in its actually sitting ;and similarly if
it is capable of being moved or moving, or of standing or
making to stand, or of being or coming to be, or of not
being or not coming to be.
30 The word actuality ,which we connect with complete
reality , has, in the main, been extended from movements to
other things ;for actuality in the strict sense is thought to
be identical with movement. And sopeople
do notassign
movement to non-existent things, though they do assign
some other predicates. E.g. they say that non-existent
things are objects of thought and desire, but not that they
35 are moved;and this because, while ex hypotkesi \hey do not
actually exist, they would have to exist actually if they
iO47b were moved. For of non-existent things some exist poten
tially ; but they do not exist^ because they do not exist in
complete reality.
It what we have describedlis identical with the capable or
,
convertible with it, evidently it cannot be true to say*
this
5 is capable of being but will not be \ which would imply that
the things z>/capableof being would on this showing vanish.
Suppose, for instance, that a man one who did not take
Cf. 1047*24-26.
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BOOK 0. 4 i047b
account of that which is incapable of being- were to say
that the diagonal of the square is capable of being1 measured
but will not be measured, because a thing may well be
capable
of
being
or
comingto be, and
yet
not be or be
about to be. But from the premisses this necessarily follows,
that if we actually supposed that which is not, but is cap- 10
able of being, to be or to have come to be, there will be
nothing impossible in this;
but the result will be im
possible, for the measuring of the diagonal is impossible.
For the false and the impossible are not the same;that you
are standing now is false, but that you should be standingis not impossible.
At the same time it is clear thatif,
when A is real, Bmust be real, then, when A is possible, B also must be 15
possible. For ifB need not be possible, there is nothing
to prevent its not being possible. Now let A be supposed
possible. Then, when A was possible, we agreed that
nothing impossible followed ifA were supposed to be real ;
and then B must of course be real. But we supposed B to 20
be impossible. Let it be impossible, then. If, then, B is
impossible, A also must be so. But the first was supposed
impossible ;therefore the second also is impossible. If,
then, A is possible, B also will be possible, if they were so
related that if A is real, B must be real. If, then, A and^
being thus related,1 B is not possible on this condition,
2 A 25
and B will not be related as was supposed.3 And if when
A is possible, B must be possible, then ifA is real, B also
must be real. For to say that B must be possible, ifA is
possible, means this, that ifA is real both at the time wrhen
and in the way in which it was supposed capable of being
real, Balso
mustthen
andin that
waybe real.
3o
5 As all potencies are either innate, like the senses, or come
by practice, like the power of playing the flute, or by learn
ing, like artistic power, those which come by practice or byrational formula we must acquire by previous exercise but
1Sc. so related that if the reality of A implies the reality of B the
possibility
of Aimplies
thepossibility
of B."
Sc. if A is possible.3
Sc. so related that the reality of A implies the reality of B.
N 2
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io47b METAPHYSICA
this is not necessary with those which are not of this nature
and which imply passivity.
35 Since that which is*
capable is capable of something and
iO48
aat
some time andin
someway (with all the other qualificationswhich must be present in the definition), and since some
things can produce change according to a rational formula
and their potencies involve such a formula, while other things
are non-rational and their potencies are non-rational, and
the former potencies must be in a living thing, while the
5 latter can be both in the living and in the lifeless;as regards
potencies of the latter kind, when the agent and the patient
meet in the way appropriate to the potency in question, the
one must act and the other be acted on, but with the former
kind of potency this is not necessary. For the non-rational
potencies are all productive of one effect each, but the
rational produce contrary effects, so that if they produced
their effects necessarily they would produce contrary effects
10 at the same time;but this is impossible. There must, then,
be something else that decides;
I mean by this, desire
or will. For whichever of two things the animal desires
decisively, it will do, when it is present, and meets the
passive object, in the way appropriate to the potency in
question. Therefore everything which has a rational
potency, when it desires that for which it has a potencyand in the circumstances in which it has the potency, must
5 do this. And it has the potency in question when the
passive object is present and is in a certain state;
if not it
will not be able to act. (To add the qualification if no
thing external prevents it is not further necessary ;for it has
the potency on the terms on which this is a potency of act
ing, and it is this not in all circumstances but on certain
conditions, among which will be the exclusion of external
20 hindrances;for these are barred by some of the positive
qualifications.)And so even if one has a rational wish, or an
appetite,to do two things or contrary things at the same time,
one will not do them;for it is not on these terms that one has
the
potencyfor them, nor is it a potency of doing both at
the same time, since one will do the things which it is a potency
of doing, on the terms on which one has the potency.
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BOOK 0. 6 1048*
6 Since we have treated 1 of the kind of potency which is 25
related to movement, let us discuss actuality what, and
what kind of thing, actuality is. For in the course of our
analysis it will also become clear, with regard to the poten
tial, that we not only ascribe potency to that whose nature
it is to move something else, or to be moved by something
else, either without qualification or in some particular way,
but also use the word in another sense, wrhich is the reason of
the inquiry in the course ofwhich we have discussed these pre- 3
vioussenses also.
Actuality, then,is the existence ofa
thingnot in the way which we express by potentially ;
we say that
potentially, for instance, a statue of Hermes is in the block of
wood and the half-line is in the whole, because it might be
separated out, and we call even the man \vho is not studying
a man of science, if he is capable of studying; the thing that
stands in contrast to each of these exists actually. Our mean- 35
ing can be seen in the particular cases by induction, and wemust not seek a definition of everything but be content to
grasp the analogy, that it is as that which is building is to that
which is capable of building, and the wr
aking to the sleep- 1048
ing, and that which is seeing to that which has its eyes
shut but has sight, and that which has been shaped out of
the matter to the matter, and that which has been wrought
up to the unwrought. Let actuality be defined by one
member of this antithesis, and the potential by the other. 5
But all things are not said in the same sense to exist
actually, but only by analogy as A is in B or to B, C is
in D or to D;for some are as movement to potency, and
the others as substance to some sort of matter.
But also the infinite and the void and all similar things
are said to exist potentially and actually in a different sense 10
from that which applies to many other things, e. g. to that
which sees or walks or is seen. For of the latter class these
predicates can at some time be also truly asserted without
qualification ;for the seen is so called sometimes because it
is being seen, sometimes because it is capable of being seen.
But the infinite
does notexist
potentiallyin the sense that
it will ever actually have separate existence;
it exists
1Cf. e. 1-5.
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io48b METAPHYSICA
15 potentially only for knowledge. For the fact that the pro
cess of dividing never comes to an end ensures that this
activity exists potentially, but not that the infinite exists
separately.
Since of the actions which have a limit none is an end but
all are relative to the end, e. g.the removing of fat, or fat-
20 removal, and the bodily parts themselves when one is
making them thin are in movement in this way (i. e. with
out being already that at which the movement aims), this is
not an action or at least not a complete one (for it is not
an end) ;but that movement in which the end is present is
an action. E.g. at the same time we are seeing and have
seen, are understanding and have understood, are thinking
and have thought (while it is not true that at the same time
we are learning and have learnt, or are being cured and
25 have been cured). At the same time we are living well
and have lived well, andare
happyand
havebeen
happy.If not, the process would have had sometime to cease, as
the process of making thin ceases : but, as things are, it
does not cease;we are living and have lived. Of these
processes, then, we must call the one set movements, and
the other actualities. For every movement is incomplete
making thin, learning, walking, building ;these are move-
so ments, and incomplete at that. For it is not true that
at the same time a thing is walking and has walked, or is
building and has built, or is coming to be and has come to
be, or is being moved and has been moved, but what is
being moved is different from what has been moved, and
what is moving from what has moved. But it is the same
thing that at the same time has seen and is seeing, or is
thinking and has thought. The latter sort of process, then,
I call an actuality, and the former a movement.
35 What, and what kind of thing, the actual is, may be
taken as explained by these and similar considerations.
But we must distinguish when a thing exists potentially and 7
whenit does not
;
for it is not at
anyand
everytime.
1049* E.g. is earth potentially a man ? No but rather when it
has already become seed, and perhaps not even then. It is
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BOOK 0. 7 1049*
just as it is with being healed ;not everything can be healed
by the medical art or by luck, but there is a certain kind of
thingwhich is capable of it, andonly this is potentiallyhealthy.
And (i)the delimiting mark of that which as a result of 5
thought comes to exist in complete reality from having
existed potentially is that if the agent has willed it it comes
to pass if nothing external hinders, while the condition on
the other side viz. in that which is healed is that nothing
in it hinders the result. It is on similar terms that we have
what is potentially a house;if nothing in the thing acted on
i. e. in the matter prevents it from becoming a house, and 10
if there is nothing which must be added or taken away or
changed, this is potentially a house;and the same is true
of all other things the source ofwhose becoming is external.
And(2)
in the cases in which the source of the becoming is
in the very thing which comes to be, a thing is potentially
allthose things which
it
will be of itself if nothing external hinders it. E. g. the seed is not yet potentially
a man;for it must be deposited in something other than
itself and undergo a change. But when through its own 15
motive principle it has already got such and such attributes,
in this state it is already potentially a man;while in the
former state it needs another motive principle, just as earth
is not yet potentially a statue (for it must first change in
order to become brass).1
It seems that when we call a thing not something else but
thaten e. g. a casket is not wood but wooden,and 20
wood is notl
earth but4
earthen,and again earth will illus
trate our point if it is similarly not something else but* thaten
that other thing is always potentially (inthe full sense of
that word) the thing which comes after it in this series.
E.g. a casket is not earthen nor earth,but wooden
;
for this is potentially a casket and this is the matter of a
casket, wood in general of a casket in general, and this par
ticular wood of this particular casket. And ifthere is a first
thing, which is no longer, in reference to something else,
1 The classes marked by (i) and (2) are the works of art and of
nature respectively, but at the end (2) is illustrated by an examplefrom (i).
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i049a METAPHYSICA
25 calledl
thaten,this is prime matter
; e.g. if earth is airy
and air is not4
fire butl
fiery ,fire is prime matter, which is
not a this . For the subject or substratum is differentiated
by being a this or not being one; i.e. the substratum of
modifications is, e.g.,
a man, i. e. a body and a soul, while the
30 modification is musical or pale . (The subject is called,
when musiccomes tobe present init, not music but musical
,
and the man is not(
paleness but4
pale ,and not ambula-
tion or movement but walking or*
moving ,which is
akin to the thaten.)
Wherever this is so, then, the ulti
mate subject is a substance ; but when this is not so but the
35 predicate is a form and a this,the ultimate subject is
matter and material substance. And it is only right that
6 thaten should be used with reference both to the matter
iO49band to the accidents
;for both are indeterminates. 1
We have stated, then, when a thing is to be said to exist
potentially and when it is not.
From our discussion of the various senses of*
prior ,
2it 8
5 is clear that actuality is prior to potency. And I mean by
potency not only that definite kind which is said to be
a principle of change in another thing or in the thing itself
regarded as other, but in general every principle of move
ment or of rest. For nature also is in the same genus as
10 potency ;for it is a principle of movement not, however,
in something else but in the thing itself gtia itself. To all
such potency, then, actuality is prior both in formula and
in substantiality; and in time it is prior in one sense, and
in another not.
(i) Clearlyit is
priorin formula
;for that which is in the
primary sense potential is potential because it is possible
1Aristotle points out that there are two kinds of derivative predi
cates those derived from the matter of thesubject,
like wooden,
and those formed from the accidents of the subject, like musical .
Matter and accidents have this in common, that they are indetermi
nate matter having (relatively) no character and accidents not being
confined to one special subject as essential predicates are. He mentions
at the same time that there are two kinds of substratum the bare
matter which underlies form or essence, and the complete individual
which underlies accidents. Cf. Z. iO38b
5.2
Cf. A. ii.
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BOOK 0. 8 io49b
for it to become active;
e. g. I mean by capable of build
ing that which can build, and by capable of seeing that 15
which can see, and by visible that which can be seen.
And the same account applies to all other cases, so that the
formula and the knowledge of the one must precede the
knowledge of the other.
(2)In time it is prior in this sense : the actual which is
identical in species though not in number with a potentially
existing thing is prior to it. I mean that to this particular man
who now exists
actually
and to the corn and to the
seeing20
subject the matter and the seed and that which is capable of
seeing, which are potentially a man and corn and seeing,
but not yet actually so, are prior in time;but prior in time
to these are other actually existing things, from which they
were produced. For from the potentially existing the
actually existing is always produced by an actually existing
thing, e. g. man from man, musician by musician ; there is 25
always a first mover, and the mover already exists actually.
We have said in our account of substance 1 that everything
that is produced is something produced from something
and by something, and that the same in species as it.
This is why it is thought impossible to be a builder if
one has built nothing or a harper if one has never played 3
the harp ; for he who learns to play the harp learns to play
it by playing it, and all other learners do similarly. Andthence arose the sophistical quibble, that one who does not
possess a science will be doing that which is the object of
the science;for he who is learning it does not possess it.
But since, of that which is coming to be, some part must 35
have come to be, and, of that which, in general, is chang
ing, some part must have changed (this is shown in the
treatise on movement 2
),he who is learning must, it would
seem, possess some part of the science. But here too, then,
it is clear that actuality is in this sense also, viz. in order of
generation and of time, prior to potency.
But (3)it is also prior in substantiality; firstly, (a] because
the
thingsthat are
posteriorin
becomingare
priorin form
and in substantiality (e. g. man is prior to boy and human 5
1Cf. Z. 7, 8.
2Cf. Phys. vi. 6.
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iosoa METAPHYSICA
being to seed;for the one already has its form, and the other
has not), and because everything that comes to be moves to
wards a principle, i. e. an end (for that for the sake of which
a thing is, is its principle, and the becoming is for the sakeof the end), and the actuality is the end, and it is for the
10 sake of this that the potency is acquired. For animals do
not see in order that they may have sight, but they have
sight that they may see. And similarly men have the art
of building that they may build, and theoretical science that
they may theorize;but they do not theorize that they may
have theoretical science, except those who are learning by
practice ;and these do not theorize except in a limited
15 sense, or because they have no need to theorize. Further,
matter exists in a potential state, just because it may come
to its form;and when it exists actually
r
,then it is in its
form. And the same holds good in all cases, even those in
which the end is a movement. And so, as teachers think
they have achieved their end when they have exhibited the
pupil at work, nature does likewise. For if this is not the
20 case, we shall have Pauson s Hermes over again, since it will
be hard to say about the knowledge, as about the figure in
the picture, whether it is within or without. 1 For the
action is the end, and the actuality is the action. And so
even the word4
actuality is derived from action , and
points to the complete reality.
And while in some cases the exercise is the ultimate
thing (e.g. in sight the ultimate thing is seeing, and no
25 other product besides this results from sight), but from
some things a product follows (e. g. from the art of build
ing there results a house as well as the act of building),
yet none the less the act is in the former case the end and
in the latter more of an end than the potency is. For the
act of building is realized in the thing that is being built, and
comes to be, and is, at the same time as the house.
30 Where, then, the result is something apart from the
exercise, the actuality is in the thing that is being made,
e.
g.
the act of
building
is in the
thing
that is
being
built
1 The reference is apparently to a tricky painting in which the
figure was painted so as to stand out in high relief.
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BOOK 0. 8 iosoa
and that of weaving in the thing that is being woven, and
similarly in all other cases, and in general the movement is
in the thing that is beingmoved ;butwherethere is noproduct
apart from the actuality, the actuality is present in the agents, 35
e. g. the act of seeing is in the seeing subject and that oftheo
rizing in the theorizing subject and the life is in the soul (and
therefore well-being also;for it is a certain kind of
life). iO5Ob
Obviously, therefore, the substance or form is actuality.1
According to this argument, then, it is obvious that actuality
is
priorin substantial
beingto
potency;and as we have
said,2 one actuality always precedes another in time right
back to the actuality of the eternal prime mover. 5
But (b) actuality is prior in a stricter sense also;for
eternal things are prior in substance to perishable things,
and no eternal thing exists potentially. The reason is this.
Every potency is at one and the same time a potency of the
opposite ; for, while that which is not capable of being
present in a subject cannot be present, everything that is 10
capable of being may possibly not be actual. That, then,
which is capable of being may either be or not be;the
same thing, then, is capable both of being and of not being.
And that which is capable of not being may possibly not
be;and that which may possibly not be is perishable,
either in the full sense, or in the precise sense in which it is
said that it possibly may not be, i.e. in respect either of 15
place or of quantity or quality ;in the full sense means
in respect of substance . Nothing, then, which is in the
full sense imperishable is in the full sense potentially existent
(though there is nothing to prevent its being so in some
respect, e. g. potentially of a certain quality or in a certain
place) ;all imperishable things, then, exist actually. Nor
can anything which is of necessity exist potentially; yet
these things are primary ;for if these did not exist, nothing
would exist. Nor does eternal movement, if there be such, 20
exist potentially ; and, if there is an eternal mobile, it is not
in motion in virtue of a potentiality, except in respect of4 whence and* whither
(thereis
nothingto
preventits
having
1This follows from the whole section a
4~b 2
;cf. esp.
a15, 16.
17-29.
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iosob METAPHYSICA
matter which makes it capable of movement in various
directions). And so the sun and the stars and the whole
heaven are ever active, and there is no fear that they may
sometime stand still, as the natural philosophers fear they
may.1 Nor do they tire in this activity ;
for movement is
25 not for them, as it is for perishable things, connected with
the potentiality for opposites, so that the continuity of
the movement should be laborious;for it is that kind of
substance which is matter and potency, not actuality, that
causes this.
Imperishable things2 are imitated by those that are in
volved in change, e. g. earth and fire. For these also are
ever active;for they have their movement of themselves
30 and in themselves.3 But the other potencies, according to
our previous discussion,4 are all potencies for opposites ;
for
that which can move another in this way can also move it
not in this
way,
i. e. if it acts
according
to a rational formula;
and the same non-rational potencies will produce opposite
results by their presence or absence.
35 If, then, there are any entities or substances such as the
dialecticians6
say the Ideas are, there must be something
much more scientific than science-itself and something more
1051* mobile than movement-itself;for these will be more of the
nature of actualities, while science-itself and movement-itself are potencies for these.
Obviously, then, actuality is prior both to potency and to
every principle of change.
That the actuality is also better and more valuable than 9
the good potency is evident from the following argument.5
Everythingof
which we saythat it
can do something,is
alike capable of contraries, e. g. that of which we say that it
can be well is the same as that which can beill, and has
1e. g. Empedocles (cf. De Caelo, 284* 24-6).
2Sc. the heavenly bodies.
3i.e. they are both movers and moved. 4
Cf. b 8-i2.5 The Platonists are meant; cf. A. 987
b3i.
6 The Idea, being the universal apart from its special manifestations,will be a potentiality, and will therefore be inferior to the correspond
ing particulars e. g. the Idea of science will be inferior to particularacts of scientific thought.
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BOOK 0. 9 iosia
both potencies at once;for the same potency is a potency
of health and illness, of rest and motion, of building and
throwing down, of being built and being thrown down.
The capacity for contraries, then, is present at the same 10
time;but contraries cannot be present at the same time, and
the actualities also cannot be present at the same time, e. g.
health and illness. Therefore, while the good must be one
of them, the capacity is both alike, or neither;the actuality,
then, is better. Also in the case of bad things the end or 15
actuality must be worse than the potency ;for that which
4 can is both contraries alike. Clearly, then, the bad does
not exist apart from bad things ;for the bad is in its nature
posterior to the potency.1 And therefore we may also say
that in the things which are from the beginning, i. e. in
eternal things, there is nothing bad, nothing defective, 2o
nothing perverted (for perversion is something bad).2
B D C
It is by an activity also that geometrical constructions3 are
discovered;for we find them by dividing. If the figures
had been already divided, the constructions would have been
obvious;
but as it is they are present only potentially.
1Sc. while the eternal and substantial must be better than the
potency.2 The paragraph seems to be directed against Plato
;cf. Rep. 402 C,
476 A, Theaet. i;6E, Laws 896 E, 8980.3 The figures required for the two theorems are as above.
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iosia METAPHYSICA
Why are the angles of the triangle equal to two right
angles ? Because the angles about one point are equal to two
25 right angles. If, then, the line parallel to the side had been
already drawn upwards,the reason would have been evident
to any one as soon as he saw the figure. Why is the angle
in a semicircle in all cases a right angle ? If three lines
are equal the two which form the base, and the perpen
dicular from the centre the conclusion is evident at a
glance to one who knows the former proposition. Obvi
ously, therefore, the potentially existing constructions are
30 discovered by being brought to actuality ; the reason is that
the geometer s thinking is an actuality ;so that the potency
proceeds from an actuality ;and therefore it is by making
constructions that people come to know them (though the
single actuality is later in generation than the corresponding
potency).
The terms being and non-being are employed firstly 10
35 with reference to the categories, and secondly with refer
ence to the potency or actuality of these or their non-
iO5ibpotency or non-actuality, and thirdly in the sense of true and
false. This depends, on the side of the objects, on their
being combined or separated, so that he who thinks the
separatedto
be separated and the combinedto be
combinedhas the truth, while he whose thought is in a state contrary
5 to that of the objects is in error. This being so, when is
what is called truth or falsity present, and when is it not ?
We must consider what we mean by these terms. It is not
because we think truly that you are pale, that you are pale,
but because you are pale we who say this have the truth.
If, then, some things are always combined and cannot be
10 separated, and others are always separated and cannot be
combined, while others are capable either of combination
or of vSeparation,4
being is being combined and one, and
not being is being not combined but more than one.
Regarding contingent facts, then, the same opinion or the
same statement comes to be false and true, and it is possible
15 for it to be at one time correct and at another erroneous;but
regarding things that cannot be otherwise opinions are not
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BOOK 0. 10 iosib
at one time true and at another false, but the same opinions
are always true or always false.
But with regard to incomposites^ what is being or not
being, and truth or falsity ?
A thing of this sort is not
composite, so as to* be when it is compounded, and not
to be if it is separated, like that the wood is white or 2o
1
that the diagonal is incommensurable;nor will truth and
falsity be still present in the same way as in the previous
cases. In fact, as truth is not the same in these cases, so
also being is not the same;but (a) truth or falsity is as
follows contact and assertion are truth (assertion not being
the same as affirmation), and ignorance is non-contact.25
For it is not possible to be in error regarding the question
what a thing is, save in an accidental sense;and the same
holds good regarding non-composite substances (forit is
not possible to be in error about them). And they all
exist
actually,
notpotentially
;for otherwise
theywould
have come to be and ceased to be; but, as it is, being itself
does not come to be (nor cease to be) ;for if it had done
so it would have had to come out of something. About 30
the things, then, which are essences and actualities, it is not
possible to be in error, but only to know them or not to
know them. But we do inquire what they are, viz. whether
they are of such and such a nature or not.
(b) As regards the*
being that answers to truth and the
non-being that answers to falsity, in one case there is truth
if the subject and the attribute are really combined, and
falsity if they are not combined;in the other case, if the 35
object is existent it exists in a particular way, and if it does
not exist in this way it does not exist at all.1 And truth io52
means knowing these objects, and falsity does not exist,
nor error, but only ignorance and not an ignorance which
is like blindness;for blindness is akin to a total absence of
the faculty of thinking.
It is evident also that about unchangeable things there
can be no error in respect of time, if we assume them to be
unchangeable. E. g. if we suppose that the triangle does
1i. e. we have not here A and B, which may or may not be com
bined, but A, which if it exists at all exists as A.
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i052a METAPHYSICA
not change, we shall not suppose that at one time its angles
are equal to two right angles while at another time they
are not (for that would imply change). It is possible, how
ever, to suppose that one member of such aclass
hasa certain attribute and another has not
;e. g. while wre
may suppose that no even number is prime, we may
suppose that some are and some are not. But regarding
a numerically single number not even this form of error is
10 possible ;for we cannot in this case suppose that one in
stance has an attribute and another has not, but whether
our judgement be true or false, it is implied that the fact is
eternal.
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BOOK I
I WE have said previously, in our distinction of the various 15
meanings of words,1that one has several meanings ;
the
things that are directly and of their own nature and not acci
dentally called one may be summarized under four heads,
though the word is used in more senses, (i) There is the
continuous, either in general, or especially that which is con
tinuous by nature and not by contact nor by being tied to
gether ;and of these, that has more unity and is prior, whose 20
movement 2is more indivisible and simpler. (2) That which
is a whole and has a certain shape and form is one in a still
higher degree;and
especiallyif a
thingis of this sort
bynature, and not by force like the things which are unified by
glue or nails or by being tied together, i. e. if it has in itself
the cause of its continuity. A thing is of this sort because its 25
movement is one and indivisible in place and time;so that
evidently if a thing has by nature a principle of movement
that is of the first kind(i.
e. local movement) and the first
in that kind (i. e. circular movement), this is in the primarysense one extended thing. Some things, then, are one in
this way, qua continuous or whole, and the other things that
are one are those whose definition is one. Of this sort are the 30
things the thought of which is one, i.e. those the thought of
which is indivisible;and it is indivisible if the thing is
indivisible in kind or in number. (3)In number, then, the
individual is indivisible, and (4) in kind, that which in
intelligibility and in knowledge is indivisible, so that that
which causes substances to be one 3 must be one in the
primary sense.l One \ then, has all these meanings the
naturally continuous and the whole, and the individual and 35
the universal. And all these are one because in some cases
1
A. 6.2Nature is defined (A. ioi5
ai3) as the essence of things which
have in themselves, as such, a source of movement .
8Sc. the form.
845-28 O
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i052a METAPHYSICA
the movement, in others the thought or the definition is
indivisible.
iO52b
But it must be observed that the questions, what sort of
things are said to be one, and what it is to be one and whatis the definition of it, should not be assumed to be the same.
4 One has all these meanings, and each of the things to
5 which one of these kinds of unity belongs will be one;but
4
to be one will sometimes mean being one of these
things, and sometimes being something elsel which is even
nearer to the meaning of the word one while these other
things approximate to its application. This is also true of
4
element or4
cause,if one had both to specify the things
of which it is predicable and to render the definition of the
10 word. For in a sense fire is an element (and doubtlessalso the
indefinite or something else of the sort is by its own nature
the element), but in a sense it is not;for it is not the same
thing
to be fire and to be an element, but while as a
particular thing with a nature of its own fire is an element, the
name 4
element means that it has this attribute, that there
is something which is made of it as a primary constituent.
15 And so with cause and one and all such terms. For
this reason, too,4
to be one means to be indivisible, being
essentially a"
this"
and capable of being isolated either in
place, or in form or thought ; or perhaps*
to be wholeand indivisible
;but it means especially to be the first
measure of a kind,and most strictly of quantity ;
for it is
from this that it has been extended to the other categories.
20 For measure is that by which quantity is knowrn;
and
quantity qua quantity is known either by a one or by
a number, and all number is known by a one . There
fore all quantity qua quantity is known by the one, and
that by which quantities are primarily known is the one it
self; and so the one is the starting-point of number qua
number. And hence in the other classes too measure
25 means that by which each is first known, and the measure
of each is a unit in length, in breadth, in depth, in weight,
in
speed. (Thewords 4
weightand 4
speed
are common
to both contraries2
;for each of them has two meanings
1Cf. I052
b16-19.
2Sc. heavy and light, fast and slow.
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BOOK I. i 1052
weight means both that which has any amount ofgravity
and that which has an excess ofgravity, and speed both
that which has any amount of movement and that which
has an excess of movement;
for even the slow has a 30
certain speed and the comparatively light a certain
weight.)
In all these, then, the measure and starting-point is some
thing one and indivisible, since even in lines we treat as
indivisible the line a foot long. For everywhere we seek
as the measuresomething
one and indivisible;and this is
that which is simple either in quality or in quantity. Now 35
where it is thought impossible to take away or to add,
there the measure is exact (hence that of number is
most exact;for we posit the unit as indivisible in every iO53
a
respect) ;but in all other cases we imitate this sort of
measure. For in the case of a furlong or a talent or of
anything comparatively large any addition or subtraction
might more easily escape our notice than in the case of
something smaller;so that the first thing from which, as 5
far as our perception goes, nothing can be subtracted, all
men make the measure, whether of liquids or of solids,
whether of weight or of size;and they think they know
the quantity when they know it by means of this measure.
And indeed they know movement too by the simple move
ment and the quickest ;for this occupies least time. And 10
so in astronomy a one of this sort is the starting-point
and measure(for they assume the movement of the heavens
to be uniform and the quickest, and judge the others by
reference toit),
and in music the quarter-tone (because it is
the least interval), and in
speech
the letter. And all these
are ones in this sense not that one is something predic-
able in the same sense of all of these, but in the sense we
have mentioned.
But the measure is not always one in number some
times there are several; e.g. the quarter-tones (not to the [5
ear, but as determined by the ratios) are two, and the articu
late
sounds by which we measure are more than one, andthe diagonal of the square and its side are measured by two
quantities, and all spatial magnitudes reveal similar varieties
O 2
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io53a METAPHYSICA
of unit.1
Thus, then, the one is the measure of all things,
because we come to know the elements in the substance by
dividing the things either in respect of quantity or in
20 respect of kind. And the one is indivisible just because
the first of each class of things is indivisible. But it is not
in the same way that every one is indivisible, e. g. a foot
and a unit;
the latter is indivisible in every respect,
while the former must be placed among things which are
undivided to perception, as has been said already2
only to
perception, for doubtless every continuous thing is divisible.
The measure is always homogeneous with the thing
25 measured;the measure of spatial magnitudes is a spatial
magnitude, and in particular that of length is a length, that
of breadth a breadth, that of articulate sound an articulate
sound, that of weight a weight, that of units a unit. (For
we must state the matter so, and not say that the measure
of numbersis
a number;
we ought indeed to saythis if
wewere to use the corresponding form of words, but the
claim does not really correspond it is as if one claimed
30 that the measure of units is units, and not a unit;number
is a plurality of units.}
Knowledge, also, and perception, we call the measure of
things for the same reason, because we come to know some
thing by them while as a matter of fact they are measured
rather than measure other things. But it is with us as ifsome
one else measured us and we came to knowhow big we are by
seeing that he applied the cubit-measure to such and such
35 a fraction of us. But Protagoras says man is the measure
of all things ,
3as if he had said the man who knows or
IO53
b l
t^e man w^ perceives ;and these because they have
respectively knowledge and perception, which we say are
the measures of objects. Such thinkers are saying nothing,
then, while they appear to be saying something remark
able.
1 Alexander thinks this means that a line may be measured either
by the ideal measure (e. g. the standard yard) or by the particular
imperfect measure (the yard-wand, which slightly differs from the
standard yard). This sense does not agree with the context, andno doubt the meaning is that incommensurables must be measured by
different units.2
Cf. I052b33, io53
a5.
3Fr. I.
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BOOK I. i io53b
Evidently, then, unity in the strictest sense, if we define
it according to the meaning of the word, is a measure, and 5
most properly of quantity, and secondly of quality. And
some things will be one if they are indivisible in quantity,
and others if they are indivisible in quality ;and so that
which is one is indivisible, either absolutely or qiia one.
2 With regard to the substance and nature of the one we
must ask in which of two ways it exists. This is the very 10
question that we reviewedJin our discussion of problems,
viz. what the one is and how we must conceive of it, whetherwe must take the one itself as being a substance (as both
the Pythagoreans say in earlier and Plato in later times), or
there is, rather, an underlying nature and the one should
be described more intelligibly and more in the manner of
the physical philosophers, of whom one says the one is love, 15
another says it is air, and another the indefinite.2
If, then, no universal can be a substance, as has been said 3
in our discussion of substance and being, and if being itself
cannot be a substance in the sense of a one apart from the
many (for it is common to the many), but is only a predi
cate, clearly unity also cannot be a substance;for being 20
and unity are the most universal of all predicates. There
fore, on the onehand, genera
are not certain entities and
substances separable from other things ;and on the other
hand the one cannot be a genus, for the same reasons for
which being and substance cannot be ge era.
Further, the position must be similar in all the kinds ot
unity. Now unity has just as many meanings as being ;
so that since in the sphere of qualities the one is something 25
definite some particular kind of thing and similarly in the
sphere of quantities, clearly we must in every category ask
what the one is, as we must ask what the existent is, since
it is not enough to say that its nature is just to be one or
existent. But in colours the one is a colour, e. g. white,
and then the other colours are observed to be produced out
1B.
iooi
a
4-
b
25.2 The three thinkers referred to are Empedocles, Anaximenes,Anaximander.
3Z. 13.
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io53b METAPHYSICA
30 of this and black, and black is the privation of white, as
darkness of light.Therefore if all existent things were
colours, existent things would have been a number, indeed,
but of what ? Clearly of colours ;
and the one wouldhave been a particular one
,i. e. white. And similarly if
all existing things were tunes, they would have been a
35 number, but a number of quarter-tones, and their essence
would not have been number;and the one would have
been something whose substance was not to be one but to
iO54abe the quarter-tone. And similarly if all existent things
had been articulate sounds, they would have been a number
of letters, and the one would have been a vowel. And if
all existent things were rectilinear figures, they would have
been a number of figures, and the one would have been the
triangle. And the same argument applies to all other
5 classes. Since, therefore, while there are numbers and a
one both in affections and in
qualities
and in
quantities
and
in movement, in all cases the number is a number of
particular things and the one is one something, and its sub
stance is not just to be one, the same must be true of
substances also;for it is true of all cases alike.
10 That the one, then, in every class is a definite thing, and
in no case is its nature just this, unity, is evident;but as in
colours the one-itself which we must seek is one colour, so
too in substance the one-itself is one substance. That in a
sense unity means the same as being is clear from the facts
that its meanings correspond to the categories one to one,
15and it is not comprised within any category (e. g. it is
comprised neither in what a thing is nor in quality, but
is related to them just as being is) ;that in one man
nothing more is predicated than in man (just as being is
nothing apart from substance or quality or quantity) ;and
that to be one is just to be a particular thing.
20 The one and the many are opposed in several ways, of 3
which one is the opposition of the one and plurality as
indivisible and divisible ; for that which is either divided or
divisible is called a plurality, and that which is indivisible
or not divided is called one. Now since opposition is of
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BOOK I. 3 io54a
four kinds, and one of these two terms is privative in mean
ing, they must be contraries, and neither contradictory nor 25
correlative in meaning.1 And the one derives its name and
its explanation from its contrary, the indivisible from the
divisible, because plurality and the divisible is more per
ceptible than the indivisible, so that in definition plurality is
prior to the indivisible, because of the conditions of percep
tion.
To the one belong, as we indicated graphically in our 30
distinction of the contraries,2 the same and the like and the
equal, and to plurality belong the other and the unlike and
the unequal.* The same has several meanings ; (i) we
sometimes mean the same numerically ; again, (2) we call
a thing the same if it is one both in definition and in num
ber, e. g. you are one with yourself both in form and in
matter;and again, (3)
if the definition of its primary 35
essence is one;
e.
g. equal straightlines are the
same,and
iO54
b
so are equal and equal-angled quadrilaterals ;there are
many such, but in these equality constitutes unity.
Things are like if, not being absolutely the same, nor
without difference in respect of their concrete substance, they
are the same in form; e.g. the larger square is like the smaller, 5
and unequal straight lines are like; they are like, but not
absolutely the same. Other things are like, if, having the
same form, and being things in which difference of degree
is possible, they have no difference of degree. Other things,
if they have a quality that is in form one and the same
e. g. whiteness in a greater or less degree, are called like i
because their form is one. Other things are called like if
the qualities they have in common are more numerous than
those in which they differ either the qualities in general or
the prominent qualities ;e. g. tin is like silver, qua white,
and gold is like fire, qua yellow and red.
Evidently, then, other and unlike also have several
meanings. And the other in one sense is the opposite of
the same (so that everything is either the same as or other 15
1 Two of the kinds, contrariety and privation, are not mutually ex
clusive, for contrariety is the relation between a form and its complete
privation. Cf. r. ioo4b2;, I. io55
b 26.2
Cf. r. ioo4a2.
