Realist ontology of categories (a work in progress)

Paul Thom

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Basic ontological relationships ab

abab: is from

… the beautiful are beautiful by beauty.Phaedo.

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Thus, for example, the grammarian gets his name from grammar,

the brave get theirs from bravery.Categories 1a14-15

The Categories formula is equivalent to stating that if two genera have a common differentia (thus a common species), then one genus is subordinate to the other. That formula implies Rule 5. Suppose that both A and B are genera of C. If we assume that

two genera having a common species have a common differentia, then A and B have a common differentia. So, by the Categories formula, either A is a genus to B or B is a genus to A. In other

words, the Categories formula implies Rule 3, on the assumption that two genera having a common species have a common

differentia.

Basic ontological relationships de

de

For footed and two-footed are said of man as subject.

Categories 5, 3a22-24.

de: said of

deD: said of as a differentia

What is said of a subject has its name and definition predicated of the subject.

Categories.

Rule 1. If A de B, whatever is B is A

deG

Whenever one thing is predicated of another as of a subject, all things said

of what is predicated will be said of the subject also.

Categories 1b10ff.

Rule 2. If A de B and B de C, A de C

The genus [is said of] both the speciesand the individual.Categories 3a39.

Rule 3. If A deG B, A de B

deD

Rule 4. If A deD B, A de B

deG: said of as a genus

de

de

de G

The differentiae of genera which are different and not subordinate one to the

other are themselves different in kind.Categories 1b16ff.

Rule 5. If A deG C and B deG C, either A deG B or B deG A

de G

de G

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ab

Basic ontological relationships in

in: inheres in

Rule 7. If A in B and A de C, C in B

… the individual knowledge-of-grammar is in a subject, the soul … . … knowledge is in a

subject, the soul, and is also said of a subject, knowledge-of-grammar.

Categories 1a25-26; 1b1-3

Rule 6. If A in B and C ab A, whatever is C is B

de

in

in

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By ‘in a subject’ I mean what is in something, not as a part, and cannot exist separately from what it is in.

Categories 1a24-25.

Basic ontological relationships ad

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Relatives are what they are ‘to’ something.Categories.

Correlatives

adad: stands to

Correlation

ab ab

A relation is an accident that is truly and simply one, not requiring a multitude in

which it is, but just one thing – only in respect of another…. A correlation is a pair

of relations mutually respecting one another.

Kilwardby, De Natura Relationis 16:19-24

… paternity is not of filiation … but father is stands to son and son to father. A relation,

then, … is not relative except through the concrete [being] which it is in…. And so a

relation is relative per accidens.

Kilwardby, De Natura Relationis 5:22-28.

co

co: are a correlation

BeingsPer se beings, denominatives

Definition 2. denom(A) iff not perse(A), and for some B: perse(B) and A ab B

denom: is a denominative

Definition 1. perse(A) iff for some B [B de A]

perse: is a per se being

DenominativesPer se beings

.Categories.

Paronyms [denominatives] take their name from what they are from but with a difference of ending.

Categories.

deab

Rule 8. If A de B, perse(A)

Rule 9. If A in B, perse(A)

Rule 10. If A in B, perse(B)

Definition 1 implies that if A de B, perse(B)

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BeingsUniversals, individuals

de

Definition 3. indiv(A) iff perse(A) and for no B [A de B]

indiv: is an individual

Things that are individual and numerically one are, without

exception, not said of a subject.Categories 2, 1b6-7.

Definition 4. univ(A) iff for some B [indiv(B) and A de B]

univ: is a universal

Universals

Individuals

… it is necessary that the thingspredicated in what something is

are finite.Posterior Analytics A22, 83a1.

Rule 11. If A de B, for some C {A de C and for all D [if C de D, D de C]}

Rule 12. If A de B and univ(B), B de B

… colour is in a body and therefore also in an individual body. Categories 2b1-2

Definition 3 implies that if A de B and indiv(B), it’s not the case

that B de B

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BeingsSubstances, accidents

Definition 5. subst(A) iff perse(A) and for no B, A in B

Definition 6. subst1(A) iff subst(A) and indiv(A)

It is a characteristic common to every substance not to be in a

subject…. This is not, however, peculiar to substance; the

differentia also is not in a subject.Categories 5, 3a7-8; 21-22.

A substance – that which is called a substance most strictly,

primarily, and most of all – is that which is neither said of a subject

nor in a subject.Categories 5, 2a11-13.

subst: is a substance

subst1: is a primary substance

de

Definition 7. acc(A) iff for some B, A in B

Rule 14. If acc(A) and A de B, acc(B)

acc: is an accident

de

The species in which the things primarily calledsubstances are, are called secondary substances,

as also are the genera of these species.Categories 2a14-17.in

in

Rule 13. If subst(A) and A de B, subst(B)

Substances Accidents

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Rule 15. An individual accident inheres in exactly one individual substance

A particular case of grammatical knowledge would be, for example,

the grammatical knowledge that Aristarchus possesses.