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io54b METAPHYSICA
than everything else). In another sense things are other
unless both their matter and their definition are one (so that
you are other than your neighbour). The other in the third
sense is
exemplified
in the
objects
of mathematics.1 Other
or the same can therefore be predicated ofeverything with
regard to everything else but only ifthe things are one and
existent, for other is not the contradictory of*
the same;
20 which is why it is not predicated of non-existent things
(while not the same is so predicated). It is predicated
of all existing things ;for everything that is existent and
one is by its very nature either one or not one with
anything else.
The other, then, and the same are thus opposed. But
difference is not the same as otherness. For the other and
that which it is other than need not be other in some
definite respect (for everything that is existent is either
25 other or the same), but that which is different is different
from some particular thing in some particular respect, so
that there must be something identical whereby they differ.
And this identical thing is genus or species ;for everything
that differs differs either in genus or in species,2in genus if
the things have not their matter in common and are not
generated out of each other (i.e. if they belong to different
figuresof
predication),
3 and inspecies
if
theyhave the same
3o genus ( genus meaning that identical thing which is essen
tially predicated of both the different things).
Contraries are different, and contrariety is a kind of differ
ence. That we are right in this supposition is shown byinduction. For all of these too are seen to be different
;
35 they are not merely other, but some are other in genus,
iO55a
and others are in the same line of predication,3
and there
fore in the same genus, and the same in genus. We have
distinguished4elsewhere what sort of things are the same or
other in genus.
Since things which differ may differ from one another 4
more or less, there is also a greatest difference, and this
1Cf.
a35-
b3.
2See note on io5;
b36.
8 See note on A. 986*23.*
A. 9.
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BOOK 1. 4 io55a
I call contrariety. That contrariety is the greatest differ- 5
ence is made clear by induction. For things which differ
in genus have no way to one another, but are too far
distant and are not comparable ; and for things that differ
in species the extremes from which generation takes place
are the contraries, and the distance between extremes and
therefore that between the contraries is the greatest.
But surely that which is greatest in each class is complete. 10
For that is greatest which cannot be exceeded, and that is
complete beyond which nothing can be found. For the com
plete difference marks the end of a series (just as the other
things which are called complete are so called because they
have attained an end), and beyond the end there is nothing ;
for in everything it is the extreme and includes ajl else, and 15
therefore there is nothing beyond the end, and the complete
needs nothing further. From this, then, it is clear that con
trarietyis
completedifference
;
and as contraries are so
called in several senses, their modes of completeness will
answer to the various modes of contrariety which attach to
the contraries.
This being so, it is clear that one thing cannot have
more than one contrary (for neither can there be anything 20
more extreme than the extreme, nor can there be more
than two extremes for the one interval), and, to put the
matter generally, this is clear if contrariety is a difference
and if difference, and therefore also the complete differ
ence, must be between two things.
And the other commonly accepted definitions of con
traries are also necessarily true. For not only is (i) the
complete difference the greatest difference (for we can get 25
no difference beyond it of things differing either in genusor in species ;
for it has been shown Tthat there is no
difference between anything and the things outside its
genus, and among the things which differ in species the
complete difference is the greatest) ;but also (2) the things
in the same genus which differ most are contrary (for the
complete
difference is thegreatest
difference betweenspecies
of the same genus) ;and (3) the things in the same receptive
1Cf. a
6. But how can we reconcile this with io54b27-30, 35 ?
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i055a METAPHYSICA
30 material which differ most are contrary (for the matter is
the same for contraries) : and (4) of the things which fall
under the same faculty the most different are contrary (for
onescience deals with one class of
things, and in these the
complete difference is the greatest).1
The primary contrariety is that between positive state
and privation not every privation, however (for priva
tion has several meanings), but that which is complete.
35 And the other contraries must be called so with reference
to these, some because they possess these, others because
they produce or tend to produce them, others because they
are acquisitions or losses of these or of other contraries.
Now if the kinds of opposition are contradiction and priva-
iO55btion and contrariety and relation, and of these the first is
contradiction, and contradiction admits of no intermediate,
while contraries admit of one, clearly contradiction and
contrariety are not the same. But privation is a kind of
contradiction ; for what suffers privation, either in general
or in some determinate way, is either that which is quite
5 incapable of having some attribute or that which, being of
such a nature as to have it, has it not;
here we have
already a variety of meanings, which have been distin
guished2 elsewhere. Privation, therefore, is a contradiction
or incapacity whichis
determinate or taken along with the
receptive material. This is the reason why, while contra
diction does not admit of an intermediate, privation some-
10 times does;
for everything is equal or not equal, but not
everything is equal or unequal, or if it is, it is only within
the sphere of that which is receptive of equality. If, then,
the comings-to-be which happen to the matter start from
the contraries, and proceed either from the form and the
possession of the form or from a privation of the form or
shape, clearly all contrariety must be privation, but presum-
15 ably not all privation is contrariety (the reason being that
that which has suffered privation may have suffered it in
several ways) ;for it is only the extremes from which
changes proceed that are contraries.
And this is obvious also by induction. For every con-
1
Punctuating in 11. 32-3 p.ia, Iv . . . /neyiVr^).2A. 22.
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BOOK I. 4 io55b
trariety involves, as one of its terms, a privation, but not
all cases are alike; inequality is the privation of equality
and unlikeness of likeness, and on the other hand vice is the
privation of virtue. But the cases differ in a way already 20
described;
1in one case we mean simply that the thing has
suffered privation, in another case that it has done so either
at a certain time or in a certain part (e. g. at a certain age or
in the dominant part), or throughout. This is why in some
cases there is a mean (there are men who are neither good
nor bad), and in others there is not (a number must be either
odd or even). Further, some contraries have their subject 25
defined, others have not. Therefore it is evident that one
of the contraries is always privative ;but it is enough if this
is true of the first i. e. the generic contraries, e. g. the
one and the many ;for the others can be reduced to these.
5 Since one thing has one contrary, we might raise the 30
question how the one is opposed to the many, and the
equal to the great and the small. For if we use the word4 whether only in an antithesis such as whether it is white
or black,or whether it is white or not white (we do not
ask whether it is a man or white),
unless we are pro
ceeding on a prior assumption and asking something such 35
aswhether
it
was Cleon or Socrates that came butthis is not a necessary disjunction in any class of things ;
yet even this is an extension from the case of opposites ;for
opposites alone cannot be present together ;and we assume
this incompatibility here too in asking which of the two
came;
for if they might both have come, the question iO56a
would have been absurd;but if they might, even so this
falls just as much into an antithesis, that of the one or
many ,i. e. whether both came or one of the two : if,
then, the question whether is always concerned with
opposites, and we can ask whether it is greater or less or
equal ,what is the opposition of the equal to the other 5
two ? It is not contrary either to one alone or to both;for
why should it be contrary to the greater rather than to the
less ? Further, the equal is contrary to the uneqiiaL There-
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io56a METAPHYSICA
fore if it is contrary to the greater and the less, it will be
contrary to more things than one. But if the unequal means
the same as both the greater and the less together, the equal
10 will beopposite
to both(and
thedifficulty supports
those
who say the unequal is a two 1
),but it follows that one
thing is contrary to two others, which is impossible. Again,
the equal is evidently intermediate between the great and
the small, but no contrariety is either observed to be inter
mediate, or, from its definition, can be so;for it would not
be complete2if it were intermediate between any two things,
but rather it always has something intermediate between its
own terms.
J 5 It remains, then, that it is opposed either as negation or
as privation. It cannot be the negation or privation of one
of the two;for why of the great rather than of the small ?
It is, then, the privative negation of both. This is whywhether is said with reference to both, not to one of the
two (e. g. whether it is greater or equal or whether it is
20equal or less
) ;there are always three cases. But it is not
a necessary privation ;for not everything which is not
greater or less is equal, but only the things which are of
such a nature as to have these attributes.
The equal, then, is that which is neither great nor small
but is
naturallyfitted to be either
greator small
;and it is
opposed to both as a privative negation (and therefore is
also intermediate). And that which is neither good nor
2 5 bad is opposed to both, but has no name;for each of these
has several meanings and the recipient subject is not one;
but that which is neither white nor black has more claim to
unity. Yet even this has not one name, though the colours
of which this negation is privatively predicated are in a waylimited
;for they must be either grey or yellow or some-
3 thing else of the kind. Therefore it is an incorrect criticism
that is passed by those who think that all such phrases are
used in the same way, so that that which is neither a shoe
nor a hand would be intermediate between a shoe and
a hand, since that which is neither good nor bad is inter
mediate between the good and the bad as if there must
1This is a Platonic doctrine
;cf. N. io8;
b7.
2Cf. 1055* 16.
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BOOK I. 5 ios6a
be an intermediate in all cases. But this does not necessarily
follow. For the one phrase is a joint denial of opposites 35
between which there is an intermediate and a certain natural
interval;but between the other two there is no differ- ios6
b
ence l
;for the things, the denials of which are combined,
belong to different classes, so that the substratum is not one.
6 We might raise similar questions about the one and the
many. For if the many are absolutely opposed to the one,
certain impossible results follow. One will then be few 2,5
whether few be treated here as singular or plural ;for the
many are opposed also to the few. Further, two will be
many, since the double is multiple and double derives its
meaning from * two;therefore one will be few
;for what
is that in comparison with which two are many, except
one, which must therefore be few ? For there is nothing
fewer.
Further,
if the much and the little are in
plurality
10
what the long and the short are in length, and whatever is
much is also many, and the many are much (unless, indeed,
there is a difference in the case of an easily-bounded con
tinuum),3 the little (or few) will be a plurality. Therefore
one is a plurality if it is few; and this it must be, if two are
many. But perhaps, while the many are in a sense said
to be also
4
much, it is with a difference ; e. g. water is much 15
but not many. But *
many is applied to the things that
are divisible;in one sense it means a plurality which is
excessive either absolutely or relatively (while few is
similarly a plurality which is deficient), and in another
sense it means number, in which sense alone it is opposed
to the one. For we say*
one or many , just as if one were 20
to say4
one and ones or white thing and white things ,
or to compare the things that have been measured with the
measure. It is in this sense also that multiples are so called.
1Cf. 105 s
a6, 2.6.
2 The Greek is o\iyov 77 oX/ya, which, it might seem, should be trans
lated a little or a few . But the singular oXiyov is used only because
of the difficulty of predicating the plural oX/-ya of one . On the other
hand, TTO\V and rroXXa are used in the really distinct senses of muchand many . oXiyov has been translated few in this chapter exceptwhere it is opposed to TTO\V and must be translated
*
little .
3i. e. a fluid. Cf. 1. 16.
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ios6b METAPHYSICA
For each number is said to be many because it consists of
ones and because each number is measurable by one;and
it is many as that which is opposed to one, not to the few.
25 In thissense, then,
even two is
many not, however,in the
sense of a plurality which is excessive either relatively or
absolutely ;it is the first plurality. But without qualifi
cation two is few;
for it is the first plurality which is
deficient (for this reason Anaxagoras was not right in
leaving the subject with the statement 1 that all things
were together, boundless both in plurality and in smallness
3 where for*
and in smallness he should have said and in
fewness;for they could not have been boundless in few
ness), since it is not one, as some say, but two, that make
a few.
The one is opposed then to the many in numbers as
measure to thing measurable;and these are opposed as
are the relatives which are not from their very nature
relatives. We have distinguished2 elsewhere the two senses
35 in which relatives are so called: (i) as contraries; (2)
as
knowledge to thing known, a term being called relative
because another is relative to it. There is nothing to
prevent one from being fewer than something, e. g. than
two;for if is few
T
er, it is not therefore few. Plurality is as
it were the class to which number belongs;
for numberis
plurality measurable by one, and one and number are in
a sense opposed, not as contrary, but as we have said some
5 relative terms are opposed ;for inasmuch as one is measure
and the other measurable, they are opposed. This is whynot everything that is one is a number
;i. e. if the thing is
indivisible it is not a number. But though knowledge is
similarly spoken of as relative to the knowable, the relation
does not work out similarly ;for while knowledge might
be thought to be the measure, and the knowable the thing
10 measured, the fact is that all knowledge is knowable, but not
all that is knowable is knowledge, because in a sense know
ledge is measured by the knowable. Plurality is contrary
neither to the few (the many being contrary to this as
excessive plurality to plurality exceeded), nor to the one in
1Fr. i.
2A. 1021*26-30.
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BOOK I. 6 ios7a
every sense; but in one sense these are contrary, as has
been said, because the former is divisible and the latter
indivisible, while in another sense they are relative as 15
knowledge is to knowable, if plurality is number and the
one is a measure.
7 Since contraries admit of an intermediate and in some
cases have it, intermediates must be composed of the con
traries. For (i) all intermediates are in the same genus as ao
thethings
between whichthey
stand. For we call those
things intermediates, into which that which changes must
change first;e. g. if we were to pass from the highest string
to the lowest by the smallest intervals, we should come
sooner to the intermediate notes, and in colours if we were
to pass from white to black, we should come sooner to 35
crimson and grey than to black;and similarly in all other
cases. But to change from one genus to another genus is
not possible except in an incidental way, as from colour to
figure. Intermediates, then, must be in the same genus both
as one another and as the things they stand between.
But (2) all intermediates stand between opposites of some 30
kind;
for only between these can change take place in
virtue of their own nature (so that an intermediate is im
possible between things which are not opposite ;for then
there would be change which was not from one opposite
towards the other). Of opposites, contradictories admit of
no middle term;
for this is what contradiction is an 35
opposition, one or other side of which must attach to any
thing whatever, i. e. which has no intermediate. Of other
opposites, some are relative, others privative, others con
trary. Of relative terms, those which are not contrary have
no intermediate;the reason is that they are not in the same
genus. For what intermediate could there be between
knowledge and knowable ? But between great and small io57b
there zs one.
(3) If intermediates are in the same genus, as has been
shown, andstand
between contraries, they mustbe
composed of these contraries. For either there will be a genus
including the contraries or there will be none. And if(a)
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io57b METAPHYSICA
there is to be a genus in such a way that it is something
5 prior to the contraries, the differentiae which constituted
the contrary species-of-a-genus will be contraries prior to
the species ; for species are composed of the genus and thedifferentiae. (E. g. if white and black are contraries, and
one is a piercing colour and the other a compressing
colour,1these differentiae piercing and compressing
10 are prior ;so that these are prior contraries of one an
other.) But, again, the species which differ contrarywise are
the more truly contrary species.2 And the other species,
i. e. the intermediates, must be composed of their genus and
their differentiae. (E. g. all colours which are between white
and black must be said to be composed of the genus, i. e.
15 colour, and certain differentiae. But these differentiae will
not be the primary contraries; otherwise every colour
would be either white or black. They are different, then,
from the primary contraries;and therefore they will be
between the primary contraries;the primary differentiae
are piercing and compressing .)
Therefore it is(d)
with regard to these contraries which
do not fall within a genus that we must first ask of what
20 their intermediates are composed. (For things which are
in the same genus must be composed of terms in which the
genus is not an element, or else be themselves incomposite.
3
)
Now contraries do not involve one another in their com
position, and are therefore first principles ;but the inter
mediates are either all incomposite, or none of them. But
there is something compounded out of the contraries, so that
there can be a change from a contrary to it sooner than to
25 the other contrary ;for it will have less of the quality in
1Cf. PI. Tim. 67 E ff.
8I now make the parenthesis end at Trportpa (1. n) and treat aXXa
fjtrjvas beginning a new argument.
8Aristotle has first (ei /xV, 1. 4) considered the case of contraries in
a genus, and shown that they involve prior contraries which are not
in the genus, but when added to the genus constitute its species. These
are the primary contraries, and it is primarily of them that we must
ask, Of what are their intermediates composed? The sentence,
11. 20-22, in which he reverts to contraries in a genus must be paren
thetical. A species in a genus must either contain an element (sc. the
differentia) which does not itself contain the genus, or (which is incom
patible with its being a species) be an unanalysable term.
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BOOK I. 7 i057b
question than the one contrary and more than the other.
This also,1then, will come between the contraries. All the
other intermediates also, therefore, are composite \for that
which has more of a quality than one thing and less than
another is compounded somehow out of the things than
which it is said to have more and less respectively of the
quality. And since there are no other things prior to the
contraries and homogeneous with the intermediates, all 30
intermediates must be compounded out of the contraries.
Therefore also all the inferior classes, both the contraries
and their intermediates, will be compounded out of the
primary contraries.2
Clearly, then, intermediates are (i)
all in the same genus and (2) intermediate between con
traries, and (3) all compounded out of the contraries.
8 That which is other in species is other than something 35
in something, and this must belong to both 3
;e. g. if it is
an animal other in species, both are animals. The things,
then, which are other in species must be in the same genus.
For by genus I mean that one identical thing which is
predicated of both and is differentiated in no merely acci
dental way, whether conceived as matter or otherwise. iO58a
For not only must the common nature attach to the differ
ent things, e. g. not only must both be animals, but this
very animality must also be different for each (e. g. in the
one case equinity, in the other humanity), and so this
common nature is specifically different for each from what it
1i. e. this intermediate differentia comes between the extreme
differentiae, as the intermediate species comes between the extreme
species.2 This seems to mean that each extreme as well as each intermediate
species is compounded out of both the extreme differentiae. E. g. white
would have to be to some extent compressing as well as piercing .
But this is not in itself a likely doctrine, and it can hardly be said to be
proved in the present passage ;the meaning probably is that each
extreme species contains one differentia as a logical element, the other
element being the genus ;while each intermediate contains both the
differentiae.3
It might seem that the respect in which things differ is just whatdoes not belong to both. But Aristotle s meaning is this : If A differs
from>,
it must be a different something, and this something is the
genuscommon to both. Horse and man are different animals. And
when two things differ in their essence, they differ just in that in which
(in another sense of in) they agree. Difference in a genus makes
the genus itself other(ic>58
a7-8). Cf. io54
b25-28.
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ios8a METAPHYSICA
5 is for the other. One, then, will be in virtue of its own
nature one sort of animal, and the other another, e. g. one
a horse and the other a man. This difference, then, must
be an otherness of the genus. For I give the name of
1
difference in the genus to an otherness which makes the
genus itself other.
This, then, will be a contrariety (as can be shown also by10 induction). For all things are divided by opposites, and it
has been proved that contraries are in the same genus1
.
For contrariety was seen 2to be complete difference
;and
all difference in species is a difference from somethingin something ;
so that this is the same for both and is their
genus. (Hence also all contraries which are different in
species and not in genus are in the same line of predica-
IKk tion,3 and other than one another in the highest degree
for the difference is complete ,and cannot be present
along with one another.) The difference, then, is a con
trariety.
This, then, is what it is to be *
other in species to have
a contrariety, being in the same genus and being indivis
ible4(and those things are the same in species which have
no contrariety, being indivisible5
); we say being indi
visible,for in the process of division contrarieties arise
20 even in the intermediate stages before we come to the
indivisibles.4
Evidently, therefore, with reference to that
which is called the genus, none of the species-of-a-genus
is either the same as it or other than it in species (and
this is fitting ;for the matter is indicated by negation,
6 and
the genus is the matter of that of which it is called the
genus, not in the sense in which we speak of the genus or
family of the Heraclidae, but in that in which the genus is
an element in a thing s nature 7
),nor is it so with reference
25to things which are not in the same genus, but it will differ
in genus from them, and in species from things in the same
1
Ch. 4.
2
io55ai6.
3Cf. I054
b35 and note on A. 986* 23.
4Sc. individuals or infimae species.
5
Sc. individuals.6
i. e. by eliminating the form which characterizes the concrete thing.7
Cf. A. io24a3i-6,
b4-6.
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BOOK I. 8 ios8a
genus. For a thing s difference from that from which it
differs in species must be a contrariety ;and this belongs
only to things in the same genus.
g One might raise the question, why woman does not differ
from man in species, when female and male are contrary and 3
their difference is a contrariety ;and why a female and
a male animal are not different in species, though this
difference belongs to animal in virtue of its own nature,
and not as paleness or darkness does;both female and
male belong to it qua animal. This question is almostthe same as the other, why one contrariety makes things
different in species and another does not, e. g. with feet 35
and with wings do, but paleness and darkness do not.
Perhaps it is because the former are modifications peculiar
to the genus, and the latter are less so. And since one
element is definition and one is matter, contrarieties which io58b
are in the definition make a difference in species, but those
which are in the thing taken as including its matter do not
make one. And so paleness in a man, or darkness, does
not make one, nor is there a difference in species between
the pale man and the dark man, not even if each of them
be denoted by one word. For man is here being con- 5
sidered on his material side, and matter does not create
a difference;for it does not make individual men species
of man, though the flesh and the bones of which this man
and that man consist are other. The concrete thing is
other, but not other in species, because in the definition
there is no contrariety. This lis the ultimate indivisible
kind. Callias is definition + matter;the pale man, then, is 10
soalso, because
it is theindividual
Callias that is
pale;
man, then, is pale only incidentally. Neither do a brazen
and a wooden circle, then, differ in species ;and if a brazen
triangle and a wooden circle differ in species, it is not
because of the matter, but because there is a contrariety in
the definition. But does the matter not make things other I5
in species, when it is other in a certain way, or is there
a sense in which it does ? For why is this horse other than
1i. e. that in whose definition no contrarieties are included.
P 2
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io58b METAPHYSICA
this man in species, although their matter is included with
their definitions ? Doubtless because there is a contrariety
in the definition. For while there is a contrariety also
betweenpale
man and darkhorse,
and it is acontrariety
in
30species, it does not depend on the paleness of the one and
the darkness of the other, since even if both had been pale,
yet they would have been other in species. But male and
female, while they are modifications peculiar to4
animal,
are so not in virtue pf its essence but in the matter, i. e. the
body. This is why the same seed becomes female or male
by being acted on in a certain way. We have stated, then,
25 what it is to be other in species, and why some things differ
in species and others do not.
Since contraries are other in form, and the perishable 10
and the imperishable are contraries (for privation is a deter
minate incapacity), the perishable and the imperishable
must be differentin
kind.
1
Now so far we have spoken of the general terms them-
3o selves, so that it might be thought not to be necessary that
every imperishable thing should be different from every
perishable thing in form, just as not every pale thing is
different in form from every dark thing. For the same
thing can be both, and even at the same time if it is
a universal (e. g. man can be both pale and dark), and if it
is an individual it can still be both;for the same man can
35 be, though not at the same time, pale and dark. Yet pale
is contrary to dark.
But while some contraries belong to certain things by
accident (e. g. both those now mentioned and many
others), others cannot, and among these are perishable and
1 To translate ytvos and ei<W as genus and species makes non
sense of the argument of this chapter. They have therefore been
rendered kind and form . The only trace of the technical distinc
tion is found in the last sentence of the chapter, and there it is not
justified by what precedes. It looks as if the first part of the chapterhad been written before the distinction was drawn, and io59
a10-14
(or perhaps only 1. 14) added under the supposition that a genericdifference between the perishable and the imperishable had been
proved. For the absence of distinction between yews and fl&os cf. A.
1071*25 with 27, Cat. 8b 27 with 9a
14, Hist. An. i. 49Ob 16 with 17,
Pol. iv. 1290^33 with 36. To read eifift in io5&b 28 is useless in view
of 1059* 10-14.
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BOOK I. 10 io59a
imperishable . For nothing is by accident perishable. For 1059**
what is accidental is capable of not being present, but
perishableness is one of the attributes that belong of neces
sity to the things to which they belong ; or else one and
the same thing may be perishable and imperishable, if 5
perishableness is capable of not belonging to it. Perishable-
ness then must either be the essence or be present in the
essence of each perishable thing. The same account holds
good for imperishableness also;
for both are attributes
which are present of necessity. The characteristics, then,
in respect of which and in direct consequence of which one
thing is perishable and another imperishable, are opposite,
so that the things must be different in kind.
Evidently, then, there cannot be Forms such as some i
maintain, for then one man l would be perishable and an
other 2
imperishable. Yet the Forms are said to be the
same in form with the individuals and notmerely
to have
the same name;
but things which differ in kind 3are
farther apart than those which differ in form.
1 The sensible individual.2 The ideal man.
3 As the perishable and the imperishable have been shown to do.
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BOOK K
THAT Wisdom is a science of first principles is evident i
from the introductory chapters,1in which we have raised
objections to the statements of others about the first prin-
20ciples ;
but one might ask the question whether Wisdom is
to be conceived as one science or as several. If as one, it
may be objectedthat
one science alwaysdeals
withcon
traries, but the first principles are not contrary. If it is
not one, what sort of sciences are those with which it is to
be identified ?2
Further, is it the business of one science, or of more than
one, to examine the first principles of demonstration ? If of
2 5 one, why of this rather than of any other? If of more,
what sort of sciences must these be said to be ?3
Further, does Wisdom investigate all substances or not ?
If not all, it is hard to say which;but if, being one, it
investigates them all, it is doubtful how the same science
can embrace several subject-matters.4
Further, does it deal with substances only or also with
3 their attributes ? If in the case of attributes demonstration
is possible,5in that of substances it is not. But if the two
sciences are different, what is each of them and which is
Wisdom ? If we think of it as demonstrative, the science of
the attributes is Wisdom, but if as dealing with what is
primary, the science of substances claims the title.6
But again the science we are looking for must not be
supposedto deal with the causes
which havebeen mentioned
35 in the Physics? For (A) it does not deal with the final
cause (for that is the nature of the good, and this is found
in the field of action and movement; and it is the first
mover for that is the nature of the end but in the case
of things unmovable there is nothing that moved them
1Cf. Bk. A. 3-10.
2Cf. B. 996
a i8-b 26.
3 Cf. B. 996b 26-997* 15.4 Cf. B. 997 a 15-25.
5
Reading in 1. 31 an-ada^is (<TTIV.
6Cf. B. 997
a25-34.
1 The material, formal, efficient, and final causes (Pkys. ii. 3).
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BOOK K. i i059a
first),
1 and (B)in general it is hard to say whether per
chance the science we are now looking for deals with
perceptible substances or not with them, but with cer
tain others. If with others, it must deal either with the
Forms or with the objects of mathematics. Now (a) evi
dently the Forms do not exist. (But it is hard to say, even
if one suppose them to exist, why in the world the same is
not true of the other things of which there are Forms, as of
the objects of mathematics. I mean that these thinkers 5
place the objects of mathematics between the Forms and per
ceptible things, as a kind of third set of things apart both
from the Forms and from the things in this world;
but
there is not a third man or horse besides the ideal and the
individuals. If on the other hand it is not as they say, with
what sort of things must the mathematician be supposed to
deal ? Certainly not with the things in this world;for 10
none of these is the sort of
thing
which the mathematical
sciences demand.) Nor (6) does the science which we
are now seeking treat of the objects of mathematics;
for
none of them can exist separately. But again it does
not deal with perceptible substances;for they are perish
able.2
In general one might raise the question, to what kind of 15
science it belongs to discuss the difficulties about the matterof the objects of mathematics. Neither to physics (because
the whole inquiry of the physicist is about the things that
have in themselves a principle of movement and rest), nor
yet to the science which inquires into demonstration and
science;for this is just the subject which it investigates.
It remains then that it is the philosophy which we have set 20
before ourselves that treats of those subjects.
One might discuss the question whether the science we
are seeking should be said to deal with the principles which
are by some called elements;
all men suppose these to be
present in composite things. But it might be thought that
the science we seek should treat rather of universals;for 25
every definition and every science is of universals and not
of infimae speciesf so that as far as this goes it would deal
1Cf. B. 996
a 2i-b i.2
Cf. B. 997* 34-998* 19.3
Cf. B. 998b
15.
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io59b METAPHYSICA
with the highest genera. These would turn out to be being
and unity ;for these might most of all be supposed to con
tain all things that are, and to be most like principles
30 because they are first by nature;for if they perish all other
things are destroyed with them;for everything is and is one.
But inasmuch as, if one is to suppose them to be genera,
they must be predicable of their differentiae, and no genus
is predicable of any of its differentiae, in this way it would
seem that we should not make them genera nor principles.
Further, if the simpler is more of a principle than the less
35simple, and
the ultimatemembers of
thegenus
aresimpler
than the genera (for they are indivisible, but the genera
are divided into many and differing species), the species
might seem to be the principles, rather than the genera.
But inasmuch as the species are involved in the destruction
of the genera, the genera are more like principles ;for that
which involves another in its destruction is a principle of
io6oa
it. 1 These and others of the kind are the subjects that
involve difficulties.
Further, must we suppose something apart from indi- 2
vidual things, or is it these that the science we are seeking
5 treats of? But these are infinite in number. Yet the things
that are apart from the individuals are genera or species ;
but the science we now seek treats of neither of these. Thereason why this is impossible has been stated.
2
Indeed, it
is in general hard to say whether one must assume that
there is a separable substance besides the sensible sub
stances (i.e. the substances in this world), or that these are
10 the real things and Wisdom is concerned with them. For
we seem to seek another kind of substance, and this is our
problem, i. e. to see if there is something which can exist
apart by itself and belongs to no sensible thing. Further,
if there is another substance apart from and corresponding
to sensible substances, which kinds of sensible substance
must be supposed to have this corresponding to them ?
15 Why should one suppose men or horses to have it, more
thaneither
the otheranimals or
evenall lifeless
things?
1Cf. B. 998*20-999*23.
2
io59b24-38.
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BOOK K. 2 io6oa
On the other hand to set up other and eternal substances
equal in number to the sensible and perishable substances
would seem to fall beyond the bounds of probability. But
if the principle we now seek is not separable from corporeal
things, what has a better claim to the name than matter ?
This, however, does not exist in actuality, but exists in 20
potency. And it would seem rather that the form or shape
is a more important principle than this;but the form is
perishable,1 so that there is no eternal substance at all
which can exist apart and independent. But this is para
doxical;for such a principle and substance seems to exist
and is sought by nearly all the most refined thinkers as some- 25
thing that exists;for how is there to be order unless there
is something eternal and independent and permanent ?2
Further, if there is a substance or principle of such a
nature as that which \ve are now seeking, and if this is one
for all things, and the same for eternal and for perishable
things, it is hard to say why in the world, if there is the same
principle, some of the things that fall under the principle are 30
eternal, and others are not eternal;this is paradoxical. But
if there is one principle of perishable and another of eternal
things, we shall be in a like difficulty if the principle of
perishable things, as well as that of eternal, is eternal;
for
why,if the
principleis
eternal,are not the
thingsthat fall
under the principle also eternal ? But if it is perishable
another principle is involved to account for it, and another
to account for that, and this will go on to infinity.3
35
If on the other hand we are to set up what are thought
to be the most unchangeable principles, being and unity,
firstly,if each of these does not indicate a this or sub
stance, how will they be separable and independent ? Yet io6ob
we expect the eternal and primary principles to be so. But if
each of them does signify a this or substance, all things
that are are substances;for being is predicated of all things
(and unity also ofsome) ;but that all things that are are sub- 5
stance is false. Further, how can they4 be right who say that
1
It must be remembered that A. is only stating common opinions
and the consequent difficulties.2
Cf. B. 999a24-
b24.
sCf. B. ioooa 5-iooi
a3.
4 The Pythagoreans and Plato.
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io6ob METAPHYSICA
the first principle is unity and this is substance, and generate
number as the first product from unity and from matter,
10 and assert that number is substance ? How are we to
think of two,
and each of the othernumbers composed
of
units, as one ? On this point neither do they say anything
nor is it easy to say anything. But if we are to suppose
lines or what comes after these(I mean the primary sur
faces) to be principles, these at least are not separable sub
stances, but sections and divisions the former of surfaces,
the latter of bodies (while points are sections and divisions
J 5 of lines) ; and further they are limits of these same things;
and all these are in other things and none is separable.
Further, how are we to suppose that there is a substance of
unity and the point ? Every substance comes into being
by a gradual process, but a point does not;for the point
is a division.1
20 A further difficulty is raised by the fact that all know
ledge is of universals and of the such,but substance
is not a universal, but is rather a this a separable
thing, so that if there is knowledge about the first prin
ciples, the question arises, how are we to suppose the first
principle to be substance ?2
Further, is there anything apart from the concrete thing
(by which I mean the matter and that which is joined with2 5
it),or not ? If not, we are met by the objection that all
things that are in matter are perishable. But if there is
something, it must be the form or shape. Now it is hard
to determine in which cases this exists apart and in which
it does not;for in some cases the form is evidently not
separable, e. g. in the case of a house.3
Further, are the principles the same in kind or in num-
3 ber ? If they are one in number, all things will be the
same. 4
Since the science of the philosopher treats of being qua 3
being universally and not in respect of a part of it, and
1
being has many senses and is not used in one only,it
follows thatifthe word
is
used equivocally andin
virtueof
1
Cf. B. iooi a 4-ioo2b
ii.2
Cf. B. 1003* 5-17.3
Cf. B. 999a24-
b24.
4Cf. B. 999
b24-1000* 4.
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BOOK K. 3 io6ob
nothing common to its various uses, being does not fall
under one science (for the meanings of an equivocal term do
not form one genus) ;but if the word is used in virtue of 35
something common, being will fall under one science. Theterm seems to be used in the way we have mentioned, like
medical and *
healthy . For each of these also we use in
many senses. Terms are used in this way by virtue of some io6ia
kind of reference, in the one case to medical science, in
the other to health, in others to something else, but in
each case to one identical concept. For a discussion and
a knife are called medical because the former proceeds from
medical science, and the latter is useful to it. And a thing 5
is called healthy in a similar way ;one thing because it is
indicative of health, another because it is productive of it.
And the same is true in the other cases. Everything that
is, then, is said to be in this same way ;each thing that is
is said to be because it is a modification ofbeing q^la being
or a permanent or a transient state or a movement of it,or
something else of the sort. And since everything that is TO
may be referred to something single and common, each of
the contrarieties also may be referred to the first differences
and contrarieties of being, whether the first differences of
being are plurality and unity, or likeness and unlikeness, or
some other differences ; let these be taken as already dis
cussed.1
It makes no difference whether that which is be re- 15
ferred to being or to unity. For even if they are not the same
but different, at least they are convertible;for that which is
one is also somehow being, and that which is being is one.
But since every pair of contraries falls to be examined byone and the same science, and in each pair one term is the
privative of the other- though one might regarding some 20
contraries raise the question, how they can be privately
related, viz. those which have an intermediate, e. g. unjust
and just in all such cases one must maintain that the
privation is not of the whole definition, but of the infima
species. E. g. if the just man is by virtue of some per
manent disposition obedient to the laws \2 the unjust man 25
1
Cf. Fr. I478b35-1479* 5, M97
a32-149^43-
2Cf. [PL] Zte/. 411 E.
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io6ia METAPHYSICA
will not in every case have the whole definition denied of
him, but may be merely4
in some respect deficient in obedi
ence to the laws,and in this respect the privation will
attach to him;and
similarly
in all other cases.
As the mathematician investigates abstractions (for before
30 beginning his investigation he strips off all the sensible quali
ties, e. g. weight and lightness, hardness and its contrary, and
also heat and cold and the other sensible contrarieties, and
leaves only the quantitative and continuous, sometimes in
one, sometimes in two, sometimes in three dimensions, and
35 the attributes of these qiia quantitative and continuous, anddoes not consider them in any other respect, and examines
the relative positions of some and the attributes of these,
io6iband the commensurabilities and incommensurabilities of
others, and the ratios of others;but yet we posit one and
the same science of all these things geometry), the same
is true with regard to being. For the attributes of this in so
5 far as it is being, and the contrarieties in it qua being, it is
the business of no other science than philosophy to investi
gate ;for to physics one would assign the study of things
not qzta being, but rather qua sharing in movement;while
dialectic and sophistic deal with the attributes of things that
are, but not of things qita being, and not with being itself
10 in so far as it is
being;therefore it remains that it is the
philosopher who studies the things we have named, in so
far as they are being. Since all that is is said to be in virtue
ofsomething single and common, though the term has many
meanings, and contraries are in the same case (for they are
referred to the first contrarieties and differences of being),
15 and things of this sort can fall under one science, the diffi
culty we stated at the beginningl
appears to be solved, I
mean the question how there can be a single science ot
things which are many and different in genus.
Since even the mathematician uses the common axioms 4
only in a special application, it must be the business of first
philosophy to examine the principles of mathematics also.
1
I059a20-23. Cf. r. 2. The question raised in 1059* 29-34 has
also incidentally been answered.
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BOOK K. 4 io6ib
That when equals are taken from equals the remainders
are equal, is common to all quantities, but mathematics ao
studies a part of its proper matter which it has detached,
e.g. lines or angles or numbers or some other kind of
quantity not, however, qua being but in so far as each of
them is continuous in one or two or three dimensions;but 25
philosophy does not inquire about particular subjects in so
far as each of them has some attribute orother>
but specu
lates about being, in so far as each particular thing is.
Physics is in the same position as mathematics;for physics
studies the attributes and the principles of the things that
are, qua moving and not qita being (whereas the primary 30
science, we have said, deals with these, only in so far as the
underlying subjects are existent, and not in virtue of any
other character) ;and so both physics and mathematics
must be classed as parts of Wisdom.1
5 There is a principle in things, about which we cannot be
deceived, but must always, on the contrary, recognize the35
truth, viz. that the same thing cannot at one and the same
time be and not be, or admit any other similar pair of oppo- io62a
sites.2 About such matters there is no proof in the full
sense, though there is proof ad hominem. For it is not
possible
to infer this truth itself from a more certain
principle, yet this is necessary if there is to be completed proof
of it in the full sense.3 But he who wants to prove to the
5
asserter of opposites that he is wrong must get from him an
admission which shall be identical with the principle that
the same thing cannot be and not be at one and the same
time, but shall not seem to be identical;for thus alone can
his thesis be demonstrated to the man who asserts that oppo- 10
site statements can be truly made about the same subject.
Those, then, who are to join in argument with one another
must to some extent understand one another;
for if this
does not happen how are they to join in argument with one
another ? Therefore every word must be intelligible and
indicate something, and not many things but only one;and 15
1Cf. r. ioos
ai9-
b2, K. 1059*23-26.
2Cf. r. ioo5
b8-34.
3Cf. r. ioc6a 5-18.
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io62a METAPHYSICA
if it signifies more than one thing, it must be made plain to
which of these the word is being applied. He, then, who
says this is and is not denies what he affirms, so that
what the word signifies, he says it does not signify; and
this is impossible. Therefore if this is signifies some
thing, one cannot truly assert its contradictory.1
Further, if the word signifies something and this is
20 asserted truly,2this connexion must be necessary ;
and it is
not possible that that which necessarily is should ever not
be;
it is not possible therefore to make the opposed
affirmations and negations truly of the same subject/
1
Further, if the affirmation is no more true than the negation,
he who says man will be no more right than he who says
254 not-man . It would seem also that in saying the man is
not a horse one would be either more or not less right than
in saying he is not a man, so that one will also be right in
saying that the same person is a horse;for it was assumed
to be possible to make opposite statements equally truly.
It follows then that the same person is a man and a horse,
or any other animal. 4
30 While, then, there is no proof of these things in the full
sense, there is a proof which may suffice against one who
will make these suppositions. And perhaps if one had
questioned
Heraclitus himself in this
wayone
might
have
forced him to confess that opposite statements can never
be true of the same subjects. But, as it is, he adopted this
35 opinion without understanding what his statement involves.5
But in any case if what is said by him is true, not even this
io62bitself will be true viz. that the same thing can at one and
the same time both be and not be. For as, when the state
ments are separated, the affirmation is no more true than the
negation, in the same way the combined and complex
5 statement being like a single affirmation the whole taken
as an affirmation will be no more true than the negation.6
Further, if it is not possible to affirm anything truly,
this itself will be false the assertion that there is no true
1Cf. r. ioo6a i8-ioo7
a2o.
2
Sc. of that of which the word is asserted.3
Cf. r. ioo6b 28-34.4
Cf. r. ioo;b 18-1008*2.
6Cf. r. ioos
b23-26.
6Cf. r. ioo8a 6-7.
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BOOK K. 5 io62b
affirmation.1 But if a true affirmation exists, this appears
to refute what is said by those who raise such objections10
and utterly destroy rational discourse.
6 The saying of Protagoras is like the views we have mentioned
;he said that man is the measure of all things,
2
meaning simply that that which seems to each man also
assuredly is. If this is so, it follows that the same thing 15
both is and is not, and is bad and good, and that the
contents of all other opposite statements are true, because
often a particular thing appears beautiful to some and the
contrary of beautiful to others, and that which appears to
each man is the measure. This difficulty may be solved by20
considering the source of this opinion. It seems to have
arisen in some cases from the doctrine of the natural
philosophers, and in others from the fact that all men have
not the same views about the same things, but a particular
thing appears pleasantto some and the
contraryof
pleasantto others.
3
That nothing comes to be out of that which is not, but
everything out of that which is, is a dogma common to 2 5
nearly all the natural philosophers. Since, then, white
cannot come to be if the perfectly white and in no respect
not-white existed before, that which becomes white must
come from that which is not white ; so that it must come to
be out of that which is not (so they argue), unless the same
thing was at the beginning white and not-white. But it is 3
not hard to solve this difficulty ;for we have said in our
works on physics4in what sense things that come to be
come to be from that which is not, and in what sense from
that which is.5
But to attend equally to the opinions and the fancies of
disputing parties is childish;for clearly one of them must be
mistaken. And this is evident from what happens in respect 35
of sensation;for the same thing never appears sweet to some
and the contrary of sweet to others, unless in the one case 1063**
1Cf. r. ioi2b 13-18. Fr. i.
3
Cf. r. ioo9
a
6-i6, 22-30.4
Phys. i. 7-9, De Gen. et Corr. i. 3l7b14-319^.
5Cf. r. 1009* 30-36.
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io63a METAPHYSICA
the sense-organ which discriminates the aforesaid flavours
has been perverted and injured. And if this is so the one
party must be taken to be the measure, and the other must
5 not. And I
say
the same of
goodand bad, and beautiful
and ugly, and all other such qualities. For to maintain the
view we are opposing is just like maintaining that the
things that appear to people who put their finger under
their eye and make the object appear two instead of one
must be two (because they appear to be of that number) and
again one (for to those who do not interfere with their eye
the one object appears one).1
10 In general, it is absurd to make the fact that the things
of this earth are observed to change and never to remain
in the same state, the basis of our judgement about the
truth. For in pursuing the truth one must start from the
things that are always in the same state and suffer no
15 change. Such are the heavenly bodies;for these do not
appear to be now of one nature and again of another, but
are manifestly always the same and share in no change.2
Further, if there is movement, there is also something
moved, and everything is moved out of something and into
something ;it follows that that which is moved must first
be in that out of which it is to be moved, and then not be in
20 it, and move into the other and come to be in it, and that
the contradictory statements are not true at the same time, as
these thinkers assert they are.
And if the things of this earth continuously flow and
move in respect of quantity if one were to suppose this,
although it is not true why should they not endure in
respect of qualify ? For the assertion of contradictory
statements about the same thing seems to have arisen
35 largely from the belief that the quantity of bodies does not
endure, which, our opponents hold, justifies them in saying
that the same thing both is and is not four cubits long.
But essence depends on quality, and this is of determinate
nature, though quantity is of indeterminate.3
Further, when the doctor orders people to take some
1Cf. r. ioiob i-26, ioii a
3i-4.2
Cf. r. ioioa 25-32.3
Cf. r. 1010*22-25.
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BOOK K. 6 io63a
particular food, why do they take it ? In what respect is 30
4
this is bread truer than this is not bread ? And so it
would make no difference whether one ate or not. But as
a matter of fact they take the food which is ordered,
assuming that they know the truth about it and that it is
bread. Yet they should not, if there were no fixed constant
nature in sensible things, but all natures moved and flowed
for ever.1
Again, if we are always changing and never remain the 35
same, what wonder is it if to us, as to the sick, things never
appear the same ? (For to them also, because they are not 1063
in the same condition as when they were well, sensible
qualities do not appear alike; yet, for all that, the sensible
things themselves need not share in any change, though
they produce different, and not identical, sensations in the
sick. And the same must surely happen to the healthy if 5
the aforesaid2
change takes place.) But if we do not
change but remain the same, there will be something that
endures.3
As for those to whom the difficulties mentioned are
suggested by reasoning, it is not easy to solve the diffi
culties to their satisfaction, unless they will posit something
and no longer demand a reason for it;for it is only thus 10
that all
reasoningand all
proofis
accomplished;
if
theyposit nothing, they destroy discussion and all reasoning.
Therefore with such men there is no reasoning. But as for
those who are perplexed by the traditional difficulties, it is
easy to meet them and to dissipate the causes of their per
plexity. This is evident from what has been said.4
It is manifest, therefore, from these arguments that con- 15
tradictory statements cannot be truly made about the same
subject at one time,5nor can contrary statements, because
every contrariety depends on privation. This is evident if
we reduce the definitions of contraries to their principle.6
Similarly, no intermediate between contraries can be
predicated of one and the same subject, of which one of the
Cf. r. ioo8b
12-27.
2
Cf. io63a
35.3
Cf. r. ioo9a38-
b33.
4In io62b 2o-io63
b7.
5Cf. r. ioo9
a16-22, ioii a
3-i6.6
Cf. r. ioii b15-22.
645-28 O
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io63b METAPHYSICA
jo contraries is predicated. If the subject is white we shall be
wrong in saying it is neither black nor white, for then it
follows that it is and is not white;for the second of the
two terms we have put together
lis
true of it, and thisis
the contradictory of white.2
We could not be right, then, in accepting the views
25 either of Heraclitus 3 or of Anaxagoras. If we were, it
would follow that contraries would be predicated of the
same subject ;for when Anaxagoras says that in everything
there is a part of everything, he says nothing is sweet any
more than it is bitter, and so with any other pair of con
traries, since in everything everything is present not poten-
30 daily only, but actually and separately. And similarly all
statements cannot be false nor all true, both because ot
many other difficulties which might be adduced as arising
from this position, and because if all are false it will not be
true to say even this, and if all are true it will not be false
35 to say all are false.4
Every science seeks certain principles and causes for each 7
1064 of its objects e.g. medicine and gymnastics and each of
the other sciences, whether productive or mathematical.
For each of these marks off a certain class of things for
itself and busies itself about this as about something exist
ing and real, not however qua real; the science that does
this is another distinct from these. Of the sciences men-
5 tioned each gets somehow thel what in some class of
things and tries to prove the other truths, with more or less
precision. Some get the what through perception, others
by hypothesis ;so that it is clear from an induction of this
sort that there is no demonstration of the substance or
1 what .
10 There is a science of nature, and evidently it must be
different both from practical and from productive science.
For in the case of productive science the principle of move
ment is in the producer and not in the product, and is either
an art or some other faculty. And similarly in practical
1 Sc. not white and not black .
2Cf. r. ioii b
23-iol2a24.
3Cf. io62a
3i-b2.
4Cf. r. ioi2a
24-bi8.
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BOOK K. 7 io64a
science the movement is not in the thing done, but rather
in the doers. But the science of the natural philosopher 15
deals with the things that have in themselves a principle
of movement. It is clear from these facts, then, that natural
science must be neither practical nor productive, but theoreti
cal (for it must fall into some one of these classes).And
since each of the sciences must somehow know the what
and use this as a principle, we must not fail to observe 20
how the natural philosopher should define things and how
he should state the definition of the essence whether as akin
to snub or rather to concave . For of these the defini
tion of snub includes the matter of the thing, but that of
concave is independent of the matter;for snubness is 2 5
found in a nose, so that we look for its definition without
eliminating the nose, for what is snub is a concave nose.
Evidently then the definition of flesh also and of the eye
and of the otherparts
mustalways
be stated without
eliminating the matter.
Since there is a science of being qua being and capable
of existing apart, we must consider whether this is to be
regarded as the same as physics or rather as different.
Physics deals with the things that have a principle of 30
movement in themselves;mathematics is theoretical, and
is a science that deals with things that are at rest, but its
subjects cannot exist apart. Therefore about that which
can exist apart and is unmovable there is a science different
from both of these, if there is a substance of this nature
(I mean separable and unmovable), as we shall try to prove 35
there is.1 And if there is such a kind of thing in the world,
here must surely be the divine, and this must be the first
and most dominant principle. Evidently, then, there are io64b
three kinds of theoretical sciences physics, mathematics,
theology. The class of theoretical sciences is the best, and
of these themselves the last named is best;for it deals with
the highest of existing things, and each science is called 5
better or worse in virtue of its proper object.
One might raise the question whether the science of
being qua being is to be regarded as universal or not.
1Cf. A. 6, 7.
Q2
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1064 METAPHYSICA
Each of the mathematical sciences deals with some one
determinate class of things, but universal mathematics ap
plies alike to all. Now if natural substances are the first of
10 existing things, physics must be the first of sciences ; but if
there is another entity and substance, separable and un-
movable, the knowledge of it must be different and prior
to physics and universal because it is prior.1
15 Since being in general has several senses, of which one 8
is being by accident,we must consider first that which
is in this sense. Evidently none of the traditional sciencesbusies itself about the accidental. For neither does archi
tecture consider what will happen to those who are to use
20 the house (e. g. whether they will have a painful life in it
or not), nor does weaving, or shoemaking, or the con
fectioner s art, do the like;
but each of these sciences
considers only what is peculiar to it, i. e. its proper end.
And as for the argument that when he who is musical
becomes lettered he will be both at once, not having been
25 both before;and that which is, not always having been,
must have come to be;
therefore he must have at once
become musical and lettered,
this none of the recognized
sciences considers, but only sophistic ;for this alone busies
itself about the accidental, so that Plato is not far \vrong
when he says2that the sophist spends his time on non-
being.
3o That a science of the accidental is not even possible \vill
be evident if we try to see what the accidental really is.
We say that everything either is always and of necessity
(necessity not in the sense of violence, but that which we
35 appeal to in demonstrations), or is for the most part, or is
neither for the most part, nor always and of necessity, but
merely as it chances;
e. g. there might be cold in the dog-
days, but this occurs neither always and of necessity, nor
io65afor the most part, though it might happen sometimes. The
accidental, then, is what occurs, but not always nor of
necessity, nor for the most part. Now we have said what
the accidental is, and it is obvious why there is no science
1Cf. E. I,
K. I059a26-29.
2Cf. Sophistes 254 A.
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BOOK K. 8 io6sa
of such a thing; for all science is of that which is always
or for the most part, but the accidental is in neither of 5
these classes.
Evidently there are not causes and principles of the acci
dental, of the same kind as there are of the essential;for
if there were, everything"would be of necessity. If A is
when B is, and B is when C is, and if C exists not by
chance but of necessity, that also of which C was cause ro
will exist of necessity, do\vn to the last causatum as it is
called (but this was supposed to be accidental). Therefore
all things will be of necessity, and chance and the possibility
of a thing s either occurring or not occurring are removed
entirely from the range of events. And if the cause be
supposed not to exist but to be coming to be, the same
results will follow; everything will occur of necessity. 15
For to-morrow s eclipse will occur if A occurs, and A if B
occurs, and B if C occurs;and in this
wayif we subtract
time from the limited time between now and to-morrow we
shall come sometime to the already existing condition.
Therefore since this exists, everything after this will occur 20
of necessity, so that all things occur of necessity.
As to that which is in the sense of being true or of
being by accident, theformer depends on a combination in
thought and is an affection of thought (which is the reason
why it is the principles, not of that which is in this sense,
but of that which is outside and can exist apart, that are
sought) ;and the latter is not necessary but indeterminate
(I mean the accidental) ;and of such a thing the causes are 25
unordered and indefinite.1
Adaptation to an end is found in events that happen by
nature or as the result of thought. It is luck when one
of these events2
happens by accident. For as a thing may
exist, so it may be a cause, either by its own nature or by
accident.15 Luck is an accidental cause at work in such 3
events adapted to an end as are usually effected in accor
dance with purpose. And so luck and thought are concerned
1Cf. E. 2-4.
2Sc. which happen usually by nature or as the result of thought.
3Cf. Pliys. ii. I96
b21-25.
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io65a METAPHYSICA
with the same sphere ;for purpose cannot exist without
thought. The causes from which lucky results might
happen are indeterminate ; and so luck is obscure to human
calculation and is a cause by accident, but in the unqualified
35 sense a cause of nothing.1
It is good or bad luck when
io6sbthe result is good or evil
;and prosperity or misfortune
when the scale of the results is large.2
Since nothing accidental is prior to the essential, neither
are accidental causes prior. If, then, luck or spontaneity is
a cause of the material universe, reason and nature are
causes before it.:3
5Some things are only actually, some potentially, some 9
potentially and actually, what they are, viz. in one case
a particular reality, in another, characterized by a particular
quantity, or the like.4 There is no movement apart from
things ;for change is always according to the categories
of being, and there is nothing common to these and in noone category. But each of the categories belongs to all its
10 subjects in either of two ways (e. g. this-ness for one
kind of it is*
positive form,and the other is
*
privation ;
and as regards quality one kind is white and the other
black,and as regards quantity one kind is complete
and the other*
incomplete ,and as regards spatial move
ment one is upwards and the other downwards,or one
thing is light and another heavy ) ;so that there are as
many kinds of movement and change as of being. ThereJ 5
being a distinction in each class of things between the
potential and the completely real, I call the actuality of the
potential as such, movement. That what we say is true, is
plainfrom the
followingfacts. When the buildable
,in
so far as it is what we mean by buildable V5exists actually,
it is being built, and this is the process of building. Simi
larly with learning, healing, walking, leaping, ageing, ripen-
20 ing.G Movement takes place when the complete reality itself
exists, and neither earlier nor later.7 The complete reality,
1Cf. Phys. ii. I97
a5-14.
2Cf. Phys. ii. I97
a25-27.
3
Cf. Phys. ii. 198* 5-13.
4
Cf. Phys. iii. 200^26-28.6i. e. not as so much matter, but as matter capable of being made
into a building.fi
Cf. Phys. iii. 2OOb 32-201* 19.7
Cf. Phys. iii. 2oi b6, 7.
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BOOK K. 9 io6sb
then, of that which exists potentially, when it is completely
real and actual, not q2ia itself, but qua movable, is movement.
By qua I mean this : bronze is potentially a statue;but
yet it is not the complete reality of bronze qzia bronze that
is movement. For it is not the same thing to be bronze 25
and to be a certain potency. If it were absolutely the same
in its definition, the complete reality of bronze would have
been a movement. But it is not the same. (This is evident
in the case of contraries;for to be capable of being well
and to be capable of being ill are not the same for if they
were, being well and being ill would have been the sameit is that which underlies and is healthy or diseased, whether 30
it is moisture or blood, that is one and the same.) And
since it is not the same, as colour and the visible are not
the same, it is the complete reality of the potential, and as
potential, that is movement. That it is this, and that move
ment takes place when the complete reality itself exists, and 35
neither earlier nor later, is evident. For each thing is io668
capable of being sometimes actual, sometimes not, e. g. the
buildable qua buildable;and the actuality of the buildable
qua buildable is building. For the actuality is either this
the act of building or the house. But when the house
exists, it is no longer buildable;the buildable is what is
beingbuilt. The
actuality,then, must be the act
of building^5
and this is a movement. And the same account applies to
all other movements.
That what we have said is right is evident from what all
others say about movement, and from the fact that it is not
easy to define it otherwise. For firstly one cannot put it in
any other class. This is evident from what people say.i
Some call it otherness and inequality and the unreal ;
2
none of these, however, is necessarily moved, and further,
change is not either to these or from these any more than
from their opposites. The reason why people put move
ment in these classes is that it is thought to be something
1 The argument is that the house cannot be the eW/ryeia of the
buildable, for when the house exists the buildable has ceased to exist;
therefore its eV/ryeia must be \\\& process of building.2 The Pythagoreans and Platonists are meant; cf. PI. Soph. 256 D,Tim. 57Eff.
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io66a METAPHYSICA
indefinite, and the principles in one of the two columns of
15 contrarieslare indefinite because they are privative, for
none of them is either a this or a such or in any of the
othercategories.
And the reason
whymovement is
thought to be indefinite is that it cannot be classed either
with the potency of things or with their actuality ;for
neither that which is capable of being of a certain quantity,
nor that which is actually of a certain quantity, is of neces-
20sity moved, and movement is thought to be an actuality,
but incomplete ;the reason is that the potential, whose
actuality it is, is incomplete. And therefore it is hard to
grasp what movement is;
for it must be classed either
under privation or under potency or under absolute actu
ality, but evidently none of these is possible. Therefore
25 what remains is that it must be what we said both actu
ality and the actuality we have described which is hard to
detect but capable of existing.2
And evidently movement is in the movable;for it is the
complete realization of this by that which is capable of
causing movement. And the actuality of that which is
capable of causing movement is no other than that of the
movable. For it must be the complete reality of both.
For while a thing is capable of causing movement because
30it can do
this,it is a
moverbecause it is active
;
but it is on
the movable that it is capable of acting, so that the actuality
of both is one, just as there is the same interval from one
to two as from two to one, and as the steep ascent and the
steep descent are one, but the being of them is not one;
the case of the mover and the moved is similar.3
35 The infinite is either that which is incapable of being 10
traversed because it is not its nature to be traversed (this
corresponds to the sense in which the voice is invisible),
or that which admits only of incomplete traverse or scarcely
admits of traverse, or that which, though it naturally
admits of traverse, is not traversed or limited; further, a
thing may be infinite in respect of addition or of subtrac-
1 Cf. note on A. 986** 23.&
With io65b 22-io66a 27 cf. Phys. iii. 2oi a
27-202* 3.3
Cf. Phys. iii. 2O2a 13-21.
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BOOK K. 10 io66b
tion, or both. The infinite cannot be a separate, indepen- io66b
dent thing. For if it is neither a spatial magnitude nor a
plurality, but infinityitself is its substance and not an acci
dent of it, it will be indivisible ; for the divisible is either
magnitude or plurality. But if indivisible, it is not infinite,
except as the voice is invisible;but people do not mean 5
this, nor are we examining this sort of infinite, but the in
finite as untraversable.1
Further, how can an infinite exist
by itself, unless number and magnitude also exist by them
selves, since infinity is an attribute of these ?2
Further,
if the infinite is an accident of something else, it cannot be
qua infinite an element in things, as the invisible is not an 10
element in speech, though the voice is invisible.3 And
evidently the infinite cannot exist actually. For then any
part of it that might be taken would be infinite (for to be
infinite and *
the infinite are the same, if the infinite is
substance and not
predicated
of a subject). Therefore it is
either indivisible, or if it is partible, it is divisible into in
finites;but the same thing cannot be many infinites (as a 15
part of air is air, so a part of the infinite would be infinite,
if the infinite is a substance and a principle). Therefore it
must be impartible and indivisible. But the actually infinite
cannot be indivisible;for it must be of a certain quantity.
Therefore infinity belongs to its subject incidentally. Butif so, then (as we have said 4
)it cannot be it that is a prin- 3o
ciple, but that of which it is an accident the air or the
even number.5
This inquiry is universal;but that the infinite is not
among sensible things, is evident from the following argu
ment. If the definition of a body is that which is bounded
by planes , there cannot be an infinite body either sensible
or intelligible ;nor a separate and infinite number, for 25
number or that which has a number is numerable. 5 Con
cretely, the truth is evident from the following argument.
The infinite can neither be composite nor simple. For (a)
it cannot be a composite body, since the elements are limited
1 Cf. Phys. iii. 2O4a 3-14.2 Cf. Phys. iii. 204* 17-19.
3Cf. Phys. iii. 2O4
a14-17.
41. 9.
5Cf. Phys. iii. 2O4
a20-32.
6Cf. Phys. iii. 2O4
a34~
b8.
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io66b METAPHYSICA
in multitude. For the contraries must be equal and no one
of them must be infinite;for if one of the two bodies falls
30 at all short of the other in potency, the finite will be de
stroyed bythe infinite.
And that each should be infiniteis impossible. For body is that which has extension in all
directions, and the infinite is the boundlessly extended, so
that if the infinite is a body it will be infinite in every direc
tion. Nor (d) can the infinite body be one and simple
35 neither, as some say,1
something apart from the elements,
from which they generate these2
(for there is no such body
apart from the elements ; for everything can be resolved
into that of which it consists, but no such product of
io67aanalysis is observed except the simple bodies), nor fire nor
any other of the elements. For apart from the question
how any of them could be infinite, the All, even if it is
finite, cannot either be or become any one ofthem, as Hera-
5 clitus says3
all things sometime become fire. The same
argument applies to this as to the One which the natural
philosophers posit besides the elements.4 For everything
changes from contrary to contrary, e. g. from hot to cold.5
Further, a sensible body is somewhere, and whole and
part have the same proper place, e. g. the whole earth
and part of the earth. Therefore if (a) the infinite body is
homogeneous, it will be unmovable or it will be always10 moving. But this is impossible ;
for why should it rather
rest, or move, down, up, or anywhere, rather than anywhere
else ? E. g. if there were a clod which were part of an in
finite body, where will this move or rest ? The proper place
of the body which is homogeneous with it is infinite. Will
the clod occupy the whole place, then ? And how ? (This
is impossible.) What then is its rest or its movement ? It
will either rest everywhere, and then it cannot move;or it
15 will move everywhere, and then it cannot be still. But (b]
if the All has unlike parts, the proper places of the parts
are unlike also, and, firstly,the body of the All is not
one except by contact, and, secondly, the parts will be
either finite or infinite in variety of kind. Finite they can-
1 Anaximander is meant.2
Cf. Phys. iii. 2O4b10-24.
3Fr. 30, 64, 66, 90.
4 For this argument cf. io66b 35~io67a
I.
5Cf. Phys. iii. 204* 32-205* 7.
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BOOK K. 10 io67a
not be;for then those of one kind will be infinite in quan
tity and those of another will not(if
the All is infinite),
e.g. fire or water would be infinite, but such an infinite
element would be destruction to the contrary elements. 1
But if the parts are infinite and simple, their places also 20
are infinite and there will be an infinite number of elements;
and if this is impossible, and the places are finite, the All
also must be limited.2
In general, there cannot be an infinite body and also a
proper place for bodies, if every sensible body has either
weight or lightness. For it must move either towards the 25
middle or upwards, and the infinite either the whole or
the half of it cannot do either;for how will you divide
it ? Or how will part of the infinite be down and part up,
or part extreme and part middle ? Further, every sensible
body is in a place, and there are six kinds of place,3 but
these cannot exist in an infinite
body.In
general,
if there 30
cannot be an infinite place, there cannot be an infinite body ;
(and there cannot be an infinite place,} for that which is in a
place is somewhere, and this means either up or down or in
one of the other directions, and each of these is a limit.4
The infinite is not the same in the sense that it is a single
thing whether exhibited in distance or in movement or in
time, but the posterior among these is called infinite in
virtue of its relation to the prior ;i.e. a movement is called 35
infinite in virtue of the distance covered by the spatial
movement or alteration or growth, and a time is called
infinite because of the movement which occupies it.5
ii Of things which change, some change in an accidental 1067
sense, like that in which the musical
maybe said to walk,
1
Cf. Phys. iii. 205* 10-25. Cf. also io66b 28-34, from which it appearsthat the argument is as follows. If a finite number of kinds is to makean infinite whole, at least one kind must be infinite in extent. Theycannot all be infinite, for they limit one another. But if one is infinite
and another finite, the former destroys the latter and there ceases to be
the variety of kinds within the whole which is at present presupposed.Aristotle omits to mention that the supposition of a finite kind co
existing with an infinite kind is in itself absurd, because the finite
limits the infinite. But this would only make his case stronger.2 Cf. Phys. iii. 205* 29-32.3Sc. up and down, right and left, before and behind.
4Cf. Phys. iii. 20^24-206^ 7.
5Cf. Phys. iii. 2o;
b21-25.
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io67b METAPHYSICA
and others are said, without qualification, to change, because
something* in them changes, 1. e. the things that change in
parts ;the body becomes healthy, because the eye does.
But there is something which is by its own nature moved5 directly, and this is the essentially movable. The same
distinction is found in the case of the mover;for it causes
movement either in an accidental sense or in respect of a
part of itself or essentially. There is something that
directly causes movement;and there is something that is
moved, also the time in which it is moved, and that from
which and that into which it is moved. 1 But the forms and
the affections and the place, which are the terminals of the
10 movement of moving things, are unmovable, e.g. know
ledge or heat;
it is not heat that is a movement, but heat
ing.2
Change which is not accidental is found not in all
things, but between contraries, and their intermediates, and
between contradictories. We may convince ourselves of
this by induction.3
15 That which changes changes either from positive into
positive, or from negative into negative, or from positive
into negative, or from negative into positive. (By positive
I mean that which is expressed by an affirmative term.)
Therefore there must be three changes ;for that from
20
negative into negative is not change, because (since theterms are neither contraries nor contradictories) there is no
opposition.4 The change from the negative into the posi
tive which is its contradictory is generation absolute
change absolute generation, and partial change partial
generation ;and the change from positive to negative is
destruction absolute change absolute destruction, and
25 partial change partial destruction. If, then, that which is
not has several senses,5 and movement can attach neither
to that which implies putting together or separating,6 nor
1Cf. Phys. v. 224
a 2i-b i.
2Cf. Phys. v. 224
b 11-16.*
Cf. Phys. v. 224b28-30.
4
1067^ 20-21. I now read ovre yap . . . Icrnv as a parenthesis givingthe justification for OVK dvTidfo-is and idiomatically thrown forward.
8Cf. E. I026a 33-
b2, I027
bi8-i9.
6i. e. to that which is not in the sense of the judgement which is
false .
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BOOK K. ii io67b
to that which implies potency and is opposed to that which
is in the full sensel
(true, the not-white or not-good can be
moved incidentally, for the not-white might be a man;but
that which is not a particular thing at all can in no wise be
moved), that which is not cannot be moved (and ifthis is so, 30
generation cannot be movement;for that which is not is
generated ;for even if we admit to the full that its genera
tion is accidental, yet it is true to say that not-being is
predicable of that which is generated absolutely).2
Simi
larly rest cannot belong to that which is not. These con
sequences, then, turn out to be awkward, and also this, 35
that everything that is moved is in a place, but that which
is not is not in a place ;for then it would be somewhere.
Nor is destruction movement;for the contrary of move
ment is movement or rest, but the contrary of destruction
is generation. Since every movement is a change, and the io68a
kinds of change are the three named above,3 and of these
those in the way of generation and destruction are not
movements, and these are the changes from a thing to its
contradictory, it follows that only the change from positive
into positive is movement. And the positives are either 5
contrary or intermediate (for even privation must be
regarded as contrary), and are expressed by an affirmative
term, e. g. naked or toothless
4
or black.
12 If the categories are classified as substance, quality,
place, acting or being acted on, relation, quantity, there must
be three kinds of movement of quality, of quantity, of
place. There is no movement in respect of substance 10
(because there is nothing contrary to substance), nor of
relation (for it is possible that if one of two things in rela
tion changes, the relative term which was true of the other
thing ceases to be true, though this other does not change
1i. e. a thing cannot be moved when it does not exist actually, but
exists potentially.2
i. e. even if the not-being (privation) which is the starting-point of
generation can exist only as an accident of prime matter, still not-
being is the starting-point of absolute generation (i.e. generation of a
substance, not of a quality).3 In io6;b 19.4
Toothless is more obviously negative in form than the corre
sponding Greek word.
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io68a METAPHYSICA
at all, so that their movement is accidental), nor of agent
and patient, or mover and moved, because there is no
15 movement of movement nor generation of generation, nor,
in general, change of change. For there might be movement of movement in two senses; (i) movement might be
the subject moved, as a man is moved because he changes
from pale to dark, so that on this showing movement,
too, may be either heated or cooled or change its place or
increase. But this is impossible ;for change is not a sub-
20 ject. Or (2) some other subject might change from change
into some other form of existence (e. g. a man from disease
into health). But this also is not possible except incident
ally. For every movement is change from something into
25 something. (And so are generation and destruction; only,
these are changes into things opposed in certain ways
while the other, movement, is into things opposed in
another
way.
1
)A
thing changes,then, at the same time
from health into illness, and from this change itself into
another. Clearly, then, if it has become ill, it will have
changed into whatever may be the other change concerned
(though it may be at rest2
), and, further, into a determinate
change each time;and that new change will be from some-
30 thing definite into some other definite thing ;therefore it
will be the opposite change, that of growing well. Weanswer that this happens only incidentally ;
e. g. there is a
change from the process ofrecollection to that of forgetting,
only because that to which theprocess attaches is changing,
now into a state of knowledge, now into one of ignorance.
Further, the process will go on to infinity, if there is to be
change of change and coming to be ofcoming to be. What
35 is true of the later, then, must be true of the earlier;
e. g. if
the simple coming to be was once coming to be, that which
io68b comes to be something was also once coming to be
;there
fore that which simply comes to be something was not yet
in existence, but something which was coming to be coming
to be something was already in existence. And this was
1
Change between contraries is movement, change between contra
dictories is generation or destruction.2 This is possible, though excluded by the theory in question.
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BOOK K. 12 io68b
once coming1
to be, so that at that time it was not yet
coming to be something else. Now since of an infinite
number of terms there is not a first, the first in this series
will not exist, and therefore no following term will exist.
Nothing, then, can either come to be or move or change. 5
Further, that which is capable of a movement is also capable
of the contrary movement and rest, and that which comes
to be also ceases to be. Therefore that which is coming
to be is ceasing to be when it has come to be coming to
be;for it cannot cease to be as soon as it is coming to be
coming to be, nor after it has come to be;for that which is
ceasing to be must be} Further, there must be a matter TO
underlying that which comes to be and changes. What
will this be, then, what is it that becomes movement or
becoming, as body or soul is that which suffers alteration ?
And, again, what is it that they move into ? For it must
be themovement
orbecoming of something from some
thing into something. How, then, can this condition be
fulfilled ? There can be no learning of learning, and there
fore no becoming of becoming.2
Since there is not movement either of substance or of15
relation or ofactivity and passivity, it remains that move
ment is in respect of quality and quantity and place ;for
each of these admits of contrariety. By quality I mean not
that which is in the substance (for even the differentia is a
quality), but the passive quality, in virtue of which a thing
is said to be acted on or to be incapable of being acted on.3
The immobile is either that which is wholly incapable of 20
being moved, or that which is moved with difficulty in a
long time or begins slowly, or that which is of a nature to
be moved and can be moved but is not moved when and
where and as it would naturally be moved. This alone amongimmobiles I describe as being at rest
;for rest is contrary
1If that which comes to be comes to be coming to be, it also ceases
to be. When ? Not when it is only coming to be coming to be, for then
it is not and . . cannot cease to be;nor after it has come to be, for then
also that which comes to be is not and . . cannot cease to be. /. It
is
ceasing
to be, at the
verytime when it is
comingto be Which is
absurd.2 W7
ith io67b 4-io68
b15 cf. Phys. v. 225* 3-226** 16.
5Cf. Phys. v. 226a 23-29.
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io68b METAPHYSICA
25to movement, so that it must be a privation in that which is
receptive ofmovement?-
Things which are in one proximate place are together in
place, and things which are in different places are apart:
things whose extremes are together touch : that at which
a changing thing, if it changes2
continuously according to
its nature, naturally arrives before it arrives at the extreme
3ointo which it is changing, is between? That which is most
distant in a straight line is contrary in place. That is
successive which is after the beginning (the order being
determined by position or form or in some other way) and
has nothing of the same class between it and that which it
succeeds, e.g. lines in the case of a line, units in that of a
unit, or a house in that of a house. (There is nothing to
prevent a thing of some other class from being between.)