Porphyry, Categories Commentary 76,1.

ab

ab

Derived ontological relationships

in

Definition 8. A in2 B iff for some C [A ab C and C in B]

Definition 9. A was B iff for some C, D [A ab C and C de D and B ab D]

Definition 10. H sus C iff for some B [H in B and B in C]

in2: inheres in secondarily(Garlandus)

sus: sustenation (Abaelard)

was: wasfi predication(Avicenna)

[Denominatives] are in a subject secondarily, i.e., through their forms, which are primarily in subjects.

Garlandus, Dialectica 18:3-4

‘All moving things are changing’is not to be taken to mean thatthis is so absolutely, but rather

while the substance of the movingthing is moving.

Avicenna, Pointers 265.

de

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in

sus

was

in2

Ontological dependencies Among per se beings

Rule 16. If a per se individual exists, a specific per se universal (which is said of it) exists

de

For if one is to say of the primary substance what it is, it will be

more informative and apt to give the species than the genus.

Categories 2b8-10

Rule 17. If a per se universal exists, it is said of some per se individual

For example, animal is predicated of man and therefore also of the

individual man; for were it predicated of none of the

individual men it would be predicated of man at all.

Categories 2a36ff.

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Ontological dependencies Among relatives

Rule 18. If A ad B and A exists, B exists

Rule 19. If A ad B and B exists and both correlatives are essential, A exists

Both correlatives essential

Those relatives are said to be essential whose being depends on the correlative.

Kilwardby, De Natura Relationis 18:21-22

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Correlatives

ad

Correlation

ab ab

Ontological dependencies Inter-category

Rule 20. An individual accident inheres in at least one individual substance

de

All the other things are either said of the primary substances as subjects or in them as subjects. This is clear from an examination of cases.

Categories 2a34-36

Cf. Marenbon, The Philosophy of Peter Abelard p.120-122

He does not say that it is incapableof existing separately from what it wasin, but that ‘it is incapable of existingseparately from what it is in’. The smellis capable of being separated from whatit is in; but it cannot exist separately andon its own.Porphyry in Cat. 79,23-34

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Knowledge Kilwardby’s account, Notulae

Knowable but not known

Relative

Knowledge

ad

de de

Knowable and known ad

de

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Knowable

Knowledge Kilwardby’s account, De Natura Relationis

Relative

Knowledge

ad

ab

Quality

de

Knower

Medical knowledge

de de de

Knownad

de de

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Extreme conditions Different denominatives, same accident

ab

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Aequiparentia (different relatives, same relation)

ad

dede

Correlatives that agree in name anddefinition respect one another by arelation that is one is species buttwo in number.Kilwardby, De Natura Relationis 18:10-12

ab

in in

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Extreme conditions

Kilwardby’s argument is flawed. It is relatives, not relations, that are ‘ad aliquid’. So, the most the argument could show is that a relative may be a substance. However it can’t even show that,

because a relative, being a denominative, is neither substance nor accident.

Extreme conditionsA relation is a substance

a

ad

And it is to be said that substance and accident differ in this, that a substance subsists through itself and an accident through a substance in which it inheres. Hence accident has this property that it inheres. Relation however, as such, has this property, that it respects another. So where these two (inhering and standing toward something) concur, relation is an accident – not because it stands towards something but because it inheres, since this (namely that it inheres) is the nature of accident. So take away the inhering and leave the standing towards something, and you have taken away the nature of accident. Leaving the nature of relation, but taking away the nature of accident, you necessarily leave the nature of substance. And so a substance can stand toward something and be a relative or relation, because this is not repugnant to it.Kilwardby, De Natura Relationis 34:14-24.

A B

C D

de

… paternity is not of filiation … but father is stands to son and son to father. A relation, then, … is not relative except through the concrete [being] which it is in…. And so a relation is relative per accidens.Kilwardby, De Natura Relationis 5:22-28.

Here is an alternative argument. Subst(A) iff for some B, B de A.

Reln(A) iff for some C,D, C a A and C ad D. Thus, Subst(A) and Reln(A) iff for some B,C,D, B de A and C a A

and C ad D. The constructive problem is to show that this is a

possibility.

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The Trinity Augustine’s account

a

FatherSon

God

Gift (Holy Spirit)

in

a

in in

With God, though, nothing is said modification-wise, because there is nothing changeable with him. And yet not everything that is said of him is said substance-wise. Some things are said with reference to something else, like Father with reference to Son and Son with reference to Father. De Trinitate V.i.6.