35 For the successive succeeds something and is something
later;
* one does not succeed two,nor the first
dayof
io6gathe month the second. That which, being successive,
touches, is contiguous. (Since all change is between oppo-
sites, and these are either contraries or contradictories, and
there is no middle term for contradictories, clearly that
which is between is between contraries.4)
The continuous
5 is a species of the contiguous. I call two things continuous
when the limits ofeach, with which they touch and by which
they are kept together, become one and the same, so that
plainly the continuous is found in the things out of which
a unity naturally arises in virtue of their contact. And
plainly the successive is the first of these concepts (for the
successive does not necessarily touch, but that which touches
10 is successive;and if a thing is continuous, it touches, but if
it touches, it is not necessarily continuous ;and in things in
which there is no touching, there is no organic unity) ;
therefore a point is not the same as a unit;
for contact
belongs to points, but not to units, which have only suc
cession : and there is something between two of the former,
but not between two of the latter.5
1
Cf.Phys. v. 226
b
io-i6.2io68b 29 omit TO.
3Cf. Phys. v. 226b 21-25.
4 This sentence should probably come after the first in this para
graph.5
Cf. Phys. v. 226b 32-227* 31.
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BOOK A
i THE subject of our inquiry is substance;for the principles
and the causes we are seeking are those of substances.
For if the universe is of the nature of a whole, substance is
its first part ;and if it coheres merely by virtue of serial 20
succession, on this view" also substance is first, and is suc
ceeded by quality, and then by quantity. At the same
time these latter are not even being in the full sense, but
are qualities and movements of it, or else even the not-
white and the not-straight would be being ;at least we say
even these are, e. g.*
there is a not-white V Further, none
of the categories other than substance can exist apart. And 25
the early philosophers also in practice testify to the primacy
of substance;for it was of substance that they sought the
principles and elements and causes. The thinkers of the
present2
day tend to rank universals as substances (for
genera are universals, and these they tend to describe as
principles and substances, owing to the abstract nature of
their inquiry) ;but the thinkers of old ranked particular
things as substances, e. g. fire and earth, not what is common to both, body.
There are three kinds of substance one that is sensible 3
(of which one subdivision is eternal and another is perish
able;the latter is recognized by all men, and includes e. g.
plants and animals), of which we must grasp the elements,
whether one or many ;and another that is immovable, and
this certain thinkers assert to be capable of existing apart,
some dividing it into two, others identifying the Forms and 35
the objects of mathematics, and others positing, of these
two, only the objects of mathematics.3 The former two
kinds of substance are the subject of physics (for they
1 This is an implication of the ordinary type of judgement, x is not
white .
2 The Platonists.3 The three views appear to have been held respectively by Plato,
Xenocrates, and Speusippus.
645-28 R
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io69b METAPHYSICA
io6gb
imply movement) ;but the third kind belongs to another
science, if there is no principle common to it and to the
other kinds.
Sensible substance is changeable. Now if change proceeds from opposites or from intermediates, and not from
all opposites (for the voice is not-white(, but it does not
5 therefore change to white}), but from the contrary, there
must be something underlying which changes into the con
trary state;for the contraries do not change. Further, 2
something persists, but the contrary does not persist ;there
is, then, some third thing besides the contraries, viz. the
matter. Now since changes are of four kinds either in
respect of the what or of the quality or of the quantity
10 or of the place, and change in respect of thisnessJ
is
simple generation and destruction, and change in quantity
is increase and diminution, and change in respect of an
affection is alteration, andchange
ofplace
is motion,
changes will be from given states into those contrary to
them in these several respects. The matter, then, which
15 changes must be capable of both states. And since that
which *
is has two senses, we must say that everything
changes from that which is potentially to that which is
actually, e. g. from potentially white to actually white, and
similarly in the case of increase and diminution. Thereforenot only can a thing come to be, incidentally, out of that
which is not, but also all things come to be out of that
33 which is, but is potentially, and is not actually. And this
is the One of Anaxagoras ;for instead of *
all things
were togetherc
and the Mixture of Empedocles and
Anaximander and the account given by Democritus it is
better to say all things were together potentially but not
actually . Therefore these thinkers seem to have had some
notion of matter. Now all things that change have matter,
25 but different matter;and of eternal things those which are
not generable but are movable in space have matter not
matter for generation, however, but for motion from one
place to another.
One might raise the question from what sort of non-being
1
Reading in I. 1 1 TO ro 8f.2
Anaxagoras, fr. I.
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BOOK A. 2 io6gb
generation proceeds ;for non-being has three senses.
1
If,
then, one form of non-being exists potentially, still it is not
by virtue of a potentiality for any and every thing, but
different things come from different things ;nor is it satis
factory to say that all things were together ;for they 30
differ in their matter, since otherwise why did an infinity of
things come to be, and not one thing ? For reason2
is
one, so that if matter also were one, that must have come
to be in actuality which the matter was in potency.:i The
causes and the principles, then, are three, twobeing
the
pair of contraries of which one is definition and form and
the other is privation, and the third being the matter.
3 Note, next, that neither the matter nor the form comes 35
to be and I mean the last matter and form. For every
thing that changes is something and is changed by some
thing and into something. That by which it is changed iO7oa
is the immediate mover ;that which is changed, the matter;
that into which it is changed, the form. The process, then,
will go on to infinity, if not only the bronze comes to be
round but also the round or the bronze comes to be;
therefore there must be a stop.
Note, next, that each substance comes into being out of
somethingthat shares its name.
(Natural objects
and 5
other things both rank as substances.) For things come
into being either by art or by nature or by luck or by
spontaneity. Now art is a principle of movement in some
thing other than the thing moved, nature is a principle
in the thing itself (for man begets man 4
),and the other
causes are privations of these two.
1 Alexander points out thataTrop^o-fie
. . . 6V refers to 1. 20. Thethree senses are probably the non-being that answers to the categoriesof being, the false, and the potential (cf. N. io89
a26-28).
2Sc. the voiis of Anaxagoras doctrine, summarized by D. L. (II. 3.
l) in the words, irdvra xprjfiara rjv 6/j.oiietra 6 vovs eXOav aura
Su/cdo-fi^o-ev.3Sc. an undifferentiated unity.
4 This is not a good instance of what A. says about nature, for the
principle of generation is not in the child but in the father. Thedefinition of nature applies better to other natural functions, such as
growth. The note ai Spano? yap av6pu>7rov yfwa is hastily thrown inbecause A. is thinking mainly of his favourite thesis of ycvco-is ex
. Hence Alexander says TOVTO crvvexf? earn TCO /uera ravraOTl fKCKJTT] K (TVVtOVV[J.OV y L V T (1 L O V (T I a.
R 2
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io7oa METAPHYSICA
There are three kinds of substance the matter, which is
10 a*
this in appearance (for all things that are characterized
by contact and not by organic unity are matter and sub-
i
9 stratum,e.
g. fire, flesh,head
;
for these are all
matter, andthe last matter is the matter of that which is in the full
1 1 sense substance T
) ;the nature, which is a this or positive
state towards which movement takes place ;and again,
thirdly, the particular substance which is composed of these
two, e. g. Socrates or Callias. Now in some cases the
4
this does not exist apart from the composite substance,
e.g. the form of house does not so exist, unless the art of
15 building exists apart (nor is there generation and de
struction of these forms, but it is in another way that the
house apart from its matter, and health, and all ideals of art,
exist and do not exist) ;but if the this exists apart from
the concrete thing, it is only in the case of natural
objects. And so Plato was not far wrong when he said
that there are as many Forms as there are kinds of natural
object (if there are Forms distinct from the things of this
21earth). The moving causes exist as things preceding the
effects, but causes in the sense of definitions are simultaneous
with their effects. For when a man is healthy, then health
also exists;and the shape of a bronze sphere exists at the
same timeas
the bronze sphere. (But we must examine25 whether any form also survives afterwards. For in some
cases there is nothing to prevent this;
e. g. the soul maybe of this sort not all soul but the reason; for presumably
it is impossible that all soul should survive.) Evidently
then there is no necessity, on this ground at least, for the
existence of the Ideas. For man is begotten by man, a given
man by an individual father ; and similarly in the arts ; for
30 the medical art is the formal cause of health.
The causes and the principles of different things are in 4
a sense different, but in a sense, if one speaks universally
and analogically, they are the same for all. For one might
raise the question whether the principles and elements are
1I adopt Alexander s suggestion that olov . .. reAevrma
(11. 19-20)
should be placed after {nr-jKfipevov (1. u).
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BOOK A. 4 io7oa
different or the same for substances and for relative terms,
and similarly in the case of each of the categories. But it 35
would be paradoxical if they were the same for all. For
then from the same elements will proceed relative terms
and substances. What then will this common element be ? io7ob
For(i) (a) there is nothing common to and distinct from sub
stance and the other categories, viz. those which are predi
cated;but an element is prior to the things of which it is
an element. But again (6)substance is not an element in
relative terms, nor is any of these an element in substance.
Further, (2)how can all things have the same elements ?
For none of the elements can be the same as that which 5
is composed of elements, e. g. b or a cannot be the same
as ba. (None, therefore, of the intelligibles,1
e. g. being or
unity, is an element;for these are predicable of each of
the compounds as well.) None of the elements, then, will
be either a substance or a relative term;
butit
must be oneor other. All things, then, have not the same elements.
Or, as we are wont to put it,in a sense they have and in 10
a sense they have not;
e. g. perhaps the elements of per
ceptible bodies are, zsform, the hot, and in another sense
the cold, which is the privation ; and, as matter, that
which directly and of itself potentially has these attributes;
and substances comprise both these and the things com
posed of these, of which these are the principles, or any unity
which is produced out of the hot and the cold, e. g. flesh or
bone;for the product must be different from the elements. 15
These things then have the same elements and principles
(though specifically different things have specifically differ
ent elements) ;but all things have not the same elements
in this sense, but only analogically ;i. e. one might say that
there are three principles the form, the privation, and the
matter. But each of these is different for each class;
e. g.20
in colour they are white, black, and surface, and in day and
night they are light, darkness, and air.
Since not only the elements present in a thing are causes,
but also
something external,i.e. the
moving cause, clearly1
This is apparently almost a technical name for the abstract termswhich are found in all the categories alike.
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io7ob METAPHYSICA
while*
principle and element are different both are causes,
and principle is divided into these two kinds 1: and that
which acts as producing movement or rest is a principle
25 and a substance. Thereforeanalogically
there are three
elements, and four causes and principles ;but the elements
are different in different things, and the proximate moving
cause is different for different things. Health, disease,
body; the moving cause is the medical art. Form, dis
order of a particular kind, bricks;the moving cause is the
30 building art. And since the moving cause in the case ol
natural things is for man, for instance, man, and in the
products ofthought the form or its contrary, there will be in
a sense three causes, while in a sense there are four. For
the medical art is in some sense health, and the building
art is the form of the house, and man begets man;
2
further, besides these there is that which as first of all
35 things moves all things.
Some things can exist apart and some cannot, and it is 5
io7iathe former that are substances. And therefore all things
have the same causes,3
because, without substances, modi
fications and movements do not exist. Further, these causes
will probably be soul and body, or reason and desire and
body.
And in yet another way, analogically identical things are
5 principles, i. e. actuality and potency ;but these also are
not only different for different things but also apply in
different ways to them. For in some cases the same
thing exists at one time actually and at another potentially,
e. g. wine or flesh or man does so. (And these too fall
under the above-named causes.4 For the form exists
actually, if it can exist apart, and so does the complex
of form and matter, and the privation, e. g. darkness or
10 disease;but the matter exists potentially ;
for this is that
1i.e. the principles which are elements and those which are not.
2i. e. the efficient cause is identical with the formal.
3i. e. the causes of substance are the causes of all things.
4i. e. the division into potency and actuality stands in a detinite
relation to the previous division into matter, form, and privation.r<>
e| a/z0oty is not strictly in point, but is suggested by the frequent
division of ova-ia into v\rj, eldos, and ro e aptyolv.
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BOOK A. 5 1071*
which can become qualified either by the form or by the
privation.) But the distinction of actuality and potentiality
applies in another way to cases where the matter of cause
and of effect is not the same, in some of which cases the
form is not the same but different;
e. g.the cause of man
is (i) the elements in man (viz. fire and earth as matter, and
the peculiar form), and further (2) something else outside,
i.e. the father, and (3) besides these the sun and its oblique 15
course, which are neither matter nor form nor privation of
man nor of the same species with him, but moving causes.1
Further, one must observe that some causes can be ex
pressed in universal terms, and some cannot. The proximate
principles of all things are the this which is proximate in
actuality, and another which is proximate in potentiality.2
The universal causes, then, of which we spoke:i do not
exist. For it is the individual that is the originative prin- 20
ciple
of the individuals. For while man is the
originativeprinciple of man universally, there is no universal man, but
Peleus is the originative principle of Achilles, and your
father of you, and this particular b of this particular ba,
though b in general is the originative principle of ba taken
without qualification.
Further, if the causes of substances are the causes of all
things, yet different things have different causes and elements,as was said
4;the causes of things that are not in the same 25
class, e. g. of colours and sounds, of substances and quan
tities, are different except in an analogical sense;and those
of things in the same species are different, not in species,
but in the sense that the causes of different individuals are
1Aristotle distinguishes two ways in which things may be related as
&vvafj.is and eWpyeia. (i) The same thing is <Wa/iei what it later comesto be evepyei a. But (2) one thing may be called Svvanis and another
eWpyeui though they have nothing in common. Here duvams and eWp-
yeia almost = cause and effect, and dvvafjus is the duvajus Kara Kivrjcriv
\eyofjievr) (transeunt potentiality or rather power) spoken of in (3. i.
The movement of the sun in the ecliptic is the cause of generation and
decay (Phys. ii. I94b
13, De Gen. et Corr. ii. 356* 3i-b9) and is thus
a transeunt dvvapis of each man who is born.2
e. g. the proximate causes of a child are the individual father (whoon Aristotle s view is the efficient and contains the formal cause) and
the germ contained in the individual mother (which is the material
cause).3
In 1. 17.4In io;o
b17.
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io7i* METAPHYSICA
different, your matter and form and moving cause being
different from mine, while in their universal definition they
3o are the same. And if we inquire what are the principles or
elements of substances and relations and qualities whetherthey are the same or different clearly when the names of
the causes are used in several senses the causes of each are
the same, but when the senses are distinguished the causes
are not the same but different, except that in the following
senses the causes of all are the same. They are (i) the
same or analogous in this sense, that matter, form, priva
tion, and the moving cause are common to all things ; and
(2) the causes of substances may be treated as causes of all
things in this sense, that when substances are removed all
35 things are removed; further, (3) that which is first in
respect of complete reality is the cause of all things. But
in another sense there are different1
first causes, viz. all
the contraries which are neither generic nor ambi
guous terms;
2
and, further, the matters of different things
io7ibare different. We have stated, then, what are the principles
of sensible things and how many they are, and in what
sense they are the same and in what sense different.
Since there were 8three kinds of substance, two of them 6
physical and one unmovable, regarding the latter we must
assert that it is necessary that there should be an eternal
5unmovable substance. For substances are the first of exist
ing things, and if they are all destructible, all things are
destructible. But it is impossible that movement should
either have come into being or cease to be (for it must
always have existed), or that time should. For there could
not be a before and an after if time did not exist. Move
ment also is continuous, then, in the sense in which time is;
for time is either the same thing as movement or an attri-
10 bute of movement. And there is no continuous movement
except movement in place, and of this only that which is
circular is continuous.
1First is now taken in the sense of proximate ,
not of* ultimate
as in TO
TrpcoTov(i>T(\e\(ia.
zSc. but taken as individual qualities. All things include f 8os and
<TTcpr)<ris,but each thing has a distinct ddos and oWpgo-if of its own.
8Cf. io69
a3o.
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BOOK A. 6 ioyib
But if there is something which is capable of moving
things or acting on them, but is not actually doing so, \there will not necessarily be movement
;for that which has
a potency need not exercise it. Nothing, then, is gained
even if we suppose eternal substances, as the believers in
the Forms do, unless there is to be in them some principle 15
which can cause change ; nay, even this is not enough, nor
is another substance besides the Forms enough ;for if it is
not to act, there will be no movement. Further, even if it
acts,this will not be
enough,if its essence is
potency;
for
there will not be eternal movement, since that which is
potentially may possibly not be. There must, then, be
such a principle, whose very essence is actuality. Further, 20
then, these substances must be without matter;for they
must be eternal, if anything is eternal. Therefore they
must be actuality.
Yet there is a difficulty ; for it is thought that everything
that acts is able to act, but that not everything that is able
to act acts, so that the potency is prior. But if this is so, 25
nothing that is need be;for it is possible for all things to
be capable of existing but not yet to exist.
Yet if we follow the theologians who generate the world
from night,1or the natural philosophers who say that
*
all
things were together ,
2 the same impossible result ensues.
For how will there be movement, if there is no actually
existing cause ? Wood will surely not move itself the
carpenter s art must act on it;nor will the menstrual blood 30
nor the earth set themselves in motion, but the seeds must
act on the earth and the semen on the menstrual blood.
This is
whysome
supposeeternal
actuality
e.
g. Leucip-pus
3 and Plato 4;for they say there is always movement.
But why and what this movement is they do not say, nor,
if the world moves in this way or that, do they tell us the
cause of its doing so. Now nothing is moved at random,
but there must always be something present to move it;
1
Cf. Hesiod, Op. et D. 17, Theog. 116 ff., Orpheus fr. 12, Diels,Musaeus fr. 14, Epimenides fr.
5,Acusilaus fr. i, 3, Aristoph. Av. 693.
2
Anaxagoras, fr. I.
3Cf. De Caelo, iii. 3oo
b8.
4Cf. Timaeus, 30 A.
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io7ib METAPHYSICA
35 e.g.
as a matter of fact a thing moves in one way by nature,
and in another by force or through the influence of reason
or something else. (Further, what sort of movement is
primary ? This makes a vast difference.) But again for
Plato, at least, it is not permissible to name here that which
iO72a he sometimes supposes to be the source of movement that
which moves itself;]
for the soul is later, and coeval with
the heavens, according to his account.2 To suppose potency
prior to actuality, then, is in a sense right, and in a sense
not;and we have specified these senses.
3 That actuality
5 is prior is testified by Anaxagoras (for his reason is
actuality) and by Empedocles in his doctrine of love and
strife, and by those who say that there is always movement,
e. g. Leucippus. Therefore chaos or night did not exist for an
infinite time, but the same things have always existed (either
passing through a cycle of changes or obeying some other
law),
since
actuality
is
prior
to
potency.If, then, there is
a constant cycle, something must always remain,4
acting in
J the same way. And if there is to be generation and de
struction, there must be something else5 which is always
acting in different ways. This must, then, act in one way
in virtue of itself, and in another in virtue of something else
either of a third agent, therefore, or of the first. Now it
must be in virtue of the first. For otherwise this againcauses the motion both of the second agent and of the third.
15 Therefore it is better to say the first . For it was the
cause of eternal uniformity ;and something else is the
cause of variety, and evidently both together are the cause
of eternal variety. This, accordingly, is the character which
the motions actually exhibit. What need then is there to
seek for other principles ?
Since (i) this is a possible account of the matter, and (2) 7
if it were not true, the world would have proceeded out
of night and 4
all things together6 and out of non-being,
20 these difficulties may be taken as solved. There is, then,
1Cf. Phaedrus, 245 C; Laivs, 894 E.
2Cf.
Timaeus, 346.
3Cf.
io;i
b22-26.
4i. e. the sphere of the fixed stars.
Gi. e. the sun. Cf. De Gen. et Corr. ii. 336* 23 ff.
6
Anaxagoras, fr. i.
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BOOK A. 7 i072a
something which is always moved with an unceasing motion,
which is motion in a circle;and this is plain not in theory
only but in fact. Therefore the first heaven 1 must be
eternal. There is therefore also something which moves it.
And since that which is moves and moved is intermediate,
there is something which moves without being moved,
being eternal, substance, and actuality. And the object of 25
desire and the object of thought move in this way ; they
move without being moved. The primary objects of desire
and ofthought
are the same. For theapparent good
is the
object of appetite, and the real good is the primary object
of rational wish. But desire is consequent on opinion
rather than opinion on desire;
for the thinking is the
starting-point. And thought is moved by the object of 30
thought, and one of the two columns of opposites2
is in
itself the object of thought ;and in this, substance is first,
and in substance, that which is simple and exists actually.
(The one and the simple are not the same;for one means
a measure, but simple means that the thing itself has
a certain nature.) But the beautiful, also, and that which is
in itself desirable are in the same column;and the first in 35
any class is always best, or analogous to the best.3
That a final cause may exist among unchangeable en- iO72b
tities is shown by the distinction of its meanings. For the
final cause is (a) some being for whose good an action is
done, and (b) something at which the action aims;and of
these the latter exists among unchangeable entities though
the former does not. The final cause, then, produces motion
as being loved, but all other things move by being moved.
1
i. e. the outer sphere of the universe, that in which the fixed stars
are set.
2Cf. note on A. 986*23.
3Sc. where there is no best in the strict sense. The argument for
the identity of the primary forms of TO opfKrov and TO VOI]TOV is not very
clearly stated, but seems to be as follows. The opfKrov is the Ka\6i>.
(In parenthesis it is stated that desire depends on thought rather than
thought ondesire.) The positive side of the list ot contraries is the
object of thought, and the first term on this side (which must be the
primary object of thought) is simple actual substance. But the objectof desire, which we have seen to be the Ka\of, is on the same side of the
list, and therefore the first member of that list (the primary object of
thought) must be the primary object of desire.
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io72b
METAPHYSICA
Now if something is moved it is capable of being otherwise
5 than as it is. Therefore if its actuality is the primary form
of spatial motion, then in so far as it is subject to change,
in this respect it is capable of being otherwise, in place,
even if not in substance. But since there is somethingwhich moves while itself unmoved, existing actually, this
can in no way be otherwise than as it is. For motion in
space is the first of the kinds of change, and motion in
a circle the first kind of spatial motion;and this the first
10 mover produces?- The first mover, then, exists of necessity ;
and in so far as it exists by necessity, its mode of being is
good,2 and it is in this sense a first principle. For the
necessary has all these sensesthat which is necessary
perforce because it is contrary to the natural impulse, that
without which the good is impossible, and that which can
not be otherwise but can exist only in a single way.
On such aprinciple, then, depend
theheavens and the
world of nature. And it is a life such as the best which we
15 enjoy, and enjoy for but a short time (for it is ever in this
state, which we cannot be), since its actuality is also
pleasure. (And for this reason3are waking, perception, and
thinking most pleasant, and hopes and memories are so
on account of these.) And thinking in itself deals with
that which is best in itself, and that which is thinking
in the fullest sense with that which is best in the fullest
sense. And thought thinks on itself because it shares the
20 nature of the object of thought ;for it becomes an object
of thought in coming into contact with and thinking
its objects, so that thought and object of thought are the
same. For that which is capable of receiving the object of
thought, i. e. the essence, is thought. But it is active when
it possesses this object. Therefore the possession rather
than the receptivity is the divine element which thought
seems to contain, and the act of contemplation is what is
1If it had any movement, it would have the first. But it produces
this and therefore cannot share in it;for if it did, we should have to
look for something that is prior to the first mover and imparts this
motion to it.2
i. e. it is necessary in the sense of/jn] ev^f\6^vov aXXcos e
^ft",and is
. . good.3
Sc. because they are activities or actualities.
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BOOK A. 7 io72b
most pleasant and best. If, then, God is always in that
good state in which we sometimes are, this compels our
wonder;and if in a better this compels it yet more. And 25
God ts in a better state. And life also belongs to God;for
the actuality of thought is life, and God is that actuality; and
God s self-dependent actuality is life most good and eternal.
We say therefore that God is a living being, eternal, most
good, so that life and duration continuous and eternal
belong to God;for this is God.
Those whosuppose,
as thePythagoreans
l andSpeusip- 30
pus2do, that supreme beauty and goodness are not present
in the beginning, because the beginnings both of plants and
of animals are causes, but beauty and completeness are in
the effects of these,3 are wrong in their opinion. For the 35
seed comes from other individuals which are prior and
complete, and the first thing is not seed but the complete
being ; e. g. we must say that before the seed there is io73a
a man, not the man produced from the seed, but another
from whom the seed comes.
It is clear then from what has been said that there is
a substance which is eternal and unmovable and separate
from sensible things. It has been shown also that this 5
substance cannot have any magnitude, but is without parts
and indivisible (for it produces movement through infinite
time, but nothing finite has infinite power; and, while every
magnitude is either infinite or finite, it cannot, for the above
reason, have finite magnitude, and it cannot have infinite 10
magnitude because there is no infinite magnitude atall).
But
it has also been shown that it is impassive and unalterable;
for all the other
changes
are
posterior
to4
change
of place.
8 It is clear, then, why these things are as they are. But
we must not ignore the question whether we have to
suppose one such substance or more than one, and if the
latter, how many ;we must also mention, regarding the
15
opinions expressed by others, that they have said nothing
about the number of the substances that can even be clearly
1
Cf. io75a
36.2
Cf. Z. io2Sb2i, N. I09i
a
34, io92a
u.;
i. e. the animal or plant is more beautiful and perfect than the
seed.4
i. e. impossible without.
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io73a METAPHYSICA
stated. For the theory of Ideas has no special discussion
of the subject ;for those who speak of Ideas say the Ideas
are numbers, and they speak of numbers now as unlimited,
20 now1
as limited by the number 10; but as for the reason
why there should be just so many numbers, nothing is said
with any demonstrative exactness. We however must dis
cuss the subject, starting1 from the presuppositions and
distinctions we have mentioned. The first principle or
primary being is not movable either in itself or accident-
25 ally, but produces the primary eternal and single movement.
But since that which is moved must be moved by something,
and the first mover must be in itself unmovable, and eter
nal movement must be produced by something eternal and
a single movement by a single thing, and since we see that be
sides the simple spatial movement of the universe, which we
3o say the first and unmovable substance produces, there are
otherspatial
movements those of the
planetswhich are
eternal (for a body which moves in a circle is eternal and
unresting ;we have proved these points in the physical
treatises2
),each of these movements also must be caused by
a substance both unmovable in itself and eternal. For the
nature of the stars3
is eternal just because it is a certain kind
35 ofsubstance, and the mover is eternal and prior to the moved,
and that which is prior to a substance must be a substance.
Evidently, then, there must be substances which are of the
same number as the movements of the stars, and in their
nature eternal, and in themselves unmovable, and without
magnitude, for the reason before mentioned.4
iO73b That the movers are substances, then, and that one of
these is first and another second according to the same
order as the movements of the stars, is evident. But in the
number of the movements we reach a problem which must
be treated from the standpoint of that one of the mathe
matical sciences which is most akin to philosophy viz. of
5 astronomy ;for this science speculates about substance
1 The reference is to Plato Ccf. Phys. 2c6b 32).2
Cf.
Phys.viii.
8, 9;
DeCaelo,
i.
2,ii.
3-8.3 This is to be understood as a general term including both fixed
stars and planets.4
Cf. 11. 5-n.
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BOOK A. 8 io73b
which is perceptible but eternal, but the other mathema
tical sciences, i.e. arithmetic and geometry, treat of no
substance. That the movements are more numerous than
the bodies that are moved is evident to those who have
given even moderate attention to the matter;for each of
the planets has more than one movement. But as to the 10
actual number of these movements, we now to give some
notion of the subject quote what some of the mathema
ticians say, that our thought may have some definite number
to grasp ; but, for the rest, we must partly investigate for
ourselves, partly learn from other investigators, and if those 1 5
who study this subject form an opinion contrary to what we
have now stated, we must esteem both parties indeed, but
follow the more accurate.
Eudoxus supposed that the motion of the sun or of the
moon involves, in either case, three spheres, of which the
first is the sphere of the fixed stars, and the second moves
in the circle which runs along the middle of the zodiac, and 20
the third in the circle which is inclined across the breadth
of the zodiac;but the circle in which the moon moves is
inclined at a greater angle than that in which the sun moves
And the motion of the planets involves, in each case, four
spheres, and of these also the first and second are the same
as the first
two mentioned above (for the sphereof
the fixed 25
stars is that which moves all the other spheres, and that
which is placed beneath this and has its movement in the
circle which bisects the zodiac is common toall),
but the
poles of the third sphere of each planet are in the circle
which bisects the zodiac, and the motion of the fourth
sphere is in the circle which is inclined at an angle to the
equator of the third sphere ; and the poles of the third sphere 30
are different for each of the other planets, but those of
Venus and Mercury are the same.
Callippus made the position of the spheres the same as
Eudoxus did, but while he assigned the same number as
Eudoxus did to Jupiter and to Saturn, he thought two 35
more spheres should be added to the sun and two to the
moon, if one is to explain the observed facts;and one more
to each of the other planets.
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io73b METAPHYSICA
But it is necessary, if all the spheres combined are to
explain the observed facts, that for each of the planets
there should be other spheres (one fewer than those hither
to assigned) which counteract those already mentioned and
bring- back to the same position the outermost sphere of
the star which in each case is situated below 1the star in
5 question ;for only thus can all the forces at work produce
the observed motion of the planets. Since, then, the spheres
involved in the movement of the planets themselves are-
eight for Saturn and Jupiter and twenty-five for the others,
and of these only those involved in the movement of the
lowest-situated planet need not be counteracted, the spheres
which counteract those of the outermost two planets will
be six in number, and the spheres which counteract those
I0 of the next four planets will be sixteen : therefore the
number of all the spheres both those which move the
planetsand those which counteract these will be
fifty-five.And if one were not to add to the moon and to the sun the
movements we mentioned,2the whole set of spheres will be
forty-seven in number.
Let this, then, be taken as the number of the spheres,
15 so that the unmovable substances and principles also may
probably be taken as just so many ;the assertion of neces
sity must be left to more powerful thinkers. But if there
can be no spatial movement which does not conduce to the
moving of a star, and if further every being and every
substance which is immune from change and in virtue of
itself has attained to the best must be considered an end,
20 there can be no other being apart from these we have
named, but this must be the number of the substances.
For if there are others, they will cause change as being
a final cause of movement;but there cannot be other
movements besides those mentioned. And it is reasonable
to infer this from a consideration of the bodies that are
25 moved ;for if everything that moves is for the sake of that
which is moved, and every movement belongs to something
1i. e. inwards from, the universe being thought of as a system of
concentric spheres encircling the earth.2In I073
b35, 38-1074*4.
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BOOK A. 8 i074a
that is moved, no movement can be for the sake of itself or
of another movement, but all the movements must be for
the sake of the stars. For if there is to be a movement for
the sake of a movement, this latter also will have to be
for the sake of something else;so that since there cannot be
an infinite regress, the end of every movement will be one 30
of the divine bodies which move through the heaven.1
(Evidently there is but one heaven. For if there are
many heavens as there are many men, the moving principles,
of which each heaven will have one, will be one in form but
in number many. But all things that are many in number
have matter;
for one and the same definition, e. g. that
of man, applies to many things, while Socrates is one.2 But 35
the primary essence has not matter;
for it is complete,
reality. So the unmovable first mover is one both in defini
tion and in number;
so too, therefore, is that which is
movedalways
andcontinuously
;
therefore there is one
heaven alone.)3
Our forefathers in the most remote ages have handed iO74b
down to their posterity a tradition, in the form of a myth,
that these bodies are gods and that the divine encloses the
whole of nature. The rest of the tradition has been added
later in mythical form with a view to the persuasion of the
multitude and to its legal and utilitarian expediency ; they 5
say these gods are in the form of men or like some of the
other animals, and they say other things consequent on and
similar to these which we have mentioned. But if one were
to separate the first point from these additions and take
it alone that they thought the first substances to be gods,
one must regard this as an inspired utterance, and reflect 10
that, while probably each art and each science has often
1 The argument is : Each unchangeable perfect substance is an end
and must cos6/>eKrdz> produce a distinct motion. But every motion is
ultimately for the sake of a<f)(p6fj.(t>ov,
and as we have enumerated the
motions necessary for the fapdpcva, there can be no more motions and
therefore no more unchangeable perfect substances.2
i. e. the \6yos is common to all men, so that it must be matter
which gives Socrates his uniqueness,3 This paragraph appears to be an early fragment embedded in
a chapter written rather late in Aristotle s life, ovroi in b3 refers back
to rooi/(frepofjLevcov 6ei<av
(ra)/Lidra)j/in a
30.
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io74b METAPHYSICA
been developed as far as possible and has again perished,
these opinions, with others, have been preserved until the
present like relics of the ancient treasure. Only thus far,
then, is the opinion of our ancestors and of our earliest
predecessors clear to us.
15 The nature of the divine thought involves certain pro- 9
blems;for while thought is held to be the most divine of
things observed by us, the question how it must be situated in
order to have that character involves difficulties. For if it
thinks ofnothing,what is there here ofdignity ? It is just like
one who sleeps. And if it thinks, but this depends on
something else, then (since that which is its substance is not
the act of thinking, but a potency) it cannot be the best
20 substance;for it is through thinking that its value belongs
to it. Further, whether its substance is the faculty of thought
or the act of thinking, what does it think of ? Either of itselt
or of something else; and if of something else, either of the
same thing always or ofsomething different. Does it matter,
then, or not, whether it thinks of the good or ofany chance
25 thing ? Are there not some things about which it is incredible
that it should think? Evidently, then, it thinks ofthat which is
most divine and precious, and it does not change ;for change
wouldbe
changefor the
worse,and this would be
alreadya movement. 1
First, then, if thought is not the act of
thinking but a potency, it would be reasonable to suppose
that the continuity of its thinking is wearisome to it.
Secondly, there would evidently be something else more
30 precious than thought, viz. that which is thought of. For both
thinking and the act ofthought will belong even to one who
thinks of the worst thing in the world, so that if this ought
to be avoided (and it ought, for there are even some things
which it is better not to see than to see), the act of thinking
cannot be the best of things. Therefore it must be of itself
that the divine thought thinks (since it is the most excellent
of things), and its thinking is a thinking on thinking.
35 But evidently knowledge and perception and opinion
and understanding have always something else as their
1Sc. while vovs is ex hypothesi unmovable.
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BOOK A. 9 i074b
object, and themselves only by the way. Further, if think
ing and being thought of are different, in respect of which
does goodness belong to thought ? For to be an act of think
ing and to <e an object of thought are not the same thing.
We answer that in some cases the knowledge is the object. In
the productive sciences it is the substance or essence of the
object, matter omitted, and in the theoretical sciences the
definition or the act of thinking is the object. Since, then,
thought and the object of thought are not different in the
case of things that have not matter, the divine thought and
its object will be the same, i. e. the thinking will be one
with the object of its thought.
A further question is left whether the object ofthe divine 5
thought is composite ;for if it were, thought would change
in passing from part to part of the whole. We answer that
everything which has not matter is indivisible as human
thought,
or rather the
thoughtof
composite beings,
is in
a certain period of time (forit does not possess the good at
this moment or at that, but its best, being something different
from it, is attained only in a whole period of time), so 10
throughout eternity is the thought which has itself for its
object.
IO We must consider also in which of two ways the natureof the universe contains the good and the highest good,
whether as something separate and by itself, or as the order
of the parts. Probably in both ways, as an army does;
for its good is found both in its order and in its leader,
and more in the latter; for he does not depend on the 15
order but it depends on him. And all things are ordered
together somehow, but not all alike, both fishes and fowls
and plants ;and the world is not such that one thing has
nothing to do with another, but they are connected. For
all are ordered together to one end, but it is as in a house,
where the freemen are least at liberty to act at random, but 20
all things or most things are already ordained for them,
while the slaves and the animals do little for the common
good, and for the most part live at random;for this is the
sort of principle that constitutes the nature of each. I mean,
S 2
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io75a METAPHYSICA
for instance, that all must at least come to be dissolved into
their elements,1 and there are other functions similarly in
which all share for the good of the whole.
25 We must not fail to observe how many impossible or
paradoxical results confront those who hold different views
from our own, and what are the views of the subtler thinkers,
and which views are attended by fewest difficulties. All make
all things out of contraries. But neither all things nor*
out
of contraries is right ;nor do these thinkers tell us how all
the things in which the contraries are present can be made
3 out of the contraries;for contraries are not affected by one
another. Now for us this difficulty is solved naturally bythe fact that there is a third element.
2 These thinkers how
ever make one of the two contraries matter;this is done
for instance by those who make the unequal matter for the
equal, or the many matter for the one.3
But this also is
refuted in the same way; for the one matter which underlies
any pair of contraries is contrary to nothing. Further, all
things, except the one, will, on the view we arecriticizing,
35 partake of evil;for the bad itself is one of the two elements.
But the other school 4 does not treat the good and the bad
even as principles ; yet in all things the good is in the
highest degree a principle. The school we first mentioned
is right in saying that it is a principle, but how the good is
a principle they do not say whether as end or as mover or
as form.
IO75 Empedocles5also has a paradoxical view
;for he identi
fies the good with love, but this is a principle both as
mover (for it brings things together) and as matter (for it is
part of the mixture). Now even if it happens that the same
5 thing is a principle both as matter and as mover, still the
being, at least, of the two is not the same. In which respect
then is love a principle ? It is paradoxical also that strife
1Sc. in order that higher forms of being may be produced by new
combinations of the elements.2
i. e. the substratum.3 The reference is to Platonists.
The reference is to the Pythagoreans and Speusippus ;cf. A. 1072
b3I6
Cf. A. 985* 4.
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BOOK A. 10 i075b
should be imperishable ;the nature of his
*
evil is just
strife.
Anaxagoras makes the good a motive principle ;for his
reason moves things. But it moves them for an end, whichmust be something other than it, except according to our
way of stating the case; for, on our view, the medical art is
in a sense health. It is paradoxical also not to suppose 10
a contrary to the good, i. e. to reason. But all who speak
of the contraries make no use of the contraries, unless we
bring their views into shape. And why some things are
perishable and others imperishable, no one tells us;for they
make all existing things out of the same principles. Further,
some make existing things out of the non-existent;and T 5
others to avoid the necessity of this make all things one.
Further, why should there always be becoming, and what
is the cause of becoming ? this no one tells us. And those
whosuppose
twoprinciples
must
supposeanother, a
superiorprinciple, and so must those who believe in the Forms; for
why did things come to participate, or why do they parti
cipate, in the Forms? And all other thinkers 1are con- 20
fronted by the necessary consequence that there is something
contrary to Wisdom, i.e. to the highest knowledge ;but we
are not. For there is nothing contrary to that which is
primary;
for all contraries have matter, and things thathave matter exist only potentially ;
and the ignorance which
is contrary to any knowledge leads to an object contrary to
the object of the knowledge2
;but what is primary has
no contrary.
Again, if besides sensible things no others exist, there 25
will be no first principle, no order, no becoming, no
heavenly bodies, but each principle will have a principle
before it, as in the accounts of the theologians and all the
natural philosophers. But if the Forms or the numbers
are to exist, they will be causes of nothing ;or if not that,
at least not of movement. Further, how is extension, i. e.
1 The special reference is to Plato;
cf. Rep. 477.2
If there were an ignorance contrary to philosophy, it would havean object contrary to TO
TT/JWTOI;, which is the object of philosophy. But
TOnpa>Tov
has no contrary.
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io75b METAPHYSICA
a continuum, to be produced out of unextended parts ?
For number will not, either as mover or as form, produce
30 a continuum. But again there cannot be any contrary that
is
also essentially a productive or moving principle;
for it
would be possible for it not to be.1 Or at least its action would
be posterior to its potency. The world, then, would not
be eternal. But it is;one of these premisses, then, must be
denied. And we have said how this must be done.2
Further, in virtue of what the numbers, or the soul and the
35 body, or in general the form and the thing, are one of this
no one tells us anything ; nor can any one tell, unless he
says, as we do, that the mover makes them one. And
those who sayamathematical number is first and go on to
generate one kind of substance after another and give
iO76adifferent principles for each, make the substance of the
universe a mere series of episodes (for one substance has
no influence on another by its existence or non-existence),
and they give us many governing principles ;but the world
refuses to be governed badly.
The rule of many is not good ;one ruler let there be.
4
1Since contraries must contain matter, and matter implies potentiality
and contingency.2
Cf. I07ibi9, 20.
8
Speusippus is meant;
cf. Z. io28 b2i, N. iO9o
b13-20.
4 Cf. Iliad) ii. 204.
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BOOK M
WE have stated what is the substance of sensible things,
dealing in the treatise on physics with matter, and later2
with the substance which has actual existence. Now since 10
our inquiry is whether there is or is not besides the sensible
substances any which is immovable and eternal, and, if
there is, what it is, we must first consider what is said
byothers, so that, if there is anything which they say wrongly,
we may not be liable to the same objections, while, if there
is any opinion common to them and us, we shall have no
private grievance against ourselves on that account; for 15
one must be content to state some points better than one s
predecessors, and others no worse.
Two opinions are held on this subject; it is said that the
objects of mathematics i. e. numbers and lines and the like
are substances, and again that the Ideas are substances.
And since (i) some recognize these as two different classes
the Ideas and the mathematical numbers, and (2) some 20
recognize both as having one nature, while (3) some others
say that the mathematical substances are the only sub
stances,15
we must consider first 4 the objects of mathematics,
not qualifying them by any other characteristic not ask
ing, for instance, whether they are in fact Ideas or not, or
whether they are the principles and substances of existing
things or not, but only whether as objects of mathematics 25
they exist or not, and if they exist, how they exist.
Then after this we must separately consider5
the Ideas
themselves in a general way, and only as far as the accepted
mode of treatment demands;
for most of the points have
been repeatedly made even by the discussions outside our
school, and, further, the greater part of our account must
finish by throwing light on that inquiry, viz. when we 30
1
Phys. i.
&
Met. ZH0.3
Plato, Xenocrates, and the Pythagoreans and Speusippus,respectively, are meant.
4Cf. chs. 2, 3.
5Cf. chs. 4, 5.
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io76a METAPHYSICA
examine l whether the substances and the principles ot
existing things are numbers and Ideas;for after the dis
cussion of the Ideas this remains as a third inquiry.
If the objects of mathematics exist, they must exist either
in sensible objects, as some say, or separate from sensible
35 objects (and this also is said by some) ;or if they exist in
neither of these ways, either they do not exist, or they
exist only in some special sense. So that the subject of
our discussion will be not whether they exist but how they
exist.
That it is impossible for mathematical objects to exist in 2
sensible things, and at the same time that the doctrine in
question is an artificial one, has been said already in our
discussion of difficulties2
;we have pointed out that it is
IO76 impossible for two solids to be in the same place, and also
that according to the same argument the other powers and
characteristics also3 should exist in sensible
thingsand
none of them separately. This we have said already. But,
further, it is obvious that on this theory it is impossible for
5 any body whatever to be divided;for it would have to be
divided at a plane, and the plane at a line, and the line at
a point, so that if the point cannot be divided, neither can
the line, and if the line cannot, neither can the plane nor
the solid. What difference, then, does it make whethersensible things are such indivisible entities, or, without
10 being so themselves, have indivisible entities in them ? The
result will be the same;
if the sensible entities are divided
the others will be divided too, or else not even the sensible
entities can be divided.
But, again, it is not possible that such entities should
exist separately. For if besides the sensible solids there
are to be other solids which are separate from them and
prior to the sensible solids, it is plain that besides the
15 planes also there must be other and separate planes and
points and lines;for consistency requires this. But if these
exist, again besides the planes and lines and points of the
1
Cf. chs. 6-9.
2
Cf. B. 998a
;-i9.8 Which nevertheless the theory in question represents as Ideas
apart from sensible things.
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BOOK M. 2 1076*
mathematical solid there must be others which are separate.
(For incomposites are prior to compounds ;and if there
are, prior to the sensible bodies, bodies which are not
sensible, by the same argument the planes which exist by 20
themselves must be prior to those which are in the motion
less solids. Therefore these will be planes and lines other
than those that exist along with the mathematical solids to
which these thinkers assign separate existence;
for the
latter exist along with the mathematical solids, while the
others are prior to the mathematical solids.) Again, there
fore, there will be, belonging to these planes, lines, and 25
prior to them there will have to be, by the same argument,
other lines and points ;and prior to these points in the
prior lines there will have to be other points, though there
will be no others prior to these. Now(i)the accumulation
becomes absurd;
for we find ourselves with one set of
solids apart from the sensible solids;three sets of planes 30
apart from the sensible planes those which exist apart
from the sensible planes, and those in the mathematical
solids, and those which exist apart from those in the
mathematical solids;
four sets of lines, and five sets of
points. With which of these, then, will the mathematical
sciences deal ? Certainly not with the planes and lines and
points
in the motionless solid;for science
alwaysdeals with 35
what is prior. And(2)
the same account will apply also to
numbers;for there will be a different set of units apart from
each set of points,and also apart from each set ofrealities, from
the objects of sense and again from those of thought ;so that
there will be various classes of mathematical numbers.
Again, how is it possible to solve the questions which we
have already enumerated in our discussion of difficulties
l
?
For the objects of astronomy will exist apart from sensible IO77a
things just as the objects of geometry will;but how is it
possible that a heaven and its parts or anything else
which has movement should exist apart ? Similarly also
the objects of optics and of harmonics will exist apart ;
for there will be both voice and sight besides the sensible or 5
individual voices and sights. Therefore it is plain that the
1B. 997^ 12-34.
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io77a METAPHYSICA
other senses as well, and the other objects of sense, will
exist apart ; for why should one set of them do so and
another not ? And if this is so, there will also be animals
existing apart, since there will be senses.
Again, there are certain mathematical theorems that are
10 universal, extending beyond these substances. Here then
we shall have another intermediate substance separate both
from the Ideas and from the intermediates,1 a substance
which is neither number nor points nor spatial magnitude
nor time. And if this is impossible, plainly it is also
impossible that \hzformer entities should exist separate
from sensible things.
And, in general, conclusions contrary alike to the truth
15 and to the usual views follow, if one is to suppose the
objects of mathematics to exist thus as separate entities.
For because they exist thus they must be prior to sensible
spatialmagnitudes,
but in truth they must be posterior ;
for the incomplete spatial magnitude is in the order of
generation prior, but in the order of substance posterior,
as the lifeless is to the living.
20 Again, by virtue of what, and when, will mathematical
magnitudes be one ? For things in our perceptible world
are one in virtue of soul, or of a part of soul, or of something
else that is reasonable enough;
2
when these are not present,
the thing is a plurality, and splits up into parts. But in the
case of the subjects of mathematics, which are divisible and
are quantities, what is the cause of their being one and
holding together ?
Again, the modes of generation of the objects of mathe
matics show that we are right. For the dimension first
25 generated is length, then comes breadth, lastly depth, and the
process is complete. If, then, that which is posterior in
the order ofgeneration is prior in the order of substantiality,
the solid will be prior to the plane and the line. And in
this way also it is both more complete and more whole,
because it can become animate. How, on the other hand,
1 A Platonic expression for ra padyuanmi, which were regarded as
intermediate between Ideas and sensible things.2
Reading in 1. 22 euAoyw.
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BOOK M. 2 io77a
could a line or a plane be animate ? The supposition passes 30
the power of our senses.
Again, the solid is a sort of substance;for it already has
in a sense completeness. But how can lines be substances ?
Neither as a form or shape, as the soul perhaps is, nor as
matter, like the solid;for we have no experience of any
thing that can be put together out of lines or planes or
points, while if these had been a sort of material substance, 35
we should have observed things which could be put to
gether out of them.
Grant, then, that they are prior in definition. Still not all iO77b
things that are prior in definition are also prior in substan
tiality. For those things are prior in substantiality which
when separated from other things surpass them in the
power of independent existence, but things are prior in
definition to those whose definitions are compounded out of
their definitions;and these two properties are not co-ex
tensive. For if attributes do not exist apart from their sub- 5
stances (e.g. a mobile or a pale ), pale is prior to the pale
man in definition, but not in substantiality. For it cannot
exist separately, but is always along with the concrete thing;
and by the concrete thing I mean the pale man. There
fore it is plain that neither is the result of abstraction prior
nor that which is produced by adding determinants posterior
;for it is by adding a determinant to pale that we 10
speak of the pale man.
It has, then, been sufficiently pointed out that the objects
of mathematics are not substances in a higher degree than
bodies are, and that they are not prior to sensibles in being,
but only in definition, and that they cannot exist some
where apart. But since it was not possible for them to
exist in sensibles either,1
it is plain that they either do 15
not exist at all or exist in a special sense and therefore
do not exist without qualification. For exist has many
3 senses. For just as the universal propositions of mathematics
deal not with objects which exist separately, apart from ex
tended magnitudes and from numbers, but with magnitudes
and numbers, not however qita such as to have magnitude or
1Cf. I076
a38-
b u.
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io77b METAPHYSICA
20 to be divisible,1
clearly it is possible that there should also
be both propositions and demonstrations about sensible
magnitudes, not however qua sensible but qua possessed
of certain definite qualities.
2
For as there are many propositions about things merely considered as in motion, apart
25 from what each such thing is and from their accidents, and
as it is not therefore necessary that there should be either
a mobile separate from sensibles, or a distinct mobile entity
in the sensibles, so too in the case of mobiles there will
be propositions and sciences, which treat them however
not qua mobile but only qua bodies, or again only q^la
30 planes, or only qua lines, or qua divisibles, or qua indivi
sibles having position, or only qua indivisibles. Thus since
it is true to say without qualification that not only things
which are separable but also things which are inseparable
exist (for instance, that mobiles exist), it is true also to say
withoutqualification
that theobjects
of mathematics exist,
and with the character ascribed to them by mathematicians.
And as it is true to say of the other sciences too, without
qualification, that they deal with such and such a subject
35 not with what is accidental to it(e. g. not with the pale, if
the healthy thing is pale, and the science has the healthy
as its subject), but with that which is the subject of each
io78ascience with the healthy if it treats its object qua healthy,
with man if qua man : so too is it with geometry ;if its
subjects happen to be sensible, though it does not treat
them qua sensible, the mathematical sciences will not for
that reason be sciences of sensibles nor, on the other
5 hand, of other things separate from sensibles. Many
properties attach to things in virtue of their own nature
as possessed of each such character;
e. g. there are attri
butes peculiar to the animal qiia female or qua male (yet
there is no female nor male separate from animals) ;
so that there are also attributes which belong to things
merely as lengths or as planes. And in proportion as we
1Cf. E. 1026*25, M. io;7
a9.
2i. e. as universal mathematics abstracts from the distinctions
between different kinds of /za^/zartKa, so geometry abstracts from the
sensible characteristics of magnitudes and attends only to their spatial
relations.
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BOOK M. 3 1078
are dealing with things which are prior in definition and
simpler, our knowledge has more accuracy, i. e. simplicity,ro
Therefore a science which abstracts from spatial magnitude
is more precise than one which takes it into account ; and
a science is most precise if it abstracts from movement, but
if it takes account of movement, it is most precise if it deals
with the primary movement, for this is the simplest ;and
of this again uniform movement is the simplest form.
The same account may be given of harmonics and optics ;
for neither considers its objects qua sight or qua voice, but [ 5
qua lines and numbers;but the latter are attributes proper
to the former. And mechanics too proceeds in the same
way. Therefore if we suppose attributes separated from
their fellow-attributes and make any inquiry concerning
them as such, we shall not for this reason be in error, any
more than when one draws a line on the ground and calls
it a footlong when
it is
not;
forthe
error is notincluded
ao
in the premisses.
Each question will be best investigated in this way by
setting up by an act of separation what is not separate, as
the arithmetician and the geometer do. For a man quaman is one indivisible thing ;
and the arithmetician supposed
one indivisible thing, and then considered whether any attri
bute belongs to a man qua indivisible. But the geometer 35
treats him neither qita man nor qzta indivisible, but as
a solid. For evidently the properties which would have
belonged to him even if perchance he had not been indivi
sible, can belong to him even apart from these attributes.1
Thus, then, geometers speak correctly ; they talk about
existing things, and their subjects do exist;
for being has 3
two forms it exists not only in complete reality but also
materially.
Now since the good and the beautiful are different (for
the former always implies conduct as its subject, while the
beautiful is found also in motionless things), those who
assert that the mathematical sciences say nothing of the
beautiful or the good2are in error. For these sciences say
1Sc. indivisibility and humanity.
2 The reference is apparently to Aristippus ;cf. B. 996*32.
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io78a METAPHYSICA
35 and prove a great deal about them;
ifthey do not expressly
mention them, but prove attributes which are their results
or their definitions, it is not true to say that they tell us
nothing about them. The chief forms of beauty are order
iO78b and symmetry and definiteness, which the mathematical
sciences demonstrate in a special degree. And since these
(e. o-. order and definiteness) are obviously causes of many
things, evidently these sciences must treat this sort of causa
tive principle also(i.
e. the beautiful) as in some sense
5 a cause. But we shall speak more plainly elsewhere l about
these matters.
So much then for the objects of mathematics;we have 4
said that they exist and in what sense they exist,2 and in
what sense they are prior and in what sense not prior/
Now, regarding the Ideas, we must first examine the
10 ideal theory itself, not connecting it in any way with the
nature of numbers, but treating it in the form in which
it wras originally understood by those who first maintained
the existence of the Ideas. The supporters of the ideal
theory were led to it because on the question about the
truth of things they accepted the Heraclitean sayings which
15 describe all sensible things as ever passing away, so that if
knowledge or thoughtis to
havean
object, there must besome other and permanent entities, apart from those which
are sensible;for there could be no knowledge of things
which were in a state of flux. But when Socrates was
occupying himself with the excellences of character, and
in connexion with them became the first to raise the
problem of universal definition (for of the physicists Demo-
20 critus only touched on the subject to a small extent, and
defined, after a fashion, the hot and the cold;while the
Pythagoreans had before this treated of a few things, whose
definitions -e. g. those of opportunity, justice, or marriage4
they connected with numbers;but it was natural that
Socrates should be seeking the essence, for he was seeking to
syllogize, and what a thing is is the starting-point of syllo-1
Apparently an unfulfilled promise.2Chs. 2, 3.
*
io;7a17-20, 24-
bii.
4Cf. Diels, Vorsokratiker^ ed. 3, i. 346. 27-347. 11.
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BOOK M. 4 1078*
gisms; for there was as yet none ofthe dialectical power which 25
enables people even without knowledge of the essence to
speculate about contraries and inquire whether the same
science deals with contraries ; for two things may be fairly
ascribed to Socrates inductive arguments and universal
definition, both of which are concerned with the starting-
point of science) : but Socrates did not make the universals 3
or the definitions exist apart ; they, however, gave them
separate existence, and this was the kind of thing they
called Ideas. Therefore it followed for them, almost by the
same argument, that there must be Ideas of all things that
are spoken of universally, and it was almost as if a man
wished to count certain things, and while they were few
thought he would not be able to count them, but made 35
more of them and then counted them;for the Forms are, one
may say, more numerous than the particular sensible things,
yetit was in
seekingthe causes of these that
they pro- 1079*ceeded from them to the Forms. For to each thing there
answers an entity which has the same name ] and exists apart
from the substances, and so also in the case of all other
groups there is a one over many, whether these be of this
world or eternal.
Again, of the ways in which it is proved that the Forms
exist, none is convincing; for from some no inference 5
necessarily follows, and from some arise Forms even of
things of which they think there are no Forms. For
according to the arguments from the sciences there will be
Forms of all things of which there are sciences, and accord
ing to the argument of the one over many there will be
Forms even of negations, and according to the argument 10
that thought has an object when the individual object has
perished, there will be Forms of perishable things ;for we
have an image of these. Again, of the most accurate argu
ments, some lead to Ideas of relations, of which they say
there is no independent class, and others introduce the
third man Y*
1
Reading in 1. 2 OUWW/JLOV TL (with A. 990^6).2
Cf. Z. 1039* 2, Soph. El. I78b36-i79
a10, and Plato, Parmenides,
132 AB, 0-133 A.
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io79a METAPHYSICA
And in general the arguments for the Forms destroy
things for whose existence the believers in Forms are more
15 zealous than for the existence of the Ideas;for it follows
that not the dyad but number is first, and that prior to
number is the relative, and that this is prior to the absolute 1
besides all the other points on which certain people, by
following out the opinions held about the Forms, came
into conflict with the principles of the theory.
Again, according to the assumption on which the belief
20 in the Ideas rests, there will be Forms not only of sub
stances but also of many other things ;for the concept is
single not only in the case of substances, but also in that
of non -substances, and there are2sciences of other things
than substance;and a thousand other such difficulties
confront them. But according to the necessities of the case
25 and the opinions about the Forms, if they can be shared in
there must be Ideas of substancesonly.
Forthey
are not
shared in incidentally, but each Form must be shared in as
something not predicated of a subject. (By being shared
in incidentally I mean that if a thing shares in4
double
itself, it shares also in eternal,but incidentally ;
for the
30 double happens to be eternal.) Therefore the Forms will
be substance. But the same names indicate substance in
this and in the ideal world (or what will be the meaning of
saying that there is something apart from the particulars
the one over many ?).
:i And if the Ideas and the things that
share in them have the same form, there will be something
common : for why should 2 be one and the same in the
35 perishable 2 s, or in the 2 s which are many but eternal,4
and not the same in the 2 itself as in the individual 2 ?
io?9b But if they have not the same form, they will have only the
1i. e. the relative in general is more general than, and therefore (on
Platonic principles) prior to, number. Number is similarly prior to the
dyad. Therefore the relative is prior to the dyad, which yet is held to
be absolute.2
Reading rrjs ovcrins eiVt in 1. 23.3 This seems to be an enthymeme, the conclusion to be supplied
being that the Forms, since they are substances, must be 0/substances.4
Sc. the abstract (eternal) 2 s of which we can say e.g. 2 + 2 = 4,
i. e. TO. /zerau, which like the Ideas are eternal, but like sensible things
are many.
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BOOK M. 4 io79b
name in common, and it is as if one were to call both Callias
and a piece of wood a man,without observing any com
munity between them.1
But if we are to suppose that in other respects the common definitions apply to the Forms, e.g. that plane figure
and the other parts of the definition apply to the circle- 5
itself, but4 what really is
2 has to be added, we must inquire
whether this is not absolutely meaningless. For to what
is this to be added ? To centre or to plane or to all
the parts of the definition ? For all the elements in the
essence are Ideas, e. g.l
animal and two-footed .
3Further,
there must be some Idea answering to plane above, some 10
nature which will be present in all the Forms as their
genus.
5 Above all one might discuss the question what in the world
the Forms contribute to sensible things, either to those that
are eternal or to those that come into being and cease to
be; for they cause neither movement nor any change in
them. But again they help in no wise either towards the \$
knowledge of other things (for they are not even the sub
stance of these, else they would have been in them), or
towards their being, if they are not in the individuals which
share in them; though if they were, they might be thought
to be causes, as white causes whiteness in a white object by
entering into its composition. But this argument, which 20
was used first by Anaxagoras, and later by Eudoxus in
his discussion of difficulties and by certain others, is very
easily upset ;for it is easy to collect many and insuperable
objections to such a view.
But, further,all other
thingscannot come from the Forms
in any of the usual senses of from . And to say that they 25
are patterns and the other things share in them is to use
empty wrords and poetical metaphors. For what is it that
works, looking to the Ideas ? And any thing can both be
and come into being without being copied from something
1 With ic78b34-io79
b3 cf. A. 99O
b2-99i
a8.
2 Reading ro 6 6 errn in 1. 6 (cf. Io86b 27) with P. Shorey (Class.Phil. xx. 271-3).
3Sc. in the essence of man.
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io79b METAPHYSICA
else, so that, whether Socrates exists or not, a man like
30 Socrates might come to be. And evidently this might be
so even if Socrates were eternal. And there will be several
patterns of the same thing, and therefore several Forms ;
e.g. animal and two-footed,and also
l man -himself,
will be Forms of man. Again, the Forms are patterns not
only of sensible things, but of Forms themselves also;
i. e.
the genus is the pattern of the various forms-of-a-genus ;
therefore the same thing will be pattern and copy.
35 Again, it would seem impossible that substance and that
io8oa whose substance it is should exist apart ; how, therefore,
could the Ideas, being the substances of things, exist apart ?
In the Pkaedo 1 the case is stated in this way that the
Forms are causes both of being and of becoming. Yet
though the Forms exist, still things do not come into being,
unless there is something to originate movement;and
manyother
thingscome into
being (e. g.a house or a
ring)5 of which they say there are no Forms. Clearly therefore
even the things of which they say there are Ideas can both
be and come into being owing to such causes as produce
the things just mentioned,2 and not owing to the Forms.
But regarding the Ideas it is possible, both in this way and
10 by more abstract and accurate arguments, to collect many
objections like those we have considered.
Since we have discussed these points, it is well to consider 5
again the results regarding numbers which confront those
who say that numbers are separable substances and first
15causes of things. If number is an entity and its substance
is nothing other than just number, as some say, it follows
that either (i) there is a first in it and a second, each beingdifferent in species, and either (a) this is true of the units
without exception, and any unit is inassociable with any
20 unit, or(6) they are all without exception successive, and
any of them are associable with any, as they say is the case
with mathematical number ; for in mathematical number no
one unit is in any way different from another. Or(c) some
units must be associable and some not ;e. g. suppose that 2
1ico D.
2 With io79b 2-io8ca S cf. A. 99i
a 8- b9.
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BOOK M. 6 io8oa
is first after i, and then comes 3 and then the rest of the
number series, and the units in each number are associable, 25
e. g. those in the first 2 are associable with one another, and
those in the first 3 with one another, and so with the other
numbers ; but the units in the 2-itself are inassociable
with those in the 3-itself ;and similarly in the case of the
other successive numbers. And so while mathematical 30
number is counted thus after i, 2 (which consists of
another i besides the formeri),
and 3 (which consists of
another i besides these two), and the other numbers simi
larly, ideal number is counted thus after i, a distinct 2
which does not include the first i, and a 3 which does not
include the 2, and the rest of the number series similarly.
Or(2)
one kind of number must be like the first that was 35
named,1 one like that which the mathematicians speak
of, and that which we have named last2 must be a third
kind.
Again, these kinds of numbers must either be separable
from things, or not separable but in objects of perception io8ob
(not however in the way which we first considered,3 but in
the sense that objects of perception consist of numbers
which are present in them) either one kind and not an
other, or all of them.
These are of necessity the only ways in which the numbers 5
can exist. And of those who say that the i is the begin
ning and substance and element of all things, and that
number is formed from the i and something else, almost
every one has described number in one of these ways ; only
no one has said all the units are inassociable. And this has
happened reasonably enough ;for there can be no way TO
besides those mentioned. Some 4 say both kinds of number
exist, that which has a before and after5
being identical
with the Ideas, and mathematical number being different
from the Ideas and from sensible things, and both being
separable from sensible things ;and others G
say mathe-
111. 15-20.
2
11.23-35.3
Cf. io;6a 38-h
u.4
Plato is meant.5
i. e. in which the numbeis differ in kind.6
Speusippus is meant.
T 2
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io8ob METAPHYSICA
15 matical number alone exists, as the first of realities, separate
from sensible things. And the Pythagoreans, also, believe
in one kind of number the mathematical; only they say it
is not separate but sensible substances are formed out of it.
For they construct the whole universe out of numbers
only not numbers consisting- of abstract units; they suppose
20 the units to have spatial magnitude. But how the first i
was constructed so as to have magnitude, they seem unable
to say.
Another thinker l
says the first kind of number, that of
the Forms, alone exists, and some 2say mathematical
number is identical with this.
The case of lines, planes, and solids is similar. For some
think that those which are the objects of mathematics are
35 different from those which come after the Ideas;
3 and of
those who express themselves otherwise some speak of the
objects of mathematics and in a mathematical
wayviz.
those wrho do not make the Ideas numbers nor say that
Ideas exist;
4 and others speak of the objects of mathe
matics, but not mathematically ;for they say that neither is
every spatial magnitude divisible into magnitudes, nor do
30 any two units taken at random make 2.5 All who say the i
is an element and principle of things suppose numbers to
consist of abstract units, except the Pythagoreans ; but they
suppose the numbers to have magnitude, as has been said
before.6
It is clear from this statement, then, in how many
ways numbers may be described, and that all the ways have
35 been mentioned;and all these views are impossible, but
some perhaps more than others.
First, then,let
us inquireif the units are
associable or inas- 7io8i
asociable, and if inassociable, in which of the two ways we dis
tinguished.7 For it is possible that any unit is inassociable
with any, and it is possible that those in the 2 -itself are
inassociable with those in the 3 -itself \ and, generally, that
those in each ideal number are inassociable with those in
1 Some unknown Platonist.2Xenocrates is meant.
3 This refers to Plato; cf. A. 992^ 13-18.4
Speusippus is meant.5 Xenocrates is meant.
R
1. 19.7
Cf. io8oa 18-20, 23-35.
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BOOK M. 7 ic8ia
other ideal numbers. Now (i)if all units are associable and 5
without difference, we get mathematical number only one
kind of number, and the Ideas cannot be the numbers. For
what sort of number will man-himself or animal-itselfor anyother Form be ? There is one Idea of each thing, e. g. one
of man-himself and another one of animal-itself; but the i
similar and undifferentiated numbers are infinitely many, so
that any particular 3 is no more man-himselfthan any other
3. But if the Ideas are not numbers, neither can they exist
at all. For from what principles will the Ideas come ? It is
number that comes from the i and the indefinite dyad, and 15
the principles or elements are said to be principles and
elements of number, and the Ideas cannot be ranked as
either prior or posterior to the numbers.
But (2) if the units are inassociable, and inassociable in
the sense that any is inassociable with any other, number of
this sort cannot be mathematical number;for mathematical
number consists of undifferentiated units, and the truths 20
proved of it suit this character. Nor can it be ideal number.
For 2 will not proceed immediately from i and the indefi
nite dyad, and be followed by the successive numbers, as
they say 2, 3, 4 for the units in the ideal 2 are generated
at the same time, whether, as the first holder of the theoryl
said, from unequals (coming into being when these wereequalized) or in some other way since, if one unit is to 25
be prior to the other, it will be prior also to the 2 com
posed of these;
for when there is one thing prior and
another posterior, the resultant of these will be prior to one
and posterior to the other.2
Again, since the i -itself is first,and then there is a parti- 30
cular i which is first among the others and next after the
i -itself, and again a third which is next after the second
and next but one after the first i, so the units must be
prior to the numbers after which they are named when we
1Plato.
2 The theory of ideal number holds that 2 comes next after the
original i, which with the indefinite 2 is the source of number. But
if all units are different in species, one of the units in 2 is prior to theother and . . to 2, and comes next after the original I. Similarlybetween 2 and 3 there will be the first unit in 3, and so on.
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io8ia METAPHYSICA
count them ; e. g. there will be a third unit in 2 before 3
exists, and a fourth and a fifth in 3 before the numbers 4 and
35 5 exist. Now none of these thinkers has said the units are
inassociablein this
way, but according totheir
principlesit
is reasonable that they should be so even in this way, though
io8ibin truth it is impossible. For it is reasonable both that
the units should have priority and posteriority if there is
a first unit or first i, and also that the 2 s should if there is
a first 2;for after the first it is reasonable and necessary
5 that there should be a second, and if a second, a third, and
so with the others successively. (And to say both things
at the same time, that a unit is first and another unit is
second after the ideal i, and that a 2 is first after it, is
impossible.) But they make a first unit or i, but not also
a second and a third, and a first 2, but not also a second and
a third.
10 Clearly, also, it is not possible, if all the units are in
associable, that there should be a 2-itself and a 3 -itself;
and so with the other numbers. For whether the units
are undifferentiated or different each from each, number
must be counted by addition, e. g.2 by adding another i to
15 the one, 3 by adding another i to the two, and 4 similarly.
This being so, numbers cannot be generated as they gene
rate them, from the 2 and thei
;
for 2 becomes part of 3,
20 and 3 of 4, and the same happens in the case of the suc
ceeding numbers, but they say 4 came from the first 2 and
the indefinite 2, which makes it two 2 s other than the
2-itself1
;if not, the 2-itself will be a part of 4 and one
other 2 will be added. And similarly 2 will consist of the
25 i -itself and another i;but if this is so, the other element
cannot be an indefinite 2 ; for it generates one unit, not, as
the indefinite 2 does, a definite 2.
Again, besides the 3-itself and the 2-itself how can there
be other 3*3 and 2 s ? And how do they consist of prior
30 and posterior units ? All this is absurd and fictitious, and
there cannot be a first 2 and then a3-itself. Yet there must,
if the i and the indefinite dyad are to be the elements. But
1 The indefinite 2 being bvorroios produces two 2 s by operating on
the ideal 2, and it is these two 2 s which are distinct from the ideal 2.
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BOOK M. 7 io8ib
if the results are impossible, it is also impossible that these
are the generating principles.
If the units, then, are differentiated, each from each, these
results and others similar to these follow of necessity. But 35
(3) if those in different numbers are differentiated, but those
in the same number are alone undifferentiated from one
another, even so the difficulties that follow are no less.
E.g. in the lo-itself there are ten units, and the 10 is com- io8aa
posed both of them and of two5*8.
But since the lo-itself
is not any chance number nor composed ofany chance 5*3
or, for that matter, units the units in this 10 must differ.
For if they do not differ, neither will the 5*3 of which the 5
10 consists differ; but since these differ, the units also will
differ. But if they differ, will there be no other 5 s in the
10 but only these two, or will there be others? If there
are not, this is paradoxical ;and if there are, what sort of
10 will consist of them ? For there is no other 10 in the 10
10 but itself. But it is actually necessary on their view that
the 4 should not consist ofany chance 2 s;for the indefinite
2, as they say, received the definite 2 and made two 2 s;
for its nature was to double what it received.
Again, as to the 2 being an entity apart from its two units, 15
and the 3 an entity apart from its three units, how is this pos
sible ? Either by one s sharing in the other, as pale manis different from pale and man (for it shares in these),
or when one is a differentia of the other, as man is
different from animal and two-footed .
Again, some things are one by contact, some by inter- 2o
mixture, some by position ;none of which can belong to
the units of which the 2 or the 3 consists;but as two men
are not a unity apart from both, so must it be with the
units. And their being indivisible will make no difference
to them;
for points too are indivisible, but yet a pair of 25
them is nothing apart from the two.
But this consequence also we must not forget, that it
follows that there are prior and posterior 2 s, and similarly
with the other numbers. For let the 2 s in the 4 be simul
taneous; yet these are prior to those in the 8, and as the 2 30
generated them, they generated the 4 s in the 8-itself.
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io82a METAPHYSICA
Therefore if the first 2 is an Idea, these 2 s also will be
Ideas of some kind. And the same account applies to the
35 units;for the units in the first 2 generate the four in 4, so
that all the units come to be Ideas and an Idea will be
composed of Ideas. Clearly therefore those things also
of which these happen to be the Ideas will be composite,
e. g. one might say that animals are composed of animals,
if there are Ideas of them.
io82b
In general, to differentiate the units in any way is an
absurdity and a fiction;and by a fiction I mean a forced
statement made to suit a hypothesis. For neither in quantity
5nor in quality do we see unit differing from unit, and
number must be either equal or unequal all number but
especially that which consists of abstract units so that if
one number is neither greater nor less than another, it is
equal to it;but things that are equal and in no wise
differentiated we take to be the same when we are speaking
of numbers. If not, not even the 2 s in the lo-itself will be
10 undifferentiated, though they are equal ;for what reason
will the man who alleges that they are not differentiated be
able to give ?
Again, if every unit + another unit makes two, a unit
from the 2-itself and one from the 3-itself will make a 2.
Now(a)
this will consist of differentiated units;
and(/3)
will
it be prior to the 3 or posterior ? It rather seems that it
15 must be prior ;for one of the units is simultaneous with
the 3, and the other is simultaneous with the 2. And we,
for our part, suppose that in general i and T, whether the
things are equal or unequal, is 2, e. g. the good and the bad,
or a man and a horse;but those who hold these views say
that not even two linits are 2.
20 If the number of the 3-itself is not greater than that ot
the 2, this is surprising ;and if it is greater, clearly there is
also a number in it equal to the 2, so that this is not different
from the 2-itself. But this is not possible, if there is a first
and a second number. 1
Nor will the Ideas be numbers. For in this particular
point they are right who claim that the units must be
1i. e. if there is a difference of kind between the numbers.
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BOOK i\l. 7 io82b
different, if there are to be Ideas;as has been said before.
1 2 5
For the Form is unique ;but if the units are not different,
the 2 s and the 3*8 also will not be different. This is also
the reason why they must say that when we count thus
i,2 we do not proceed by adding to the given number
;
for if we do, neither will the numbers be generated from 30
the indefinite dyad, nor can a number be an Idea;for then
one Idea will be in another, and all the Forms will be parts
of one Form. And so with a view to their hypothesis their
statements are right, but as a whole they are wrong ;for
their view is very destructive, since they will admit that this
question itself affords some difficulty whether, when we 35
count and say i, 2, 3, we count by addition or by separate
portions. But we do both;and so it is absurd to reason
back from this problem to so great a difference of essence.
8 First of all it is well to determine what is the differentia1083**
of a number and of a unit, if it has a differentia. Units
must differ either in quantity or in quality ;and neither of
these seems to be possible. But number qua number differs
in quantity. And if the units also did differ in quantity,
number would differ from number, though equal in number 5
of units. Again, are the first units greater or smaller, and
do the later ones increase or diminish ? All these are irra
tional suppositions. But neither can they differ in quality.
For no attribute can attach to them;for even to numbers I0
quality is said to belong after quantity. Again, quality
could not come to them either from the i or from the dyad ;
for the former has no quality, and the latter gives quantity ;
for this entity is what makes things to be many. If the
facts are really otherwise, they should state this quite at 15
the beginning and determine ifpossible, regarding the
differentia of the unit, why it must exist, and, failing this,
what differentia they mean.
Evidently then, if the Ideas are numbers, the units can
not all be associable, nor can they be inassociable in either
of the two ways.2 But neither is the way in which some 20
others speak about numbers correct. These are those who
1
1081*5-17.2
Cf. io8oa 18-20, 23-35.
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io83a METAPHYSICA
do not think there are Ideas, either without qualification or
as identified with certain numbers, but think the objects of
mathematics exist and the numbers are the first of existing
things, andthe i -itself is the
starting-pointof them. It is
paradoxical that there should be a i which is first of I s, as
25 they say, but not a 2 which is first of 2 s, nor a 3 of 3 s;
for the same reasoning applies to all. If, then, the facts with
regard to number are so, and one supposes mathematical
number alone to exist, the i is not the starting-point (for
30 this sort of i must differ from the other units;and if this is
so, there must also be a 2 which is first of 2 s, and similarly
with the other successive numbers). But if the i is the
starting-point, the truth about the numbers must rather be
what Plato used to say, and there must be a first 2 and 3,
and the numbers must not be associable with one another.
3 But ifon the other hand one supposes this, many impossible
results, as we have said,1follow. But either this or the
other must be the case, so that if neither is, number cannot
exist separately.
io83b
It is evident, also, from this that the third version2
is the
worst, theview ideal and mathematical number is the same.
For two mistakes must then meet in the one opinion, (i)
5 Mathematical number cannot be of this sort, but the holder
ofthis
view has to spinit
out by making suppositions
peculiar to himself. And (2) he must also admit all the
consequences that confront those who speak of number in
the sense of Forms .
The Pythagorean version in one way affords fewer diffi
culties than those before named, but in another way has
10 others peculiar to itself. For not thinking of number as
capable of existing separately removes many of the im
possible consequences ;but that bodies should be composed
of numbers, and that this should be mathematical number,
is impossible. For it is not true to speak of indivisible
spatial magnitudes ;and however much there might be
magnitudes of this sort, units at least have not magnitude ;
1 5 and how can a magnitude be composed of indivisibles ?
But arithmetical number, at least, consists of units, while
1Cf. ioSob 37-io83
a17.
2 That of Xenocrates;
cf. io8ob 22.
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BOOK M. 8 io83b
these thinkers identify number with real things ;at any rate
they apply their propositions to bodies as if they consisted
of those numbers.
If, then, it is necessary, if number is a self-subsistent real
thing, that it should exist in one of these ways which have 20
been mentioned,1 and if it cannot exist in any of these,
evidently number has no such nature as those who make it
separable set up for it.
Again, does each unit come from the great and the small,
equalized, or one from the small, another from the
great
?
(a) If the latter, neither does each thing contain all the ele- 25
ments, nor are the units without difference;for in one there
is the great and in another the small, which is contrary in
its nature to the great. Again, how is it with the units in
the 3-itself ? One of them is an odd unit. But perhaps it
is for this reason that they give i -itself the middle place in
odd numbers.
2
(6) But if each of the two units consists of 30
both the great and the small, equalized, how will the 2,
which is a single thing, consist of the great and the small ?
Or how will it differ from the unit ? Again, the unit is prior
to the 2;for when it is destroyed the 2 is destroyed. It
must, then, be the Idea of an Idea since it is prior to an
Idea, and it must have come into being before it. From 35
what, then ? Not from the indefinite dyad, for its function
was to double.
Again, number must be either infinite or finite;for these
thinkers think of number as capable of existing separately,
so that it is not possible that neither of those alternatives
should be true. Clearly it cannot be infinite ;for infinite
number is neitherodd nor even,but the generation ofnumbers
is always the generation either of an odd or of an even
number;in one way, when i operates on an even number, an
odd number is produced ;in another way, when 2 operates, 5
the numbers got from i by doubling are produced ;in
another way, when the odd numbers operate, the other
even numbers are produced. Again, if every Idea is an
Idea ofsomething,
and the numbers are
Ideas,
infinite
2Cf. Diels, Vorsokratiker, ed. 3, i. 346. 17-22.
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io84a METAPHYSICA
number itself will be an Idea of something, either of some
sensible thing or of something else. Yet this is not
possible in view of their thesis any more than it is
reasonable initself,
at least if
they arrangethe Ideas as
they do.
10 But ifnumber infinite, how far does it go ? With regard
to this not only the fact but the reason should be stated.
But if number goes only up to 10, as some say,1
firstly the
Forms will soon run short;
e. g. if 3 is man-himself, what
15number will be the horse-itself ? The series of the numbers
which are the several things-themselves goes up to 10. It
must, then, be one of the numbers within these limits; for
it is these that are substances and Ideas. Yet they will run
short;for the various forms of animal will outnumber them.
At the same time it is clear that if in this way the 3 is
man-himself, the other 3 s are so also (for those in identical
ao numbers are similar), so that there will be an infinite num
ber of men;
if each 3 is an Idea, each of the numbers will
be man-himself, and if not, they will at least be men. And
if the smaller number is part of the greater (being number
of such a sort that the units in the same number are associ-
able), then if the 4-itself is an Idea of something, e.g. of
horse or of white,man will be a part of horse, if man
25is 2. It is
paradoxicalalso that there should be an Idea of
10, but not of 1 1, nor of the succeeding numbers. Again,
there both are and come to be certain things of which there
are no Forms; why, then, are there not Forms of them
also ? We infer that the Forms are not causes. Again, it
is paradoxical if the number-series up to 10 is more of a
30 real thing and a Form than 10 itself. There is no genera
tion of the former as one thing, and there is of the latter.
But they try to work on the assumption that the series of
numbers up to 10 is a complete series. At least they
generate the derivatives e. g. the void, proportion, the odd,
and the others of this kind within the decade. For some
things, e. g. movement and rest, good and bad, they assign
35 to the originative principles, and the others to the numbers.
This is why they identify the odd with i;for if the odd
1This includes Plato (cf. Phys. 2o6b 32) and probably Speusippus.
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BOOK M. 8 io84a
implied 3, how would 5 be odd? ]
Again, spatial magnitudes
and all such things are explained without going beyond a
definite number;
e. g. the first, the indivisible, line,2 then io84
b
the 2, &c. ; these entities also extend only up to io.3
Again, if number can exist separately, one might ask
which is prior i, or 3 or 2 ? Inasmuch as the number is
composite, i is prior, but inasmuch as the universal and the
form is prior, the number is prior ;for each of the units is 5
part of the number as its matter, and the number acts as
form. And in a sense the right angle is prior to the acute,
because it is determinate and in virtue of its definition;
but in a sense the acute is prior, because it is a part and the
right angle is divided into acute angles. As matter, then,
the acute angle and the element and the unit are prior, but in io
respect of the form and of the substance as expressed in the
definition, the right angle, and the whole consisting of the
matter and the form, are
prior;for the concrete
thing
is
nearer to the form and to what is expressed in the definition,
though in generation it is later. How then is i the starting-
point ? Because it is not divisible, they say ;but both the
universal, and the particular or the element, are indivisible.
But they are starting-points in different ways, one in15
definition and the other in time. In which way, then, is i
the starting-point ? As has been said, the right angle is
thought to be prior to the acute, and the acute to the right,
and each is one. Accordingly they make i the starting-
point in both ways. But this is impossible. For the uni
versal is one as form or substance, while the element is one
as a part or as matter. For each of the two is in a sense 20
one in truth each of the two units exists potentially (at
least if the number is a unity and not like a heap, i. e. if
different numbers consist of differentiated units, as they say),
but not in complete reality ;and the cause of the error
they fell into is that they were conducting their inquiry at
1i. e. to account for the oddness of odd numbers they identify the
odd with the i, which is a principle present in all numbers, not with
the 3, which on their theory is not present in other numbers.
2 Cf. A. 992*22.3
Cf. N. io9ob21-24. i answers to the point (the indivisible line
),
2 to the line, 3 to the plane, 4 to the solid, and 1+2 + 3+4= io.
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io84b METAPHYSICA
the same time from the standpoint of mathematics and from
25 that of universal definitions, so that(i) from the former
standpoint they treated unity, their first principle, as a
point;for the unit is a
point
withoutposition. They put
things together out of the smallest parts, as some others 1 also
have done. Therefore the unit becomes the matter of num
bers and at the same time prior to 2;and again posterior, 2
3 being treated as a whole, a unity, and a form. But (2)
because they were seeking the universal2
they treated the
unity w ich can be predicated of a number, as in this
sense also3
a part of the number. But these characteristics
cannot belong at the same time to the same thing.
If the i -itself must be unitary4
(for it differs in nothing
from other I s except that it is the starting-point), and the
2 is divisible but the unit is not, the unit must be liker the
35 i -itself than the 2 is. But if the unit is liker it, it must be
liker to the unit than to the 2;therefore each of the units
in 2 must be prior to the 2. But they deny this;at least
io85athey generate the 2 first. Again, if the 2-itself is a unity
and the 3 -itself is one also, both form a 2. From what, then,
is this 2 produced ?
Since there is not contact in numbers, but succession, g
viz. between the units between which there is nothing, e. g.
K betwreen those in 2 or in 3, one might ask whether these suc
ceed the i -itself or not, and whether, of the terms that
succeed it, 2 or either of the units in 2 is prior.
Similar difficulties occur with regard to the classes of things
posterior to number, the line, the plane, and the solid.
For some 5construct these out of the species of the great
10 and small ;e. g. lines from the
4
long and short , planes
from the broad and narrow,masses from the deep and
shallow;which are species of the great and small . And
the originative principle of such things which answers to
1Sc. the atomists.
2
Inserting TO before in 1. 31.3
i. e. they treated the unity which is predicable of a number, as well
as the unit in a number, as a part of the number.4
Reading conjecturally in 1. 33 p-ovaSiKov for povo5 This probably includes Plato himself.
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BOOK M. 9 1085*
the ildifferent thinkers describe in different ways. And
in these also the impossibilities, the fictions, and the contra- 1 5
dictions of all probability are seen to be innumerable. For
(i) the geometrical classes are severed from one another,
unless the principles of these are implied in one another in
such a way that the broad and narrow is also long and
short (but if this is so, the plane will be a line and the solid
a plane ;
2
again, how will angles and figures and such
things be explained ?).And
(ii)the same happens as in 20
regard to number;for long and short
, &c., are attributes
of magnitude, but magnitude does not consist of these, any
more than the line consists of straight and curved,or
solids of smooth and rough .
3
(All these views share a difficulty which occurs with re
gard to species-of-a-genus, when one posits the universals,
viz. whether it is animal-itself or something other than 25
animal-itself that is in the particular animal. True, if the
universal is not separable from sensible things, this will
present no difficulty ;but if the i and the numbers are
separable, as those who express these views say, it is not
easy to solve the difficulty, if one may apply the words not
easy to the impossible. For when we apprehend the unity
in 2, or in general in a number, do we apprehend a thing- 30
itself or something else ?)
Some, then, generate spatial magnitudes from matter of
this sort, others4 from the point and the point is thought
by them to be not i but something like i and from other
matter like plurality, but not identical with it;about which
principles none the less the same difficulties occur. For if35
the matter is one, line and plane and solid will be the same;
for from the same elements will come one and the same
thing. But if the matters are more than one, and there is io85b
one for the line and a second for the plane and another for
the solid, they either are implied in one another or not, so
1i. e. that which is to the geometrical forms as the primary i is
^according to the Platonic theory) to numbers.2
With 1085* 7-19 cf. A. 992a
10-19.&
Cf. A. 992b1-7, N. io88 a
15-21.4
Speusippus is probably meant.
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io85b METAPHYSICA
that the same results will follow even so;for either the plane
will not contain a line or it will be a line.
Again, how number can consist of the one and plurality,
5
they
make no attempt to
explain;but however
they
ex
press themselves, the same objections arise as confront
those who construct number out of the one and the in
definite dyad.1 For the one view generates number from the
universally predicated plurality, and not from a particular
plurality ;and the other generates it from a particular
plurality, but the first;for 2 is said to be a first plural-
10 ity.
Therefore there is practically no difference, but the
same difficulties will follow, is it intermixture or position
or blending or generation ? and so on. Above all one
might press the question if each unit is one, what does it
come from ? Certainly each is not the one-itself. It must,
then, come from the one-itself and plurality, or a part of
15 plurality. To say that the unit is a plurality is impossible,
for it is indivisible; and to generate it from a part of
plurality involves many other objections ;for (a) each of
the parts must be indivisible (or it will be a plurality and
the unit will be divisible) and the elements will not be the
20 one and plurality ;for the single units do not come from
plurality and the one. Again, (/?)the holder of this view
doesnothing
but
presupposeanother number
;for his
plurality of indivisibles is a number. Again, we must
inquire, in view of this theory also,2 whether the number
is infinite or finite. For there was at first, as it seems,
2- a plurality that was itself finite, from which and from the
one comes the finite number of units. And there is an
other plurality that is plurality-itself and infinite plurality ;
which sort of plurality, then, is the element which co-operates with the one ? One might inquire similarly about the
point, i. e. the element out of which they make spatial
magnitudes. For surely this is not the one and only point ;
at any rate, then, let them say out of what each of the other
30 points is formed. Certainly not of some distance + the
point-itself. Nor again can there be indivisible parts of
a distance, as the elements out of which the units are said
1i. e. probably Plato and Xenocrates.
aCf. io83
b36.
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BOOK M. 9 io85b
to be made are indivisible parts of plurality ;for number
consists of indivisibles, but spatial magnitudes do not.1
All these objections, then, and others of the sort make it
evident that numberand spatial magnitudes cannotexist apart 35
from things. Again, the discord about numbers between the
various versions is a sign that it is the incorrectness of the io86a
alleged facts themselves that brings confusion into the
theories. For those who make the objects of mathematics
alone exist apart from sensible things,2
seeing the diffi
culty about the Forms and their fictitiousness, abandoned
ideal number and posited mathematical. But those who 5
wished to make the Forms at the same time also numbers, but
did not see, if one assumed these principles, how mathe
matical number was to exist apart from ideal,3 made ideal
and mathematical number the same in words, since mfactmathematical number has been destroyed; for they state 10
hypotheses peculiarto themselves and not those of mathe
matics. And he who first supposed that the Forms exist and
that the Forms are numbers and that the objects of mathe
matics exist,4
naturally separated the two. Therefore it
turns out that all of them are right in some respect, but on
the whole not right. And they themselves confirm this, for
their statements do not agree but conflict. The cause is that 15
their hypotheses and their principles are false. And it is
hard to make a good case out of bad materials, according
to Epicharmus5
: as soon as tis said, tis seen to be
wrong.
But regarding numbers the questions we have raised and
the conclusions we have reached are sufficient (for while he
who is already convinced might be further convinced by a
longer discussion, one not yet convinced would not come 20
any nearer to conviction) ; regarding the first principles and
the first causes and elements, the views expressed by those
who discuss only sensible substance have been partly
1 The point cannot have for an element of it (a) a distance, for this
would destroy the simplicity of the point ;or (b) part of a distance, for
any part of a distance must be a distance.
Speusippus is meant. 3 Xenocrates is meant.4
Plato. 5Fr. 14, Diels, Vorsokratiker.
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io86a METAPHYSICA
stated in our works on nature,1 and partly do not belong
to the present inquiry ;but the views of those who assert
25 that there are other substances besides the sensible must be
considered next after those we have beenmentioning.
Since, then, some say that the Ideas and the numbers are
such substances, and that the elements of these are elements
and principles of real things, we must inquire regarding
these what they say and in what sense they say it.
Those who posit numbers only, and these mathematical,
30 must be considered later 2;but as regards those who believe
in the Ideas one might survey at the same time their wayof thinking and the difficulty into which they fall. For
they at the same time make the Ideas universal and again
treat them as separable and as individuals. That this is
35 not possible has been argued before.3 The reason why
those who described their substances as universal combined
these two characteristics in one thing, is that they did
not make substances identical with sensible things. They
thought that the particulars in the sensible world were in
io86ba state of flux and none of them remained, but that the
universal was apart from these and something different.
And Socrates gave the impulse to this theory, as we said
in our earlier discussion,4
by reason of his definitions, but
he did not
separateuniversals from individuals
;and in this
5 he thought rightly, in not separating them. This is plain
from the results ;for without the universal it is not possible
to get knowledge, but the separation is the cause of the
objections that arise with regard to the Ideas. His suc
cessors, however, treating it as necessary, if there are to be
any substances besides the sensible and transient substances,
that they must be separable, had no others, but gave sepa-
10 rate existence to these universally predicated substances, so
that it followed that universals and individuals were almost
the same sort of thing. This in itself, then, would be one
difficulty in the view we have mentioned.
Let us now mention a point which presents a certain IO
1
Phys. i. 4-6 ; De Caelo, iii. 3-4 ; De Gen, et Corr. i. i.?
Speusippus is meant; cf. N. 1090*7-15, 2o-b 2o.8
B. ioo3a7-17.
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BOOK M. 10 io86b
difficulty both to those who believe in the Ideas and to those
who do not, and which was stated before, at the beginning, I5
among the problems.1
If we do not suppose substances to
be separate, and in the way in which individual things are
said to be separate, we shall destroy substance in the sense
in which we understandc
substance;but if we conceive
substances to be separable, how are we to conceive their
elements and their principles ?
If they are individual and not universal, (a) real things 20
will be just of the same number as the elements, and(d)
the
elements will not be knowable. For (a) let the syllables in
speech be substances, and their elements elements of sub
stances;then there must be only one ba and one of each of
the syllables, since they are not universal and the same in 25
form but each is one in number and a *
this and not a kind
possessed of a common name (and again they suppose that
the just whatathing
is2
is ineach case one). And
if
the
syllables are unique, so tooare the parts ofwhich they consist;
there will not, then, be more as than one, nor more than
one of any of the other elements, on the same principle on 30
which an identical syllable cannot3exist in the plural number.
But if this is so, there will not be other things existing
besides the elements, but only the elements. (6) Again,
the elements will not be even knowable ; for they are not
universal, and knowledge is of universals. This is clear
from demonstrations and from definitions;for we do not
conclude that this triangle has its angles equal to twro right
angles, unless every triangle has its angles equal to two 35
right angles, nor that this man is an animal, unless every
man is an animal.
But if the principles are universal, either the substances
composed of them are also universal, or non-substance will io87a
be prior to substance;for the universal is not a substance,
but the element or principle is universal, and the element
or principle is prior to the things of which it is the prin
ciple or element.
1B. 999
b 24-ioooa4, ioo3
a5-i;.
2i.e. the Idea
;cf. I079
b6.
3
Omitting aXXo>i> in 1. 30 ;there is no trace of it in ps.-Alexander.
U 2
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io87a METAPHYSICA
5 All these difficulties follow naturally, when they make
the Ideas out of elements and at the same time claim that
apart from the substances which have the same form there
areIdeas,
asingle separate entity. But if,
e.g.,
in the case
of the elements of speech, the as and the s may quite well
be many and there need be no ^-itself and ^-itself besides
the many, there may be, so far as this goes, an infinite
ic number of similar syllables. The statement that all know
ledge is universal, so that the principles of things must also
be universal and not separate substances, presents indeed,
of all the points we have mentioned, the greatest difficulty,
but yet the statement is in a sense true, although in a sense
1 5 it is not. For knowledge, like the verb to know,means
two things, of which one is potential and one actual. The
potency, being, as matter, universal and indefinite, deals
with the universal and indefinite;but the actuality, being
definite, deals with a definite object, being a this,
it
deals with a this . But per accidens sight sees universal
colour, because this individual colour which it sees is
20 colour;and this individual a which the grammarian in
vestigates is an a. For if the principles must be universal,
what is derived from them must also be universal, as in
demonstrations l
;and if this is so, there will be nothing
capable of separateexistence i. e.
no substance. Butevidently in a sense knowledge is universal, and in a sense
25 it is not.
1Sc. universal premisses do not give singular conclusions.
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BOOK N
I REGARDING this kind of substance, what we have said
must be taken as sufficient. All philosophers make the
first principles contraries : as in natural thing s, so also in 30
the case of unchangeable substances. But since there can
not be anything prior to the first principle of all things, the
principle cannot be the principle and yet be an attribute of
something else. To suggest this is like saying that the
white is a first principle, not qiia anything else but qua
white, but yet that it is predicable of a subject, i. e. that its
being white presupposes its being something else;this is 35
absurd, for then that subject will be prior. But all things
which are generated from their contraries involve an under
lying subject ;a subject, then, must be present in the case
of contraries, if anywhere. All contraries, then, are always io87b
predicable of a subject, and none can exist apart, but just
as appearances suggest that there is nothing contrary to
substance, argument confirms this. No contrary, then, is
the first principle of all things in the full sense;the first
principleis
somethingdifferent.
But these thinkers make one of the contraries matter,
some T
making the unequal which they take to be the 5
essence of plurality matter for the One, and others 2
making plurality matter for the One. (The former gene
rate numbers out of the dyad of the unequal, i. e. of the
great and small, and the other thinker we have referred to
generates them out of plurality, while according to both it
is generated by the essence of the One.) For even the philo
sopher who says the unequal and the One are the elements,
and the unequal is a dyad composed of the great and small, 10
treats the unequal, or the great and the small, as being one,
and does not draw the distinction that they are one in
definition, but not in number. But they do not describe
rightly even the principles which they call elements, for
1Plato is meant.
2
Speusippus is probably referred to.
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io87b METAPHYSICA
some 1 name the great and the small with the One and treat
15 these three as elements of numbers, two being matter, one
the form;while others
2 name the many and few, because
the great and the small are more appropriate in theirnature to magnitude than to number
;and others 3 name
rather the universal character common to these that
which exceeds and that which is exceeded . None of
these varieties of opinion makes any difference to speak
of, in view of some of the consequences ; they affect only* the abstract objections, which these thinkers take care to
avoid because the demonstrations they themselves offer are
abstract, with this exception, that if the exceeding and
the exceeded are the principles, and not the great and the
small, consistency requires that number should come from
the elements before 2 does;for number is more universal
than 2, as the exceeding and the exceeded are more uni-
25 versal than the great and the small. But as it is, they say
one of these things but do not say the other. Others
oppose the different and the other to the One,4 and others
oppose plurality to the One. 5 But if, as they claim, things
consist of contraries, and to the One either there is nothing-
contrary, or if there is to be anything it is plurality, and the
unequal is contrary to the equal, and the different to the same,
30 and the other to the thing itself, those who oppose the One to
plurality have most claim to plausibility, but even their view
is inadequate, for the One would on their view be a few;for
plurality is opposed to fewness, and the many to the few.
The one evidently means a measure. And in every
case there is some underlying thing with a distinct nature
35 of its owr
n, e. g. in the scale a quarter-tone, in spatial
magnitude a finger or a foot or something of the sort, in
rhythms a beat or a syllable ;and similarly in gravity it is
io88aa definite weight ;
and in the same way in all cases, in
qualities a quality, in quantities a quantity (and the measure
is indivisible, in the former case in kind, and in the latter to
the sense) ;which implies that the one is not in itself the
1 This includes Plato.2Unidentifiable Platonists.
3
Perhaps Pythagoreans.4
Probably certain Pythagoreans are referred to.
5
Probably Speusippus is meant.
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BOOK N. i io88
substance of anything-. And this is reasonable;
for4
the
one means the measure of some plurality, and number 5
means a measured plurality and a plurality of measures.
(Thus it is natural that one is not a number ; for the
measure is not measures, but both the measure and the one
are starting-points.) The measure must always be some
identical thing predicable of all the things it measures, e. g.
if the things are horses, the measure is horse,and if they
are men, man . If they are a man, a horse, and a god, the 10
measure is perhaps*
living being ,and the number of them
will be a number of living beings. If the things are* man
and pale and walking ,these will scarcely have a num
ber, because all belong to a subject which is one and the
same in number, yet the number of these will be a number
of kinds or of some such term.
Those who treat the unequal as one thing, and the dyad 15
as an indefinite
compoundof
great
and small,say
what is
very far from being probable or possible. For (a) these
are modifications and accidents, rather than substrata, of
numbers and magnitudes the many and few of number,
and the great and small of magnitude like even and odd,
smooth and rough, straight and curved. Again, (b) apart 20
from this mistake, the great and the small, and so on, must
be relative to something; but what is relative is least of
all thingsl a kind of entity or substance, and is posterior
to quality and quantity ;and the relative is an accident
of quantity, as was said, not its matter, since something 25
with a distinct nature of its own must serve as matter
both to the relative in general and to its parts and kinds.
For there is nothing either great or small, many or few, or,
in general, relative to something else, which without having
a nature of its own is many or few, great or small, or
relative to something else. A sign that the relative is least
of all a substance and a real thing is the fact that it alone 30
has no proper generation or destruction or movement, as
in respect of quantity there is increase and diminution, in
respect of quality alteration, in respect of place locomotion,
in respect of substance simple generation and destruction.
1
Omitting r&vK.arriyopi.u>v
in 1. 23 as a gloss.
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io88a METAPHYSICA
In respect of relation there is no proper change ; for, with
out changing, a thing will be now greater and now less or
35 equal, if that with which it is compared has changed in
io88b
quantity. And(c) the matter of each
thing,
and therefore of
substance, must be that which is potentially of the nature in
question ;but the relative is neither potentially nor actually
substance. It is strange, then, or rather impossible, to make
not-substance an element in, and prior to, substance;for
all the categories are posterior to substance. Again, (d)
elements are not predicated of the things of which they are
5 elements, but many and few are predicated both apart andtogether of number, and long and short of the line, and
both broad and narrow apply to the plane. If there is
a plurality, then, of which the one term, viz. few, is always
predicated, e.g.2 (which cannot be many, for if it were
many, i would be few), there must be also one which is
10 absolutely many, e. g. 10 is many (ifthere is no number
which is greater than 10), or 10,000. How then, in view of
this, can number consist of few and many ? Either both
ought to be predicated of it, or neither;but in fact only
the one or the other is predicated.
We must inquire generally, whether eternal things can 2
15 consist of elements. If they do, they will have matter;for
everything that consists of elements is composite. Since,
then, even ifa thing exists for ever, out of that of which it con
sists it would necessarily also, if it had come into being, have
come into being,1 and since everything comes to be what it
comes to be out of that which is it potentially (forit could not
have come to be out of that which had not this capacity,
nor could it consist of such elements), and since the poten-
20 tial can be either actual or not, this being so, however
everlasting number or anything else that has matter is, it
must be capable of not existing, just as that which is any
number of years old is as capable of not existing as that
which is a day old;
if this is capable of not existing, so is
that which has lasted for a time so long that it has no limit.
1
Punctuating in 11. l6, 17 ft KCU ati eon, K.ai}d eyevero, e< TOVTOV
yiyvfadai.
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BOOK N. 2 1088*
They cannot, then, be eternal, since that which is capable
of not existing is not eternal, as we had occasion to show in
another context.1
If that which we are now saying is 25
true universally that no substance is eternal unless it is
actuality and if the elements are matter that underlies
substance, no eternal substance can have elements present
in it, of which it consists.
There are some 2 who describe the element which acts with
the One as an indefinite dyad, and object to the unequal ,
reasonably enough, because of the ensuing difficulties;but 3
they have got rid only of those objections which inevitably
arise from the treatment of the unequal, i.e. the relative, as
an element;those which arise apart from this opinion must
confront even these thinkers, whether it is ideal number, or
mathematical, that they construct out of those elements.
There are many causes which led them off into these 35
explanations,and
especiallythe fact that
theyframed the
1089*
difficulty in an obsolete form. For they thought that all
things that are would be one (viz. Being itself),if one did
not join issue with and refute the saying of Parmenides: 3
For never will this be proved, that things that are not are.
They thought it necessary to prove that that which is not
is; for only thus ofthat which is andsomething else could 5
the things that are be composed, if they are many.
But, first, if being has many senses (for it means some
times substance, sometimes that it is of a certain quality,
sometimes that it is of a certain quantity, and at other times
the other categories), what sort of one, then, are all the
things that are, if non-being is to be supposed not to be ?
Is it the substances that are one, or the affections and 10
similarly the other categories as well, or all together so that
the this and the such and the*
so much and the other
categories that indicate each some one class of being will
all be one ? But it is strange, or rather impossible, that the
coming into play of a single thing4 should bring it about
that part of that which is is a this, part a * such
, part
a so much,
part
a here .
1
Cf. 0. io5ob7 ff.,
De Caelo, i. 12.2
Probably Xenocrates is meant.3Fr. 7.
4i. e. non-being.
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io89a METAPHYSICA
15 Secondly, of what sort of non-being and being do the
things that are consist? For non-being also has many
senses, since being has;and not being a man means
notbeing
a certainsubstance,
notbeing straight
notbeing
of a certain quality, not being three cubits long not
being of a certain quantity. What sort of being and non-
being, then, by their union pluralize the things that are ?
20 This thinker 1 means by the non-being, the union of which
with being pluralizes the things that are, the false and the
character of falsity. This is also why it used to be said
that we must assume something that is false, as geometersassume the line which is not a foot long to be a foot long.
But this cannot be so. For neither do geometers assume
anything false (for the enunciation is extraneous to the in-
25 ference), nor is it non-being in this sense that the things
that are are generated from or resolved into. But since
4
non-being taken in its various cases2 has as many senses
as there are categories, and besides this the false is said not
to be, and so is the potential, it is from this that generation
proceeds, man from that which is not man but potentially
30 man, and white from that which is not white but potentially
\vhite, and this whether it is some one thing that is gene
rated or many.
The question evidently is, how being,in the sense of the
siibstances\ is many; for the things that are generated
are numbers and lines and bodies. Now it is strange to
inquire how being in the sense of the what is many, and
35 not how either qualities or quantities are many. For surely
the indefinite dyad or4
the great and the small is not a
reason why there should be two kinds of white or many
io89bcolours or flavours or shapes ; for then these also would be
numbers and units. But if they had attacked these other
categories, they wrould have seen the cause of the plurality
in substances also;for the same thing or something analo
gous is the cause. This aberration is the reason also why
5 in seeking the opposite of being and the one, from which
with being and the one the things that are proceed, they
posited the relative term (i.e. the unequal), which is neither
1 Plato;
cf. Soph. 237 A, 240.2
Cf. 11. 16-19.
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BOOK N. 2
the contrary nor the contradictory of these, and is one kind
ofbeing"
as what and quality also are.
They should have asked this question also, how relative
terms are many and not one. But as it is, they inquire howthere are many units besides the first i, but do not go on to 10
inquire how there are many unequals besides the unequal.
Yet they use them and speak of great and small, many and
few (from which proceed numbers), long and short (from
which proceeds the line), broad and narrow (from which
proceeds the plane), deep and shallow (from which pro
ceed solids) ;and they speak of yet more kinds of relative
term. What is the reason, then, why there is a plurality of
these ?
It is necessary, then,as we say, to presuppose for each thingT 5
that which is it potentially ;and the holder of these views
further declared what that is which is potentially a*
this
and a substance but is not in itself
beingviz. that it is the
relative (as if he had said the qualitative ),which is neither
potentially the one or being, nor the negation of the one
nor of being, but one among beings. And it was much 20
more necessary, as we said,1if he was inquiring how beings
are many, not to inquire about those in the same category-
how there are many substances or many qualities but how
beings as a whole are many ; for some are substances, somemodifications, some relations. In the categories other than
substance there is yet another problem involved in the exist
ence ofplurality. Sincethey are notseparable from substances, 25
qualitiesand quantities aremanyjust because their substratum
becomes and is many ; yet there ought to be a matter for
each category ; only it cannot be separable from substances.
But in the case of thises \ it is possible to explain how the
this is many things, unless a thing is to be treated as both
a*
this and a general character.2 The difficulty arising 3
from the facts about substances is rather this, how there are
actually many substances and not one.
But further, if the this and the quantitative are not the
same, we are not told how and
why
the things that are are
1 a34-
2
Which, Aristotle thinks, the Platonists assert the Idea to be.
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io89b METAPHYSICA
many, but how quantities are many. For all number
35 means a quantity, and so does the unit,unless it means a
measure or the quantitatively indivisible. If, then, the
quantitativeand the what are
different, weare not told
iO9Oa whence or how the what is many ;
but if any one says
they are the same, he has to face many inconsistencies.
One might fix one s attention also on the question,
regarding- the numbers, what justifies the belief that they
exist. To the believer in Ideas they provide some sort of
5 cause for existing things, since each number is an Idea, and
the Idea is to other things somehow or other the cause of
their being; for let this supposition be granted them. But
as for him who does not hold this view because he sees the
inherent objections to the Ideas (so that it is not for this
reason that he posits numbers), but who posits mathema-
10 tical number,1
why must we believe his statement that such
number exists, and of what use is such number to other
things ? Neither does he who says it exists maintain that
it is the cause of anything (he rather says it is a thing
existing by itself), nor is it observed to be the cause ofany
thing ;for the theorems of arithmeticians will all be found
15 true even of sensible things, as was said before.2
As for those, then, who suppose the Ideas to exist and to 3
be numbers, by their assumption in virtue of the method
of setting out each term apart from its instances of the
unity of each general term they try at least to explain
somehow why number must exist. Since their reasons,
however, are neither conclusive nor in themselves possible,
one must not, for these reasons at least, assert the existence
20 of number.
Again,the
Pythagoreans,because
theysaw
many attributes of numbers belonging to sensible bodies,
supposed real things to be numbers not separable num
bers, however, but numbers of which real things consist.
But why ? Because the attributes of numbers are present
in a musical scale and in the heavens and in many other
25 things.3
Those, however, who say that mathematical num-
1
Speusippus is meant.2
Cf. M. 3, esp. io77b17-22.
3Cf. A. 989** 29-99o
a29.
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BOOK N. 3 io90a
her alone exists 1 cannot according to their hypotheses say
anything of this sort, but it used to be urged that these
sensible things could not be the subject of the sciences.
But we maintain that they are, as we said before. 2 And it
is evident that the objects of mathematics do not exist
apart ;for if they existed apart their attributes would not
have been present in bodies. Now the Pythagoreans in this 3
point are open to no objection ;but in that they construct
natural bodies out of numbers, things that have lightness
and weight out of things that have not weight or lightness,
they seem to speak of another heaven and other bodies,
not of the sensible. But those who make number separ- 35
able3 assume that it both exists and is separable because
the axioms would not be true of sensible things, while the
statements of mathematics are true and greet the soul;
4
and similarly with the spatial magnitudes of mathematics.
It is
evident, then,both that the rival
theory
5will
saythe
iogo
b
contrary of this, and that the difficulty we raised just now,
why if numbers are in no way present in sensible things
their attributes are present in sensible things, has to be
solved by those who hold these views.
There are some who, because the point is the limit and 5
extreme of the line, the line of the plane, and the plane of
the solid, think there must be real things of this sort. Wemust therefore examine this argument too, and see whether
it is not remarkably weak. For(i)
extremes are not sub
stances, but rather all these things are limits. For even 10
walking, and movement in general, has a limit, so that
on their theory this will be a this and a substance. But
that is absurd. Not but what(ii)
even if they are substances,
they will all be the substances of the sensible things in this
world;for it is to these that the argument applied. Why
then should they be capable of existing apart ?
Again, if we are not too easily satisfied, we may, regard
ing all number and the objects of mathematics, press this
difficulty, that they contribute nothing to one another, the 15
1
Speusippusis meant. 2
Cf. M.3.
3 The Platonists.4 This seems to be a quotation from some poet or writer of poetical
prose.5Sc. of the Pythagoreans ;
cf. 11. 20-25. &29-
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iogob METAPHYSICA
prior to the posterior ;for if number did not exist, none
the less spatial magnitudes would exist for those who
maintain the existence of the objects of mathematics only,1
and if
spatial magnitudesdid not
exist, soul and sensiblebodies would exist. But the observed facts show that
20 nature is not a series of episodes, like a bad tragedy. As
for the believers in the Ideas, this difficulty misses them;
for they construct spatial magnitudes out of matter and
number, lines out of the number 2, planes doubtless out of
3, solids out of 4, or they use other numbers, which
makes no difference. But will these magnitudes be Ideas,
25 or what is their manner of existence, and what do they
contribute to things ? These contribute nothing, as the
objects of mathematics contribute nothing. But not even
is any theorem true of them, unless we want to change the
objects of mathematics and invent doctrines of our own.
30 But it is not hard to assume any random hypotheses and
spin out a long string of conclusions. These thinkers,2
then, are wrong in this way, in wanting to unite the
objects of mathematics with the Ideas. And those who
first posited two kinds of number, that of the Forms and
that which is mathematical, neither have said nor can say
how mathematical number is to exist and of what it is
35 to consist. For they placeit
betweenideal
andsensible
number. If(i)
it consists of the great and small, it will
be the same as the other ideal number (he3 makes
spatial magnitudes out of some other small and great4
).
iogia And if
(ii)he names some other element, he will be making
his elements rather many. And if the principle of each of
the two kinds of number is a i, unity will be something
common to these, and we must inquire how the one is
these many things, while at the same time number, accord
ing to him, cannot be generated except from one and an
indefinite dyad.
5 All this is absurd, and conflicts both with itself and with
the probabilities,and we seem to see in it Simonides long
1
Speusippus is meant.2
11. 20-32 seem to refer to Xenocrates.3
Sc. Plato.
4Cf. I090
b2I, 22.
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BOOK N. 3 i09ia
rigmarole1
;for the long rigmarole comes into play, like
those of slaves, when men have nothing sound to say. And
the very elements the great and the small seem to cry
out against the violence that is done to them ; for they 10
cannot in any way generate numbers other than those got
from i by doubling.
It is strange also to attribute generation to things that
are eternal, or rather this is one of the things that are
impossible. There need be no doubt whether the Pytha
goreans attribute generation to them or not;for they say 15
plainly that when the one had been constructed, whether
out of planes or of surface or of seed or of elements which
they cannot express, immediately the nearest part of the
unlimited began to be constrained and limited by the limit.
But since they are constructing a world and wish to speak
the language of natural science, it is fair to make some
examination of their physical theories, but to let them off
from the present inquiry ;for we are investigating the ao
principles at work in unchangeable things, so that it is
numbers of this kind whose genesis we must study.
4 These thinkers say there is no generation of the odd
number, which evidently implies that there is generation of
the even;and some present the even as produced first from
unequals the great and the small when these are equal
ized. The inequality, then, must belong to them before 25
they are equalized. If they had always been equalized,
they would not have been unequal before;
for there is
nothing before that which is always. Therefore evidently
they are not giving their account of the generation of
numbers merely to assist contemplation of their nature.2
A difficulty, and a reproach to any one who finds it no
difficulty, are contained in the question how the elements 3
and the principles are related to the good and the beautiful;
the difficulty is this, whether any of the elements is such
a thing as we mean by the good itself and the best, or this
is not so, but these are later in origin than the elements.
Thetheologians
seem to
agreewith some thinkers of the
1Sim. Ceius, Fr. 189. Bergk.
2Cf. De Caelo, i. 279* 32-280* 10.
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io9ia METAPHYSICA
35 present day,1 who answer the question in the negative, and
say that both the good and the beautiful appear in the
nature of things only when that nature has made some
progress. (This they
do to avoid a real objection which
confronts those who say, as some do, that the one is a first
iogibprinciple. The objection arises not from their ascribing
goodness to the first principle as an attribute, but from
their making the one a principle and a principle in the
sense of an element and generating number from the one.)
The old poets agree with this inasmuch as they say that
5 not those who are first in time, e. g. Night and Heaven2
orChaos 3 or Ocean 4
, reign and rule, but Zeus.5 These poets,
however, are led to speak thus only because they think of
the rulers of the world as changing \for those of them
who combine the two characters in that they do not use
mythical language throughout, e. g. Pherecydes and some
10 others, make the original generating agent the Best, and
so do the Magi, and some of the later sages also, e. g. both
Empedocles and Anaxagoras, of whom one made love an
element, and the other made reason a principle. Of those
who maintain the existence of the unchangeable substances
some say the One itself is the good itself; but they thought
its substance lay mainly in its unity.
15 This, then, is the
problem,
which of the two
ways
of
speaking is right. It would be strange if to that which is
primary and eternal and most self-sufficient this very quality
self-sufficiency and self-maintenance belongs primarily
in some other way than as a good. But indeed it can be
for no other reason indestructible or self-sufficient than
because its nature is good. Therefore to say that the first
20 principle is good is probably correct;
but that this prin
ciple should be the One or, if not that, at least an element,
and an element of numbers, is impossible. Powerful ob
jections arise, to avoid wrhich some have given up the
theory6
(viz. those who agree that the One is a first
1
Speusippus is meant; cf. A. 1072* 31.2 The reference is to the Orphic cosmogony.3
Cf. Hes. Theog. 116.
4
Cf. Horn. //. xiv. 201.5
Cf. A. ic7ib 26.
6i. e. Speusippus gave up the identity of the One with the Good.
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BOOK N. 4 i09ib
principle and element, but only of mathematical number).
For on this view all the units become identical with species 25
of good, and there is a great profusion of goods. Again,
if the Forms are numbers, all the Forms are identical with
species of good. But let a man assume Ideas of anything
he pleases. If these are Ideas only of goods, the Ideas will
not be substances;but if the Ideas are also Ideas of sub
stances, all animals and plants and all individuals that share
in Ideas will be good.
These absurdities follow, and it also follows that the 30
contrary element, whether it is plurality or the unequal,
i.e. the great and small, is the bad-itself. (Hence one
thinker 1avoided attaching the good to the One, because it
would necessarily follow, since generation is from contraries,
that badness is the fundamental nature of plurality ;while
others 2
say inequality is the nature of the bad.) It follows, 35
then, that all
things partakeof the bad
except
one the
One itself, and that numbers partake of it in a more un
diluted form than spatial magnitudes, and that the bad is 1092*
the space in which the good is realized,3 and that it par
takes in and desires that which tends to destroy it;for
contrary tends to destroy contrary. And if, as we were
saying,4the matter is that which is potentially each thing,
e. g. that of actual fire is that which is potentially fire, thebad will be just the potentially good.
All these objections, then, follow, partly because they 5
make every principle an element, partly because they make
contraries principles, partly because they make the One
a principle, partly because they treat the numbers as
the first substances, and as capable of existing apart, and
as Forms.
5 If, then, it is equally impossible not to put the good
among the first principles and to put it among them in this
way, evidently the principles are not being correctly de- 10
scribed, nor are the first substances. Nor does any one
conceive the matter correctly if he compares the principles
1
Speusippus.2Plato and Xenocrates.
3Cf. PI. Tim. 52 A, B.
4io88b I.
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io92a METAPHYSICA
of the universe to that of animals and plants, on the groundthat the more complete always comes from the indefinite and
incomplete which is what leads this thinker 1
to say that
this is also true of the first
principlesof
reality,so
that ther 5 One itself is not even an existing thing. This is incorrect,
for even in this world of animals and plants the principles
from which these come are complete ;for it is a man that
produces a man, and the seed is not first.
It is out of place, also, to generate place simultaneously
with the mathematical solids (for place is peculiar to the
individual things, and hence they are separate in place ;
20 but mathematical objects are nowhere), and to say that
they must be somewhere, but not say what kind of thing
their place is.
Those who say that existing things come from elements
and that the first of existing things are the numbers, should
have first distinguished the senses in which one thing comes
from another, and then said in which sense number comes
from its first principles.
By intermixture? But (i) not everything is capable of
2 5 intermixture, and (2) that which is produced by it is differ
ent from its elements, and on this view the one will not
remain separate or a distinct entity ;but they want it to
be so.
By juxtaposition, like a syllable? But then(i) the
elements must have position ;and (2) he who thinks of
number will be able to think of the unity and the plurality
apart ;number then will be this a unit and plurality, or the
one and the unequal.
Again, coming from certain things means in one sense
that these are still to be found in the product, and in another
30 that they are not;in which sense does number come from
these elements ? Only things that are generated can come
from elements which are present in them. Does number
come, then, from its elements as from seed ? But nothing
can be excreted from that which is indivisible. Does it
come from its contrary, its contrary not persisting ? But
all things that come in this way come also from something1
Speusippus ;cf. A. io;2
b30-34.
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BOOK N. 5 iog2a
else which does persist.1
Since, then, one thinker2
places 35
the i as contrary to plurality, and another3
places it as
contrary to the unequal, treating the i as equal, number iog2b
must be being1
treated as coming from contraries. Thereis, then, something else that persists, from which and from
one contrary the compound is or has come to be. Again,
why in the world do the other things that come from con
traries, or that have contraries, perish (even when all of the
contrary is used to produce them), while number does not ?
Nothing is said about this. Yet whether present or not 5
present in the compound the contrary destroys it, e. g.
strife destroys the mixture 4
(yet it sho2ild not;for it is
not to that that it is contrary).5
Once more, it has not been determined at all in which
way numbers are the causes of substances and of being
whether (i) as boundaries (as points are of spatial magni
tudes). This is how Eurytus decided what was the number 10
of what (e. g. one of man and another of horse), viz. by
imitating the figures of living things6 with pebbles, as
some people bring numbers into the forms of triangle and
square. Or (2) is it because harmony is a ratio of numbers,
and so is man and everything else ? But how are the 15
attributes white and sweet and hot numbers ? Evidently
itis
not the numbers that are the essence or the causes ofthe form
;for the ratio is the essence, while the number is
the matter. E, g. the essence of flesh or bone is number
only in this way, three parts of fire and two of earth .
T
And a number, whatever number it is, is always a number
of certain things, either of parts of fire or earth or of units;
but the essence is that there is so much of one thing to so 20
much of another in the mixture ; and this is no longer
a number but a ratio of mixture of numbers, whether these
are corporeal or of any other kind.
1Cf. A. io69
b3~9, Phys. \. 7.
2
Speusippus.3
Plato.4
Cf. Empedocles, Fr. 17.5 a
I7~b 8 seem to refer mainly to Speusippus.
6
Eurytus may have used (pvrd in this wider sense, as Plato some
times does. The ordinary Aristotelian sense plants would be difficult
here.7
Cf. Empedocles, Fr. 96.
645-28 X 2
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io92b METAPHYSICA
Number, then, whether it be number in general or the
number which consists of abstract units, is neither the cause
as agent, nor the matter, nor the ratio and form of things.
25 Nor, of course, is it the final cause.
One might also raise the question what the good is that 6
things get from numbers because their composition is
expressible by a number, either by one which is easily
calculable or by an odd number. For in fact honey-water
is no more wholesome if it is mixed in the proportion of
three times three, but it would do more good if it were in no
particular ratio but well diluted than if it were numerically
3o expressible but strong. Again, the ratios of mixtures are
expressed by the adding of numbers, not by mere numbers;
e. g. it is three parts to two,not three times two . For
in any multiplication the genus of the things multiplied
must be the same;therefore the product 1x2x3 must be
measurable by i, and 4 x 5 x 6 by 4, and therefore all pro
ducts into which the same factor enters must be measur-
35 able by that factor. The number of fire, then, cannot be
2x5x3x6, and at the same time that of water 2x3.IO93
aIf all things must share in number, it must follow that
many things are the same, and the same number must belong
to onething
and to another. Is number the cause, then,
and does the thing exist because of its number, or is this
not certain ? E. g. the motions of the sun have a number,
5and again those of the moon, yes, and the life and prime
of each animal. Why, then, should not some of these
numbers be squares, some cubes, and some equal, others
double ? There is no reason why they should not, and
indeed they must move within these limits, since all things
were assumed to share in number. And it was assumed
that things that differed might fall under the same number.
10 Therefore if the same number had belonged to certain
things, these would have been the same as one another,
since they would have had the same form of number;
e. g.
sun and moon would have been the same. But why need
these numbers be causes ? There are seven vowels, the
scale consists of seven strings, the Pleiades are seven, at
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BOOK N. 6 logs3
seven animals lose their teeth (at least some do, though
some do not), and the champions who fought against 15
Thebes were seven. Is it then because the number is the
kind of number it is, that the champions were seven or the
Pleiad consists of seven stars ? Surely the champions were
seven because there were seven gates or for some other
reason, and the Pleiad we count as seven, as we count the
Bear as twelve, while other peoples count more stars in
both. Nay, they even say that E, IF, and Z are concords, 20
and that because there are threeconcords,
the double con
sonants also are three. They quite neglect the fact that
there might be a thousand such letters;for one symbol
might be assigned to PP. But if they say that each of
these three is equal to two of the other letters, and no other
is so, and if the cause is that there are three parts of the
mouth and one letter is in each applied to sigma, it is for
this reason that there are only three, not because the concords are three
;since as a matter of fact the concords are 25
more than three, but of double consonants there cannot be
more. These people are like the old-fashioned Homeric
scholars, who see small resemblances but neglect great
ones. Some say that there are many such cases, e. g. that
the middle strings are represented by nine and eight1
,and 30
that the epic verse has seventeen syllables, which is equal
in number to the two strings, and that the scansion is, in
the right"
half of the line nine syllables, and in the left eight. iO93b
And they say that the distance in the letters from alpha to
omega is equal to that from the lowest note of the flute to
the highest, and that the number of this note is equal
to that of the whole choir of heaven. It may be suspected 5
that no one could find difficulty either in stating such
analogies or in finding them in eternal things, since they
can be found even in perishable things.
But the lauded characteristics of numbers, and the con
traries of these, and generally the mathematical relations,
as some describe them, making them causes of nature,
1 The ratios corresponding to the fourth and the fifth are respectively8 to 6 and 9 to 6.
2i. e. first.
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io93b METAPHYSICA
10 seem, when we inspect them in this way, to vanish;for
none of them is a cause in any of the senses that have been
distinguished in reference to the first principles.1 In a sense,
however, they makeit
plainthat
goodness belongs to
numbers, and that the odd, the straight, the square, the
potencies of certain numbers, are in the column 2 of the
beautiful. For the seasons and a particular kind of number
15 go together ;and the other agreements that they collect
from the theorems of mathematics all have this meaning.3
Hence they are like coincidences. For they are accidents,
but the things that agree are all appropriate to one another,
and one by analogy. For in each category of being an
analogous term is found as the straight is in length, so is
20 the level in surface, perhaps the odd in number, and the
white in colour.
Again, it is not the ideal numbers that are the causes of
musical phenomena and the like (for equal ideal numbers
differ from one another in form;for even the units do) ;
so
that we need not assume Ideas for this reason at least.
These, then, are the results of the theory, and yet more
25 might be brought together. The fact that our opponents
have much trouble with the generation of numbers and can
in no way make a system of them, seems to indicate that
the objects of mathematics are not separable from sensible
things, as some say, and that they are not the first
principles.
1Cf. A. I, 2.
2Cf. note on A. 986*23.
3Sc. that numerical relations are found in things, but are not the
cause of anything that happens.
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INDEX
oa 93b = loooa
a privative, its meanings 22" 32.
Abstraction 36b
3, 23, 6i a29 ;
)( qualification 982a
27, 30* 33,
77b
10.
Accident, accidental A. 30, E. 2, 3,
K.8, 7aI5,2i-
b16, 13
b34-i4
a20,
1 5b
1 7, 1 7a7, 27
b33 ;
not knowable
26b 3, 64b
30, 65a
4 ;its cause
matter 27a
13; twofold 3ib22;
the same by accident 37b 6
;
nothing accidentally perishable
59a
i; )(
essential 65* 6.
Action, concerned with individuals
981* 17 ; )( motion 48b 21.
Actuality (eYepyfia) 0. 6-9, K. 9 ;
)( potency 3a
I, 7b28, 69
b16, 7i
a
6,b 22
;coni. substance, form,
definition, essence 42b
10, 43a18,
25,28, 30, 5<D
a16,
b2, 5i
b3i,7i
a
8; )( matter 43a6, 45
a35 7i
b2i,
76* 10;
differs with different
matter 43a 12
;the actual identi
cal with the potential 45b 21
;coni.
complete reality (eVreXe^aa) 47a
30, 5oa 22
; )( knowledge 48b15 ;
)(motion 48
b 28;coni. action 5o
a
22;God s actuality pleasure 72
b
16; actual, syn. individual I4a21.
Aegina I5a25.
Affection, modification, attribute
(rrddos), its meanings A. 21;
)( substance 983b
10, g85b
11,
38b
28, 7ia2; coni. states 986
a
17, 2oa 19; coni. accidents,
movements 98c;b
3, 7ia 2
; )( sub
stratum 49a29 ; essential, proper
4b6, 58
a37,
b22, 78
a16
; changein respect of 69
b12.
Alcmaeon 986a
27.
All (Traira), coni. total 24a
8.
Alteration 989a
27, 42a
36, 69b
12,
88a 32.
Analogy43
a5, 48
a37,
b7,
89
b4,
93b
19; the same by i6b 32, i8a
18-21, 988a
17, 28, 3o-b21,
99ia
1 6, 9a27, i2a 26, 63
b25-30,
b20-32, 7i
b27, 72
a5, 20, 75
b
79b
20, 9ib
ii ; quoted 7
b
25,
9 25, 56b
2
15, 28b 5, 69b3i.
Anaximander 69b 22
;referred to
988a30, 52
b10, 53
b16, 66b 35.
Anaximenes 984a
5 ;referred to
984a27, 988
a30, 996
a9, i
a15,
53b
16.
Antisthenes 24b32 ;
referred to 5b
2-5(?),6a5(?),u
a7(?), I2a 2i;
his school 43b 24.
Appearance (^aiveadai, ^avraala) Y.
5, 6, 98ob26, 7o
a10. v. Image.
Archytas 43a21.
Aristippus 996a32 ;
referred to 78a
3i-b6.
Aristotle, references to An. Post.
25a
34, 37b8; Phys. 983** 33,
98sa
12, 986b
30, 988a
22, 993*
ii,42b8(?), 49
b36, 59
a34, 62b
3i(?), 73a 32(?), 76a 9, 8 a 23
(?) ;De Caelo 986
aI2(?), 989**
24, 73a
32(?), 86a 23 (?), 88b
24 (?) ;De Gen. et Corr. 42* 8
(?),
62b 3i (?),86a23(?); Met. A.995
b
5, 996b
8, 14, 997b
4, 59a
19 5B -
993a26, 4
a32, 53
b10, 76
bI, 77*
i, 86a 34(?),bi55 A. 26a 34 ,
28a
4,b7, 56
b355 Z.
1 6, 45 a7(?) 5
b
17, 76a
9; H.
494, 52a
15, 55a
2,
4, 18, 20, 43b
32, 49b 27, 53
13, i7, , 26,
Anaxagoras 984a
11-16,b
IS, 985**
, 39a22(?),
45b27, 76
a9; 9. i7 9, 2i a 20,
27b29, 76
a9, 88b 24(?) ;
A. 27a
19, 64a
36; M. 37* i 3 (?), 42a
22 (?), 9oa
15, 28; N. 37a
i 3 (?),
42a 22 (?), 86
a30 ;
Eth. Nic. 98 ib
25 ;lost works 986
a 12 (?), 4a
2,b
34, 2i a20(?), 54
a30, 6i a
15.
Arithmetic 982a28, 5
a31, 9o
a14 ;
arithmetical number 83b 16.
Art 98ob 28
;comes by experience
98ia3; )( science 98i
b 26; )( ex-
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INDEX
perience 981* 25,b8, 31 ; genera
tion by nature, art, spontaneityZ. 7-9, 7o
a6, 17; by reason, art,
faculty 25b 22
;
= form 34a24, 70*
15; comes by learning 46b37, 47
b
33;
architectonic arts 13* 14.
Assertion, syn. affirmation 8a 4-b
i,
62a 24 ; )( affirmation, syn. con
tact 5ib24.
Associable numbers M. 6-8.b
33, 997 16, 35,
2.
Astronomy 98gb
998a
5, 53a 10
Athens iob 10.
Atlas 23a 20.
Atomists referred to 28b 5, 84b
27.
Attribute )( substance 995b 20, 3 a 25.
v. Affection.
Axioms 26, 5a20,
b33, 90* 36.
Beautiful, syn. good I3a22, 9i
a31 ;
)( good 78* 3i-b
5 ;an original
principle 72b32.
Becoming, .v. Generation.
Being (ov) A. 7, I9a
4, 28a lo, 3oa
j
21, 42b25, 45
b32, 6i a
8, 78a
30,j
89a7 ;
not a genus 998b 22, 45 b 6;
and unity I. 2, 986b
15, 9g8b
22,
ia5-
bi, 3
b22, 4o
bi6, 45
b6, 53
b
25 ; being qua being, in general,
without qualification )( particu
lar being r. i -2, E. i,6ob 3 1
;acci
dental being E. 2, 3, I7a7 ; being
as truth E. 4, e. 10, 65a 21
;in
full sense 27b
31, 5ib
i; primary
being,substance 28a
14, 30; beingof a thing 29a22, $2
b11, 75
b5 ;
being not the substance of things
ia5~
bi, 4o
b1 8
; completely real
)(material 78
a30; non-being is
non-being 3b 10
; subject of so
phistic 26b 14 ;as falsity E. 4, 0.
lo;source of becoming 62b 26,
69b
1 8;three kinds 69
b27 ;
am
biguous 89a
1 6; proof of its reality
(Platonists) 89a
2.
Between, v. Intermediate.
Broad and narrow (Platonists) 992a
12, 88b 8.
Callias 981* 8, 33b
24, 34a6.
Callippus 73b
32.
Categories 4a
29, 1 7a
23, 24b
13,
26a 36,27b3i, 28a
13, 33, 29*23,
34b
10, 5ia35, 55
ai, s8
a14, 7o
b
i, 88* 23, 89a
27,b24.
Cause A. 2, I3a
16, 26a 17 ; philo
sophy a study of first causes 98ib
28;of all causes ? 995
b6, 996
a
1 8; primary g83
a25, 3
a31 ;
proximate 44b
i;four causes 983
a
26, 7ob 26
;formal = final 44
bI
;
= efficient 7ob 26
;causes not
infinite in number a. 2, 74a
29;
cause of accident accidental 27a
8, 65a 6
; generable without being
generated E. 3. v. End, Essence,
Final, Form, Formula, Matter,
Motive, Principle.
Change, by something to something
984a
22, 69b
36 ;from opposite
to opposite or intermediate n b
34, 57a
21, 31, 69b3; contraries
do not change 69b 7 ; coni. non-being, substratum, matter, potency ioa 15, 42
a33, 69
b14, 24;
four kinds 42a32, 69
b9, cf. 72
b8
;
changeable substance 69* 3.
Complete A. 16, 23a34 ;
def. 55a
1 1;
said to proceed from incomplete
72b34, 92
a13.
Compound,composite (o-vvOfros) 23a
31,b
i, 29b
23, 43a
30, 75a
8, 88b
15-
Concrete (o-^oXo?) 995b35, 999
a33,
29a
5, 35b22, 37
a26, 30, 77
b8.
Contact 2a 34, I4b
22, 68b 27, 7oa
10, 82a20, 85
a3 ;
coni. intuitive
thought 5ib
24, 72b 21.
Contiguous 69a
i.
Continuous, def. 69a
5 ; by nature,
art, force i6 a 4, 23b34, 4o
b15 ;
in
one,two,
three dimensions 6i a
33;continuity )( form l6b 9.
Contradiction, law of F. 3-6, K.5,
6;no intermediate r. 7, 55
bj,
69* 35 )( privation, contrariety
55a38-
Contrary I. 4, 5, 7, i3b
12, i8a 25,
54a25,
b31, 58
b26, 92
a 2;con
traries said to be principles of
being 986a22,
bi, 4
b30, 7s
a28,
87
a
30;
knowledge of them one996
a20, 6i a
19, 78b26; reducible
to one principle 4a
i,b27; con
trariety )( difference, otherness,
contradiction, privation, 4a20, 54
b
32, 55b
I;one of two contraries
always privative 4b
27, n b18,
55b
14, 27, 6i a19, 63
b17; con
traries incompatible n b17, 63
b
26;coni. negation I2a g ;
contra
riety in substance i8b 3 ; contraries have same form 32
b2
;not
produced from, compounded of,
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INDEX
affected by one another 44b2
5, 57b
22, 69^ 7, 75a30; contrariety
=
greatest, complete, difference 5 5a
4, 1 6, 58* II;one term one con
trary 55
a
19;contraries relative
56b
36 ;intermediate composed
of contraries I. 7 ;which contra
rieties make difference of speciesT. 9 ; prime contrarieties in being6i a
12,b
5, 13 ;sensible con
trarieties 6i a32 ;
in place 68b 30 ;
)( opposite 69b4 ;
contraries in
volve matter 75b22, 87
bi.
Coriscus I5b17-32, 26b 18, 37
a7.
Counter-earth 86* 12.
v) 3<D
bCoupled term
(a-v
1 6, 3ia
6, 43a
4-
Cratylus 987a32, loa 12.
Definition (6piarp.6st opos) Z. 10-12,
H.6, 3ia2, 43
a 21; starting-point
of discussion I2a 22,b7; coni.
essence 3oa
7, 3ian, 44
aI
;not
of the concrete and sensible 36a
2, 39b28 ; of the universal 36
a28;
why one Z. 12, H. 6; definition|
by division 37b 28
;scientific 39
b
32 ;no Idea definable 4O
a 8;
coni. number 43b
34, 45a
7. v.
Formula.
Democritus 5-20, 9a27,
b n
Dialectic 32, 23, 4 17,
J5> 39 9? 42 II, 09 22, 78 20;
referred to 29b 21.
Demonstration 992b31 ; principles
of993b 28, 996b 26, 5b 9, ii, 13,
18, 22, 62a 3 ;not everything de
monstrable 997a
7, 6a 8, iia13;
essence not demonstrable 25b14,
64a
9 ;sensible things not de
monstrable 39b 28
;demonstra
tion of necessary truths 39b31 ;
absolute and ad hominem 62* 2;
demonstrative science 997a5-30.
Destructible, destruction, perish
able 994b 6, oa 6, 22, 27, b25, 27 a
29, 42a30, 43
b15, 44
b36, 59
ai,
67b24, 69
a31,
bu, 7o
a15.
Differentia, difference 985b
13,
23, 4a
14, 2oa 33, 35,b
2, 15,
42b
15, 58a
7; its meanings i8a
12; )( otherness, contrariety 4
a
21, 54b
23, 55a
4, 1 6, 58* u ; j
opposite, prior, contrary differen
tiae i6a
25, 57b
5,ii
; generic,
specific i8a 26, 54b 28
;kinds of
42b
32; definition by 43* 19;
what makes it I. 9 ;matter does
not make it 58b6; first differ
ences 6i b 14; of numbers, units
M. 8;
three differences
(Democritus) 985
b13, 42
b 12.
Diogenes 984a
5 ;referred to 996
a
8, ia
15.
Dionysia 23b 10.
Disposition A. 19.
Divine, the 26a 20, 64* 37 ;not
jealous 983a 2
;encloses the uni
verse 74b3 ;
visible divine bodies
26* 1 8;
the divinest knowledge
9?3a
5-
Division, mathematical 994b
23, 2a
19,b
3, 10, 48b
1 6, 6ob 14, 19;
logical 37b 28.
Dyad (two), indefinite 987b
26, 33,
988a
13, 8i a14, 22,
b21, 32, 82 a
I3,b
3o, 83b36, 8 5
b7, 87
b7, 88b
28, 89a35, 9i
a5 ;
ideal 36b14, 8ia
23,b27, 82b
9, 12, 20, 22;the
first number 999a8, 85
b10, 88 b
9.
29, 986b
Egypt 98ib
23.
Eleatics referred to
10, 28b 4, 75b
15.
Element A. 3, M. 10, 989* 4, 992b
18,
ia
1 8, 59b23, 88
b4 ;
whether only
potential 2 b 33 ;coni. principle,
four elements (Empedocles) 984a
8, 985a32, 998
a30 ;
of Ideas 987b
19.
Empedocles 984a
8, 985** 2-10,
2i-b 4, 988a
1 6, 27, 989a20-30,
993a
17, 996a
8, 998* 30,a24-
b20, i
a12, 69
b21, 72
a6, 75
b2,
9ib ii
; quoted oa 29,b
2, 6, 14,
9b
17, I4b
37 ;referred to 984
b
5, 994a
7, 4b
33, 28 b5, 5o
b24,
53b
15, 92b
7-
End, syn. final cause 994b
9, 16,
3a
33, 59a 37, 74a 3; c ni -
shape 23a
34 ;coni. actuality
5ia
1 6.
Epicharmus ioa 6, 86a 16.
Equal, def. 2i a12, 56
a22, 82b 7 ;
how opposed to great and small
I. 5 ; syn. one (Plato) 75a33.
Equivocal, equivocation 3a
34, 3oa
32, 35b
25, 46a6, 6ob 33, 86b 27.
Eristic I2a 19.
Error )( ignorance 52a 2.
Essence( rjv flvai) Z. 4-6, 8, 993*
1 8, 994bi7,25
b28,3S
bi4, 45
b3J
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INDEX
coni. definition 3Oa 6
;coni. form
33b
5-
Eternal 987b
16, I5b
14, 5ob
7, 51*
20;eternal sensible substance 69
a
3i,b25; necessity of an eternal
substance A. 6 ; time eternal
7ib
7; eternal things, whether
composite 8bb 14 ; ungenerated
9ia
12.
Eudoxus 99ia
17, 73b
17, 79b
21.
Eurytus 92b 10.
Even (Pythagoreans) 986* 18, 99oa
9; (Plato) 9ia24.
Evenus I5a29.
Evil, none apart from particular
bad things 5i a 17; none amongeternal things 5i
a20; said to be
a first principle 75a
35, 9ib34 ;
caused by strife (Empedocles)
984b32.
Excess and defect 992b
6, 4b
12,
42b
25, 35, 52b30, 57
a13, 8;
b18.
Experience 98ob 28
;coni. science,
art 98ia
I,b
31 ;
=knowledge
of individual facts
g8i
a
15.
Falsity, def. n b25; its meanings,
A. 29; non-being in sense of
falsity E. 4, e. 10; )( impossi
bility 47b
14; a first principle
(Plato) 89a
20.
Female sex, coni. matter 24a
35 ;
not a species I. 9.
Final cause (ov eWa) 31, 994
9, I3
a
2i, 33,
b
26, 44a
36, 5
a
8,
59a36, 72
b2. v. .Z^/.
First, its meanings 28a 31. v.
Primary.
Form, things referred to by namingtheir form 35
a8
;more real than,
cause of, matter 29a
5 ;coni.
essence 32b
I, 33b
5, 35b32 ; syn.
shape 999b
16, i5a
5, i7b25, 33
b
5, 44b22, 52
a23, 6oa 22,
b 26;
=
art 34a 24, 7oa 15 ; not generated
34b
7, 42a
30, 4 3b
17, 44b
21,
69b
35, 7oa15; coni. definition,
formula i6b 9, 35a21, 36
a28,
b5,
42a28, 43
a19, 44
b12, 69
b33, 84
b
10; syn. substance 32
bi, 4i
b8,
5ob
2, 84b 10
;
= final cause 44b
i; = efficient 7ob30 ; syn. posi
tive state 44b
33 ; )( becoming
5oa4 ; )( matter 5o
a15, 7o
ai,
84b 10; )( privation 44b 33, 7ob
11;
its parts Z. 10, 11. v. Shape,
Species.
Forms (Platonic), v. Ideas.
Formula, definition, account (\6yos)
987b
31, i6a 33,b
9, 28a 34,42*
28, 43aI9,47
b34> 5
b33 I prin
ciples in the 996a
I;formula of
the essence is one 998b 12; )(
word 6b i, 3oa
7 ;formula )(
definition (opio-^os-j 3oa
7, 14, 37b
II; parts of Z. 10, n, i6a 35,
23b
23, 33a
2; prior in i8b 31,
28a 3 2, 38b27,49
bii, 54
a28,77
b
i, 78a 10
; )(concrete individual,
matter 39b
20, 58b
10, 18, 64a23,
74a
34 ; separable in 42a
29 ;
coni. science 46b
7, 59b 26
;
analysis of 63b 18;cause as de
finition 7oa 22
; primary in de
finition, in time &4b
15 ;one in
definition, in number 87b
12.( From
,its meanings A. 24, 99i
a19,
994a22, 44
a23, 92
a23.
Full (Democritus) 985b
5, 9a28.
Generation, production, becoming,is of the concrete
thingZ.
8, 98ia
17, 34b
7, 42a
30, 43b
17, 44b
2i,
69b
35* ?oa
5; posterior in
generation, prior in nature, form,
substance 9&9a
15, 5oa4, 77
a 26;
two types 994a 22
;from non-
being, matter, privation, con
traries, the potential 994a27, 32*
20, 33a
9> 55bn,62
b26, 69
b18,
88b 17, 9ib
34; of something
from something by something999
b6, ioa 20, 3 2
a13,
b3i, 33
a
24, 44b24, 49
b 28; by nature, art,
spontaneity Z. 7, 9 ; )( making 32a
26; the product must be divisible
33b
12, 49b
35; from a memberof the same species 34
a21, 49
b
29, 7oa
5 ;absolute and partial
42b
7, 67b22, 69
b10, 88 a
33.
Genus A. 28, 54b
30, 57a
27,b
38,
59 b 27; proximate, ultimate 995 b
29, 998b
15, 999a
31, 23a
27,
34a
I, 37b
3<^ 59b27; whether
genera are first principles 998a
21, I4b
11, 42a
14, 69a
27;
part of species 23b
24 ;coni.
definition, differentia, species Z.
12, 998b
5, i3-999a
23, Mb9,
i6ft
24,b
32, 23a27,
b18, 37
b19,
39a
26, 54b
27, 57b
7, 59b36 ;
being and unity not genera 998b
22, 45b 6
;is matter of species
24b
8, 38a
6; other in genus
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INDEX
24b9; )( universal 28b 34; not
substantial Z. 13, 42* 21, 53b 21
;
otherness of the genus $8a
7.
Geometry 983* 20, 992a
21, 997b
27, 998a
i, 5a
ii, 31, 5ia
21, 6ib
3, 78a25, 89
a 22.
God, a first principle 983a 8
;is life
72b
14 ;identified with the One
by Xenophanes 986b
24 ; godsin human form 997
b10, 74
b5 ;
the
stars held to be gods 74b
2.
Good, syn. final cause 983a
31,
59a
36; syn. beautiful I3a
22,
91a30 ; )( apparent good I3
b27 ;
how a first principle 75a 12, 38 ;
)( beautiful 78a
31; whether
discussed by mathematics 78a3 1
;
how related to first principles
9ia30, 92^ 9 ;
Idea of 996a
28.
Great and small, how opposed to
equal I.5 ; (Plato) 987
b20, 26,
988* 26, 992a
12, 998b
10, 83b23,
32 ;kinds of 992
an, 85
a9.
Habit, having, state (cgis) A. 20,
986* 17, I5b
34, 44b
32, 46a
13,
70a 12
; )( privation 55b13.
Harmonics 997b
21, 77* 5, 78* 14.
Have, hold, its meanings A. 23.
Hearing 98ob
23.
Heaven, only one 74a31.
Hellen24a33.
Hellenes 24a33.
Heraclidae 58a24.
Heraclitus 984a
7, 987a33, 5
b25,
ioa ii, 13, I2a 24, 34, 62a 32,63b
24, 78b
14; referred to 984a27,
989a
2, 996a
8, ia
15.
Hermes 2a 22, I7b
7, 48a33, 5o
a
20.
Hermotimus 94b19.
Hesiod g84b
23, 989a
10, oa 9 ;re
ferred to 983b27, 23
a19, 9i
b 6;
quoted 984
b
27.Hippasus 984
a7 ;
referred to 996a
8, ia
15.
Hippo 984a
3.
Homer 9b
28; quoted 76a4; re
ferred to 983b30, 9t
b 6;Homeric
scholars 95a27.
Homoeomerous 984a
14.
Hot, the (Parmenides) 987** I.
Hypothesis )( necessary principle
5
b
IS-
Ideas (Platonic) A. 6, 9, B.6, Z. 6,
M, M. 4, 5, 988b
i,997b
2, ia
4,
28b 20, 33b
27, 36b
13, 42a
ii,
59a
10, 7oa
27, 73a
I7 75b
18,
76a3 i,83
b34, 86a 31,
b14, 9
a
16,b20, 9i
b 28;elements of 987
b
19; of negations 99ob
13, 79a
9 ;
of relations 99ob
16, 79a12; of
manufactured objects 99 ib
6, 6ob
28, 7oa
14 ;coni. numbers 99 i
b
9, 76a20, 8ob 12, 22,8i
a21, 83
b
3, 86a 4, 88b 34, 9b
33, 35, 9ib
26; participate 99o
b28, 40* 27 ;
eternal sensibles 997b
12; as
causes 33b 26
;how related 39
b
4 ;indefinable 4o
a 8;transcen
dent 40a 9, 86a 33 ; universal 42a
15, 86a 33 .
Ignorance )( falsity, error 52a2.
Iliad, an artificial unity 3Oa
9,b9
45a
13-/
Image (fyavraa p.o) 99ob
14, 79a
ii.
v. Appearance.Imitation (Pythagoreans) 987
b n.
Imperishable I. 10, 4ob3i.
Impossible I9b 22
; )(false 47
b14.
In ,its meanings 23a 24.
Inassociable numbers M. 6-8.
Incapacity, impotence, its mean
ings I9b
15, 46a29.
Incomposite entities 5ib
17, 27.
Increase 42a
35 ; )( diminution
6o.bn, 88a 31.
Individual (aro^12
; (naff eKaarov acton con
cerned with individuals 98 ia
17 ;
is there anything apart from
individuals ? 999a
26, 6oa 3 ; syn.
numerically one 999b
33 ;are
the first principles individual ?
M. 10, 3a
7, 7ia20; syn. actual
I4a 21
; prior in order of perception i8b 33- v. This.
Indivisible (udiaipeTov) I. i;
in
quantity, in kind 999a
2, i4a27,
l6a
19,
21;
(iiTOfjiov) lines, magnitudes 992a
22, 83b
13, 84b
i;
species, form 998b
29, 34a
8,
58a
18; indivisible in genusi8b 6.
Induction )( demonstration, defini
tion 992b
33, 48a
36 ;used 25
b
15, 54b33, 55
a6,
b17, 5
a9 64*
9 ;Socratic 78
b28.
Infinite, the a. 2, K. 10;as sub
stance and principle 987
a
16,
995b
29,
9, 4b33 ; composed of great and
small 987b 26
;causes not infinite
in number a. 2, 74* 29 ;not
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INDEX
thinkable 994b
22, 30, 999a
27 ;
by addition 994b30 ;
how potential 48
b9 ; has no separate exis
tence 48b14 ;
infinite regress 994a
3, 8, 20,b
4, ob 28, 6a 9, ica 22,
I2a
12,b
22, 22b
9, 30b
35, 32*
3, 33b
4, 41b
22, 6oa 36, 7oa
2,
74a
29; no infinite magnitude
73a
10; whether number is in
finite 83b
36 ; principles infinite
in number (Anaxagoras) 984a
13.
Intelligible )( sensible 99oa
31,
999b
2, 36a
3, 10, 45* 34.
Intermediate, def. 57a
21, 68b 27;no intermediate between contra
dictories r. 7, 55 b i, 69a 3 ; composed of contraries 1. 7 ; (Plato)
987b
1 6.
Intuition (vorjo-is), coni. perception,
definition 36* 6. v. Thinking.Ion 24
a34.
lonians 24a33.
Italian school 987a
10-31, 988a26.
Itself, used to signify Ideas 4ob34.
|
Knowledge, science (eVaa-T^/), de-j
sired by all 98oa 21
; springs i
from sensation o.8oa 28
; )( artj
98 ib 26
; theoretical, productive,j
practical 982a
i, 993b
20, 25b
21,
46b
3 ; pure, applied, superior,
ancillary o,S2a
14, 30,b
4, 27,
996b 10
;its highest object 982
b
I, 996b
13; the divinest know
ledge 983
a
5 ; is of causes 983a
25, 993b
23, 994b
29, 25b 6
;not
of the sensible or accidental Z. 15,
987a
34, 26b 3, 27a
20, 64b
30,
65a
5, 77b35 ; knowledge of con
traries one 996a
20, 6i a19, 78
b
26;
is of species, form 998b
7,
3ib
6; )( sensation 999b
3; of
universals, individuals 3a
14, 59b
26, 6ob20, 86b 6, 87
a15 ;
one
science to one genus 3b n, 55 a
31 ; )( opinion 8b 27, 30, 39b32 ;
prior in l8b 30, 28a 32 ;ratio-
cinative 25b 6
;not of matter
36a 8 ;
coni. definition, formula
28a32, 46
b7, 59
b 26; )( actuality
48b
15 ;how a measure of ob
jects 57a
9 ;its two meanings
87a
15-
Leucippus 985b 4, y
referred to 84b
27.
Libya iob u.
32, 72 a7;
Like, def. i8a 15, 2i a11, 54
b3;
said to be known by like ob5.
Limit, its meanings A. 17; of bodies
2b 10, 6ob 16; (Pythagoreans)
987a
15, 99oa
8, 4b
32.
Line 2a
5, i6b
26, 36b 12, 43a33;
perceptible lines 998a
i;not com
posed of points ib18
;indivisible
line9p2
a22, 84
bi.
Logic (dva\VTid) 5b
4.
Love (epos) (Parmenides) 984b
24,
988a
34; ((piXia, (j>i\oTr)s) (Em-
pedocles) g85a
3, 24, 988a
33,
ob n.
Luck (TVXI) 98ia
5, 984b
14, 32a29,
5-a 30- generation by nature, art,
spontaneity, luck Z. 7, 49a
3,
7oa
6.
Lycophron 45b
10.
Magi 9ib
10.
Making )( production 32a
26; )(
thinking 32b
15.
Male and female I. 9.
Many)( one I. 3, 6
; )( much56
b
15 ;matter of the one 75
a33;
and few (Platonists) 87b
16.
Mathematics 98ib23,985
b24, 992
a
32, 996a29,4
a9, 26a 7, 9, 12, 19,
6i a28,
b32, 64
a32, 77
bi,78
a33;
mathematical objects )( sensible
989b32, 99o
a15, 36
a4l )( Ideas
B. 6, 28b 20, 76* 20, 83a23, 9o
b
26; many of one species 2b 14;
whether substances M. 1-3, 42
a
n, 69a35 ;
not separable 59b13;
mathematical matter 992b
2, 59b
16; language 995a
6, 8ob 26;
parts of mathematics 4a
7 ;
mathematical sciences )( productive 64
ai
;mathematical number
M. 6, 76a20, 86a 5.
Matter H.3, 4, 983* 7-94
a18, I5
a
7, I7a
5, 42a
26, 58b
6, 14; def.
29a 20 , syn. substratum 983 a 29,
985b
10, 988au, 992
bi, 22a
18,
24b8,42
a26, 32,
b9, 6i
b22, 7o
an;
a principle 983b7,986
a17,46* 23 ;
)( definition, form, complete re
ality, actuality 986b
20, 29a
5,
35a
8, 38b6,4i
b7, 43
a6, 45
a35,
5oa
15, 7oa
i, 7ib
21, 74a34, 76
a
9, 78a30, 84
b9 ;
coni. female sex
24a35 I genus matter of species
24b 8, 38a 6;coni. motion 26a 3;
cause of accident 27a13 ;
whether
substance Z. 3, 42a27, 49
a36, 77
a
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INDEX
36 ; necessary, to explain generation and change 32* 17, 42* 32,
44b27, 69
b3 ;
unknowable in it
self 36* 8; perceptible )( intelli
gible36*
9,b
35, 45
a
34;
indefi
nite 37a27, 49
bi
;coni. potency
39b
29, 42* 27,b
9, 49a23, 50*
15, 6oa 20, 69b
14, 7obI2,7i
a10,
88b i, 92a
3; indestructible 42*
30 ;matter for locomotion, gene
ration, &c. 42a
34,b
6, 69b 26
;
actuality varies with it 43a 12
;
proximate matter 44a17; )( sub
stratum 44b9 ; proximate matter
=shape 45
b 18;
of mathematical
objects 992b
2, 59b 16
;different
things have different matter 69b
25 ;individual in appearance 7o
a
10;involved in contraries 75
b
22, 87b
i.
Measure, def. of unity $2b
18, 87b
33 ; exact, homogeneous with
thing measured, indivisible 52b
36 ) 53a
25, 88a2; how know
ledge is a measure 57a
9 ;
manthe measure of all things (Prota
goras) 53a36, 62b 14, 19, 63
a4.
Megaric school 46b29; referred to
5b35 (?).
Melissus 986b
19.
Memory 98oa
29.
Middle, excluded r. 7.
Mixture, intermixture 989b
2, 42b
29, 82a 2i, 92a
24.
Monists 986b 21.
Motion, spatial (< >pa) 6gb
12, 26,
72b
5 ;the first kind of change
72b
8, 73a12; simple 73
a29 ;
of
the planets A. 8.
Motive cause A. 3, 4, 983a30, 984
a
27, 988b
27, 996b
6, I3b9,24;
necessity of 991b
5, 8oa 4 ; priorto the moved iob 37, 7o
a 21;
unmoved prime mover A. 7, i2 b
31 ;fire a motive cause 984b 6;
the self-mover (Plato) 72a
i.
Movement(KIVTJO-IS), coni. sensation,
matter 989b
32, 26a 3, 36b29 ;
)( rest 4b
29, ioa 36, I2b 23, 25b
20, 49b
7 ;coni. activity, action
20b 20, 22a7,
b5, 23
a 18;coni.
nature 25b 20
; )( action 48b 18
;
)( actuality 48b
28; eternal 7ib
7, 33 ; simple, continuous, un
resting, uniform movement 53a
9, 7ib
9, 72a2i,78
a13.
Music of the spheres gS6&
2, 93b
4.
Mutilated A. 27.
Myth 982b
18, 983b29,995
a4, oa
9,
I8,7ib27,74
bi,4,75
b26,9i
a34.
Nature,
its
meanings
A. 4 ; )( habit,
spontaneity, luck, thought 98 ib4,
32a
12, 65a
27, 7ob
30, 7ib
35 ;
)( generation 989** 15 ;not the
whole of reality 5a
34 ; syn.
matter I4b
33, 24a4; )( force I5
b
15, 52a23, 7i
b35 ;
= that which
contains its principle of motion
in itself I4b
18, 25b
20, 49b
8,
7oa
7; by nature )( to us 29b
7 )(art
32
a
12, 7o
a
7, 17;syn. form, complete reality, posi
tive state 32a
24, 44a
9, 7oa
1 1;
the only substance in destructible
things 43b23 ; )( potency 49
b 8;
natural objects,bodies, substances
I4b
19, 32, 28b 10, 42a
7, 7oa
5,
90a32 ; )(
unnatural 33b33.
Necessity, def. 6b 32 ;its meanings
26b 28, 64b
33 ; necessary, its
meanings A. 5, 72b
II ; )( usual,accidental 25
a15, 1
8, 20, 26b 28,
27b
8, 64b33-65
a3 ; objects of
demonstration necessary truths
39b
3i-
Negation )( privation 4a12; coni.
contrariety 1 2a9, 46
b13; privative
negation 56a
17, 29 ;Ideas of
negation 99ob
13, 79a10.
Nemean games i8b 18.
Non-rational potencies 46b 2, 48a
4, 5b
33-
Number M. 6-9, N. 1-3, 5, 6, 2Oa 13,
39ai2, 53
a3o, 57
a3,85
b22,8S
a5;
numerical ratio 985b32, 99i
b13,
J7>
J 9, 993a
i7>ib3o, 53
ai6,6i
bi,
92b
14, 31 ;said to be limited by
ten 986a9, 73
a20, 84
a12, 32; ele
ments, attributes, generation of
number 986a17, 4
b10, 84
a3,
b28,
87 b 15, 89b 12, 9oa 2i, 9i a 23, 29 ;
numbers as principles, substances
985b
26, 986a
16, 987a19,
b24, i
a
25,b26, 36
bI2,76
a3i, 8oa 13, 83
a
23, 9oa
4, 23, 92b
16, 26; primenumbers 987*^34, 52
a8, 8i a
5; sen
sible )( intelligible, ideal 99oa31,
9ob36 ;
coni. Ideas 99 ib
9, 76a20,
8ob 12, 22, 8i a7, 21, 83
b3, 86a 6,
88b 34,9oa
1 6,b33, 37, 9 i
b26;
wherein does its unity consist?
992a
i, 44a
3, 45a8; numerical
unity 999b26, 33, i6b 31, i8a 13,
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INDEX
33b3i,39
a28, 54
a34, 6ob 29 , 87
b
12: unity the origin and measure
of number i6b 18, 2i a13, 52
b24,
88a 6; quality, differentia of number M. 6-8, 2o b
3; coni. definition
43
b
34, 45
a
8 ; associable )( in-associable M. 6-8 : mathematical,arithmetical number 76
a20, 8oa
21, 30,b
13, 8ia
6, 83b
3, 16, 86a
5, 9b33i 35, 9i
b24 ;
related as
prior and posterior, 8ob 1 2;num
ber composed of abstract units
Sob 19, 30, 82 b6, 83
b17, 92
b
20 infinite or finite ? 83b
36 ;
powers of two 84* 6; )( definition
87b 12; one not a number 88a6
;numerical succession 85
a4 ;
square, cube 93a
7.
Ocean 983b30, 9i
b6.
Odd (Pythagoreans) 986a
1 8, 99oa
9, 9la23.
One I. 1-3 ;its meanings A. 6, 52
a
15; one over many 99<D
b7, 13,
99la
2, 4ob29; unity and being
I. 2, 998b 22, i a5, 3 b 22, 4ob 16,
45b 6
;not a genus 998
b22, 45
b
6;= indivisible 999
a2, 4i
a19;
in quantity, species, number, ge
nus, by analogy 999a
2,b
25, 32,
I6b 3 i, i8a i 3 , 33b3 i, 39
a28, 54
a
34, 6ob 29, 87b 12
; unity of common reference, of succession, of
common predicability, of signifi
cance3
a
33,5a
10, 6b
15;one in
continuity, form, definition i6b 9;
origin and measure of numberi6b 18, 52
b24 ;
the one not sub
stance I. 2, 4ob
1 8; unity of num
ber and of definition Z. 12, H. 6,
992a
i, 44a3 ;
the one a measure
52b
1 8, 87b33 ;
one and many I.
3, 6, 87b
28; )( simple 72a32;
the many, matter of the one 75a
33 ; one by contact, intermixture,&c. 82a 20; primary one 83
a25; in
what sense a starting-point 84b
1 8; one in definition, in number 87b
J2; i not a number 88a 6; (Pytha
goreans) 986a
19, 987a
1 8, 27, ia
10; (Eleatics) 986
b15, i
a33;
(Plato) M. and N. passim, 987"^
21, 992a
8, ius; (Anaxagoras)
989 17.
Opinion )( knowledge 8b 28, 30,
39b
33-
Opposition, its kinds A. 10, 54a
23,
14,b
5,
i 55a38,57
a33;changetoopposites
n b34, 57
a3i 69
b4; opposite
differentia i6a 25 ; potency of
opposites 5ob
8, 30; opposite )(
contrary 69b
4.
Order 984b
17, 985
b
14 ; not in substance 38
a33.
Orphic cosmogony referred to 9ib
5.
Other, def. i8a 9 ;its meanings 54
b
14 ;in species 1. 8, 9, i8a 38 ;
in
genus 24 9 ;otherness of the ge
nus 58a7 ;
otherness )( difference
54b23; (Pythagoreans) 87
b 26.
Parmenides 984b
3, 986biS~987
a2,
l a 32 ; quoted 984b 25, 9b 21, 89a
3 ;referred to 4
b32.
Part, its meanings A. 25, 34b32 ;
parts of definition, of concrete
thing Z. 10, ii.
I Participation 987b
13,
30a
13, 3ib
i8, 37bi8/45
ai8,
b8,
79b
1 8;Ideas participable 99O
b
28, 40a27, 79
a25.
Pauson 5oa
20.
Perceptible, v. Settsible.
Perception, v. Sensation.
Perishable, v. Destructible.
Persian war i8b 16.
Petitio principii 6a 17, 20.
Pherecydes 9ib
9.
Philosophy is knowledge desirable
for its own sake, most accurate,
communicable, most divine and
honourable A. 2;
starts from
wonder 982b
12; turned into
mathematics 992a32 ;
is know
ledge of the truth 993b 20
;treats
of the axioms r. 3, K. 4, 995b 8
;
treats of being as being r. i, 2,
K. 3 ;has distinct parts 4
a2, 26a
18; )( dialectic, sophistic 4b17 ;
theoretical, practical, &c. E. i;
first philosophy 26a24 ;
the philo
sopher fond of myth 982b
18 ; canspeculate about anything 4
a34.
Phrynis 993b
16.
I Physics, natural philosophy, philo
sophers 986b
14, 989b3o, 99o
a3,
7,992b4,995
ai8,i
ai2,s
a31, 34,
bi, 6a 2, 25
b19, 26, 26a 4, 12,
37a
14, 1 6, 59b
1 6, 6i b6, 28, 62b
22, 26,
7 8b19
Place 92a i7; changeof42 a 34,69b i3.
i Planets A. 8.
Plato A. 6, 9, 988a
26, 990* 30, 996a
36, 7ib
27, 75b
27,
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INDEX
6, ia
9, I9a
4, 28b 19, 53b
13, 83a
32 : referred to Z. 14, M. and N.
passim (esp. 76a
19, 77an, 8ob
11, 24, 8i a24, 84
a13, 85
a9,
b7,
86a ii, 87b
5, 13, 9ia
i,b35,92
b
i), 983b
27, 995b
16, 997b i,
998b
9, ib
19, 2a ii,b
13, i7b
19,
28b 19, 3oa26, 3i
a30, 33
b19, 34
a
2, 36b
14, 39a 26 -b 19, 5o
b35,
5ia
17-21, 59a
10,b
3, 6ob 6,
69a34, 7o
a27, 7i
b15, 73
a17, 20,
75b
19-28 ;his works quoted,
Hippias Mi?ior 25a6, Laws 72
a
I (?), Phaedo 99 ib3, 8o
a2, Phae-
drus72
aI
(?), Republic 992*33, Sophistes 26b 14, 64
b29,
89a
20, Theaetetus lob 12, 7Y-
maeus 57b
8, 7ib32, 72
a2, 92
ai.
Platonists referred to M. and N.
passim, 99ob
9, 997b
3, 998a
7,
2b 14, 4b
32, 28b 24, 3ia
31, 36b
13, 4ob
2, 43b34, 45
a16, 5o
b35,
56a
10, 66a ii, 6ga26, 75
a32.
Plurality 57a
3, 87b
6, 9ib34; def.
2o
a
8, 54
a
22; )( unity 4
a
10, 87
b
28;
first plurality 85b
9.
Point 992a
19, i6b 26, 6ob 18, 85b
27.
Polus98ia
4.
Polyclitus I3b35~i4
a15.
Position 985 15, i6 b26, 22b 2, 4
b
19, 77b
30.
Possible 0. 4, I9b 28.
Potency, power, potentiality, def. A.
12, 0. 1-9 ; whether the elements j
exist potentially 2b 33; potencyor actuality prior? 0. 8, 3
ai
; )( ac-|
tuality 7b
28, 69b
15, 7ia
6,b23 ;
j
power in geometry I9b
33, 46a7 ;
j
)( reason, art, nature 25*22, 27a
6, 33b
8, 49b
8, 64a
13 ;coni.
matter 42a
27,b
10, 5oa
15, 6oa
21, 14, 7o 12, 7ia
10,
92a
3 ; irrational, rational 0. 2,
47b 3i 5ob 33; the potentialand the actual are one 45
b 21;in
what sense the infinite and the
void exist potentially 48b9 ;
whena thing exists potentially 0. 7
primary potency 49b13 ;
the eter
nal not potential 5ob7 ; potency
is of opposites 5ob
8, 30, 5ia
6,
7ib
19.
Practical knowledge 993b
21, 25b
21, 25.
Primary 3oa
10, 37b
3, 75b24; syn.
self-subsistent3ib14 ;
substance
32b 2
;coni. categories 34
b9. v.
First.
Prime numbers 987b
34.
Principle, beginning, starting-point,
originative source (apx^), its
meanings A. I;material
9>3
b7,
24, 984a
6, 986a
17, 987a4, 46
a
23 ; efficient 984a27, 46
a14,
b3,
49b
6, 7oa7,
b25; final so
a7;
formal 69a28, 76
a24, 8ob 6, 32 ;
God a first principle 983** 8;con
trary principles 986a
22,b
I, 4b
31, 75a
28, 87a30; principles of
demonstration 993b
28, 996b
26,
5
b
9, 11, 13,1
8, 22,6a
5,62 a
3;a first principle necessary a. 2;
whether genera are first princi
ples 998a 21
;whether one in
kind or in number A. 4-5, 999b
24, 6ob 29 ;whether the same for
things perishable and imperishable oa 6
;whether potential or
actual 2b 32 ; whether universal
or individual M. 10, 3a
7, 6ob 20,
6g
a
26-30, 7i
a
20; of being assuch r.
i, E. i;
the simple a
principle 59b34 ; )( element 4i
b
31, 7b23 ;
in what sense unityis a starting-point 84
b18; the
principles, how related to the
good 9ia
30, 92a
ii; infinity of
principles (Anaxagoras) 984a13;
ten (Pythagoreans) 986a 22.
Prior, its meanings A. n;
in
generation, nature 989a
15 ; in
knowledge, definition, perceptionl8b 30 ;
in formula, time, genera
tion, 38b
27 ;in formula, sub
stantiality, time 49b
1 1;in gene
ration, form, substantiality 5Oa4 ;
in definition 54a
28, 78a
9; in
definition, substantiality 77b
i;
no Idea of a class which includes
prior and posterior members
999a 6 ; numbers related as prior
and posterior 8ob 12.
Privation 4a
12, igb
7, 58b27 ;
its
meanings A. 22, 46a
31 ; one of
two contraries privative 4b27, i i
b
1 8, 55b
14, 27, 6i a20, 63
b17 ;
)( state, form I9b
7, 44b
32, 55b
13, 7ob12; primary 46
b14; per
fect 55a
35 ; )( negation, con
trariety 4a
12, 55a33; privative
negation 56a 17, 29.
Production, v. Generation.
Productive knowledge 982* I,b
II,
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INDEX
25b
21, 25 ; )( mathematical
64a
i.
Proof, negative (t\eyxos )6a 18.
Protagoras r. 5, 6, K. 6, 998** 3, ;b
22, 47a
6, 53a
35; referred to
999
b
3-
Pythagoreans 985^ 23~986b
8, 987**
13-27, ii, 23, 31, 989 29-990a
29 , 996a
6, ia 10 36*18, 53
bi2,
72b31, 78
b21, 8ob 16, 31, 8s
b 8-
19, 9oa
20-35, 9 ia 1 3) referred
to 99Sb
9, 2a
ii, 4b
31, I 7b
i 9 ,
20, 28 b5, 1 6, 36
b8, 43
b34, 6ob 6,
66au, 75
a36,
b28, 76
a2i, 87
b
I7(?), 26, 9ob
2.
Pythian games i8b
18.
Qua, def. 65b
23.
Quality A. 14, 28a 15, 68b 18; of
number 2ob 3 ;definite 63* 27 ;
change of 6gb 10
; posterior to
quantity 83a n.
Quantum, quantity, A. 13 ;attri
butes of 2oa 19; known by a
measure 52b
20; indefinite 63a
28; change of 69b 10; prior to
quality 83a
1 1;motion and time
incidentally quantitative 2Oa 29.
Ratio (Actyos) 98$b
32, 991b
13, 17,
I9 993a
I7>
ib3, 53
a16, 6i b I,
92 14,31.
Reality, realization, complete (eWe-
AeV") 7b
28; )( matter 38b
6,
78
a
30;
separates 39
a
7; coni.
substance 44a9 ; )( actuality 47
a
30, 5oa
23.
Reason, thought, mind (vovs) A. 7,
9, 7oa
26; in nature 984b
15;human 993
bn, 75
a7; )( art,
faculty 2fj
b 22;acts by contact
72b21; divinest of things 74
b16;
(Anaxagoras) 984b
15, 9&9b
15,
17, 69b3i ; (Parmenides) 9
b23.
Relation A. 15, 56b
34, 89b
6, 14;Ideas of 99o
b16, 79
a 12;rela
tive )( absolute 99ob
20; least
substantial of the categories 88a
22, 30.
Same, the 995b
21, 2ia n
;its
meanings A. 9, 54a32 ;
in speciesi8 b 7, 49
b1 8, 29, 58
a 18; by
accident 37b
6.
Scale 985 b 31, 986a 3 ; seven notesin the scale 93
a14.
Science, v. Knowledge.
Sensation, sense, perception (ai-
[email protected])IOb 32, 63 4 ) (aio OrjO is)
sight our most precious sense
98oa23 ;
sensation the source of
memory 98oa 28
; )(wisdom 98 i
b
10; )( knowledge 999
b
3 ;
not a
physical alteration 9b13 ; special
sensation always true iob 2;con
flict of sensations iob4, ll
a25 ;
coni. intuition 36a
6.
Sensible, perceptible 987a
33, 997b
12, ioa 3, 42a25, 69
a30,
b3, 78
b
16; )(
mathematical 989b
31,
99oa
15 ;no knowledge of sensi
ble things Z. 15, 987a34; )( in
telligible, ideal 99oa
31, 999b
2,
36a
3> 9, 45a
34, 9b
35 5are
there non-sensible substances ?
997a
34, 2 b 12, 59a
39; coni.
movement989" 31, 36
b28; con
trarieties 6i a32.
Sense-organ 63a
2.
Separable, capable of existing apart
I7b25 28, 26a 9, 28a 34,
a b a9, 59" 3>
6oa 8& 7
b30, 86a 33 ;
in formula )( without qualification
42a29 ; actually )(
for knowledge
48b
15.
Separate (verb) 989* 3, 4ob28, 78
b
3 i,86b
4-
Seven (Pythagoreans) 93a
13.
i Shape, coni. end 23a
34 ;coni.
formula 42a 28
;coni. actuality
43a
25, 28, 31;=
proximatematter
45
b
18;
coni. form
999
b
16, I5a
5, i7b
25, 33b
5, 52a22,
6oa 22,b 26.
Sight, the most precious sense
98oa23.
iSimonides 982
b30, 9i
a7.
Simple, coni. necessary I5b
12;
coni. principle 59b
35 ; )( one
72a32 ;
bodies 984* 6; concepts,
substance 2;b
27, 4ib
9, 72a
32 ;
movement 53
a
8, 73
a
29; generation 69
b10, 88a
33.
Snub Z. 5, 25b
31.
Socrates987" 1-4, 78
b17-31, 86b 3.
I Socrates the younger 36b25.
Solon referred to 983a
3.
Sophistic 4b
1 8;
concerned with
non-being 26b 14 ; sophistical
objections 32a6, 49
b33-
i Sophists 996a32, 4
b17, 26b 15.
i
Sophocles I5a 3o.
i Soul, partly falls within scope of
physics 2oa 5 ;substance of living
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INDEX
material 10, I, 42b
9,
essence
35b22,
things 35b
14, 43a
35 ;
= its
essence 36a
i, 43b2; )( soulless
things 46a36 ; )( reason, not all
soul can survive death 7oa
26.
Species 998b7 ;
indivisible 9gSb
29, j
34a 8; one in species 999a 2, i6b I
31, i8b 7, 49b
18, 29, s8a 18
; partj
of genus 999a4, 23
b 18. 25; otherj
in species I. 8, 9, i8a
38, 54b 28
;I
genus part of species 23b
24 ;
genus matter of species 24b
8, 38a
6; species composed of genus |
and differentiae 39a26, 57
b7.
Speusippus 28b 2l, 72b3i ;
referred
to 69a36, 75
a33, 36,
b37, 76
a2i,
8ob 14, 26, 84a
13, 8sa
32, 86a 2,j
29, 87b
6, 27, 9oa
7, 25,b
17, 9ia
|
34,b23, 32, 92
a ii-b 8.
Spheres of the stars A. 8.
Spontaneity, coni. luck, )( nature, |
art984b
14, 3 2a
13,b23, 34
a10,
b4, 7o
a7.
Stars A. 8;their nature 73
a34.
State, v. Habit.
Strife
(Empedocles)oa
27.Styx 983
b32.
Substance Z and H passim ;its
meanings A. 8, A. I;
= ultimate
subject 983b
10, 2a 3, 7a
31, I7b
13, I9a
5, 29a
8, 38b
15, 42a 26
;
)( modification, accident 983b
10,j
10, 7a
31, 38b
28, 7ia
I;
44a
15, 49a36, 77
a35 ;
are num
bers substances? 987
a
19, i
b
26,
76a30; sensible substance 997
a|
34, 42a25, 69
a30,
b3 ;
= form, I
b21, 993
a18, 32
bI,
29, 38b
14, 4ib
9, sob
[
2;are there non-sensible sub-
stances ? 997a
34, 59a
39 ;uni-
versals not substance Z. 13, 3a
7,|
53 16, 6ob 21, 87a
2; primary
being 28a 14, 30 ; prior in defini-
tion, knowledge, time 28a
32 ;
alone separable 28a34 ;
four no-\
tions of it 28b 33 ;whether mat-
|
ter is substance Z. 3 ;material
substance 42a27, 49
a36, 77
a36 ;
syn. individual 3oa
19; primary
32b 2
;
=matter, form, and con-
j
crete thing 35a
i, 7ob13 ; )(
con-j
crete thing 35b
22, 37a
29; )(j
genus 42a21, 53
b 21; being not
j
the substance of things 40 18 ;
unity not the substance I. 2, 4ob
]
1 8;a principle and cause 4i
a9, ]
b30, 43
a 2; generally recognized
substances 42a 6
;natural 42* 8,
7oa
5 ;mathematical objects as
substances M. 1-3, 42a
1 1, 69a35;
coni. actuality, complete reality,
42 b 10, 43a 23, 35, 44a 9, 5ob 2,
72a
25 ; prior in substantiality
49b n, 5o
a4, 77
b 2; incompo-
site 5ib
27; concrete 54b
4;
eternal, unmovable substance A.
6; why are there many sub
stances? 89b
31.
Substratum, def. 28b 36 ;two mean
ings 38b
5, 49a 28 ; syn. matter
983*30, 985
b10, 992
bi, 22a 1 8,
7oa ii
; proximate, ultimate i6a
20, 23, I7b
24, 24b 10
; )(matter
44b
9.
Successive, def. 68b 31 ;succession
)( common reference 5a n
;suc
cession in numbers 85a4.
Syllogism, starts from the what*
34a
31, 78b
24; primary syllo
gisms I4b
2.
Ten, limit of the number-series
986a
8, 73a
20, 84a 12
;ten prin
ciples (Pythagoreans) 986a22.
Tethys 983b30.
Thales 983b20, 984
a2
;referred to
984*27,996*91 39a 12
(?).
Thargelia 23b n.
Thaten 33a
7, 49a19,21.
Theology 26a 19, 64b
3.
Theoretical knowledge E. i, 993b
20.
Thinking, thought (v6r)(ris) )( mak
ing 32b
15 ;coni. definition 52
a
29>
bi> 75
a3 5 )( faculty of
thought A. 7, 9; )( desire 72a26;
its primary object 72a27.
Third man 99ob
17, 39a
2, 59b
8,
79a
13.
This I7b
25, 30a
4, 7oa
10. v.
Individual.
Thought (four), v. Reason.
Time, incidentally quantitative 2Oa
29 ; prior in 28a 32, 38b
27, 49b
ii;eternal 7i
b7.
Timotheus 993b
15.
Total (irav) )( whole, all 24a
I, 8.
Trojan war i8b 16.
Truth 993a30,
b20, 9
aI,
b 2;def.
0. 10, n b25 ; absolute, relative
n b 3 ; being as truth E. 4, 0. 10,
65a2i.
Two, v. Dyad.
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INDEX
Unequal, the 8;b
5, 88b 32, 89b
]
615, 9ib35 ; inequality i
b23.
Unit, def. i6b 25, 89b
35 ; pointwithout position 84
b 26; specific-
ally the same, associable M. 6-8, \
99ib
24; specifically different, \
inassociable M. 6-8, 992a 3 ;
differentia of 83a2
; unitary numbers 8ob 19, 30, 82 b
6.
Universal 42a
15, 6ga
26, 86a 32 ;
def. 23b
29, 38b II
;not sub-
|
stance Z. 13, 3a
7, 53bi6,6o
b21,
j
87a 2
;whether the first princi-
j
pies are M. 10, 3a
7, 6ob 19, 7ia
j
20; object of knowledge 3a
14,
36a
28, 59b
26, 6ob 20, 87a 16
;
essential (naff avrd) I7b35 ; prior
in definition i8b 32 ; )( genus28 b 34.
Universe, not episodic 76a
I.
Unlike, its meanings i8a 19.
Void 48b
9 ; (Democritus)
9a
28.5,
What 25b31, 26a 36, 28a i7, 3o
a17;
parts of the22a 27; starting-pointof syllogism 34
a3i, 78
b24.
Whole I3b 22, 52a 22;
its meanings A. 26
; )( total 24*1.
Wisdom, philosophy (o-o</>i a) A. I;
with what principles it deals A. 2,
K. i, 2, 995b
12, 996b9 ;
with
first causes 98ib28.
Xenocrates referred to 28b 24, 69a
35, 76a20, 8ob 22, 28, 83
b2, 85
b
7, 86a 5, 8bb
28, 9o
b
20-32, 9i
b
Xenophanes 986b21-27, Ioa 6.
Zeno ib7.
Zeus 9ib
6.
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