… every being that is called something by way of relationship is also something besides the relationship; thus a master is also a man, and a slave is a man …. So if the Father is not also something with reference to himself, there is absolutely nothing there to be talked of with reference to something else.De Trinitate VII.i.2… the substance of the Father and the Son is one.De Trinitate V.i.4.

[The Holy Spirit] insofar as he isproperly or peculiarly called the Holy Spirit is so called relationship-wise, being referred to both Father and Son, since the Holy Spirit is theSpirit of the Father and of the Son.De Trinitate V.iii.12.

He is the gift of the Father and of the Son … . So when we say ‘the gift of the giver’ and ‘the giver of the gift’, we say each with reference to the other. De Trinitate V.iii.12.

Father, giverSon, giver

There is at least no doubt that God is substance ….De Trinitate V.i.3

ada

Thus the Father is God and the Son is God and the Holy Spirit is God, and no-one denies that this is said substance-wise ….De Trinitate V.ii.9

Son and giver are different relatives; similarly, Father and giver. So there seem to be five or six relatives, not three. Reply: Father and giver may be different

considered as notions, but they are the same person.

What are these three relations? Boethius mentions filiation and paternity;

presumably the third is giving. But all these are accidents that can come and go in a

subject – whereas God has no such accidents.

Reply: It would be better to name the relations as divine or preeminent filiation

(filiation*), divine paternity (paternity*) and divine giving (giving*).

How can two correlatives have a single subject (if the corresponding

relations are asymmetrical)? Reply: Paternity* is not

asymmetrical. Every subject that stands in the relation to something (viz. God) stands in the relation to

itself.

ad

How can the three relations inhere in God? Nothing is said of God accidentally. So relations can inhere in God only if

(i) these relations are not accidents, or (ii) they are inseparable from their subject and inherences are sometimes inseparable, or (iii) these relations are

accidents said of God or (iv) are identical with God. Reply: Definitions 3 & 4 exclude (ii). Rule 2 excludes (iii).

Augustine excludes (ii).So (i) and (iv) are the remaining possibilities.

“Even though some modifications are called inseparable … like the color black in a crow’s feather, … the moment it ceases to be that animal or that feather … it loses of courses that color…. So there is no modification in God because there is nothing in him that can be changed or lost.” De Trinitate V.i.5.

“Yet when you ask ‘Three what?’ human speech labors under a great dearth of words. So we say three persons, not in order to say that precisely, but in order not to be reduced to silence.” De Trinitate V.ii.10.

“… for God even being born is everlasting, so that the Son can be coeternal with the Father.” De Trinitate VI.i.1.

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The Trinity Kilwardby’s account

God

a aa

ad ad

ad Holy SpiritFather* = spirator*Son* = spirator*

Filiation*Paternity*

Spiration*

= ==

… potius vocatur Spiritus Sanctus quam donum,Sicut Filius potius vocatur Filius quam Verbum. … Cui enim imponitur ‘Spiritus Sanctus’, est hypostasisrationalis, sed cui imponitur ‘donum’, infinitae substantiaequae dari potest, unde et nomen doni communius est de prima impositione quam nomen Spiritus Sancti.Kilwardby, Sent. 1 q.42:16-24.

… gignens, genitus et procedens sunt relativa, sed relationes non sunt accidentia, sed substantia. … Qualiter autem relatio possit esse substantia, patet illis qui noverunt quomodo prima principia substantiae compositae ad invicm referuntur, scilicet materia et forma, quomodo etiam creatura Relativa ad creatorem. Potest autem hoc esse tali ratione: Relatio accidens aliunde est accidens et aliunde relatio; accidens enim est unde inest, relatio unde ad aliquid extra se respectum habet. Tolle ergo hoc ipsum inesse et tulisti accidens. Quod ergo remanet, substantia erit. Ubi ergo Nihil est inhaerens, non est accidens. Et tamen bene potest inesse respectus ad aliquid, et illeerit substantia.Kilwardby, Sent. 1 q.35:303-315.

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The Trinity Aquinas’s account

God

God’sknowledge

God’slove

=,de

ad ad

DivineKnown, i.e. Word

DivineKnower, Lover

i.e. Father

DivineLoved

i.e. Holy Spirit

a

God understands and loves himself. Moreover, his understanding and his loving are identical with his being.

Compendium Theologiae 37

A thing as understood in the mind is, as it were, a word of mind – for what we signify by an outward word of speech is what we have understood within. Therefore, within God we set down the existence of a Word.

Compendium Theologiae 37

When the mind understands itself, the word conceived is related to mind as offspring to father. Therefore in dealing with God’s understanding, the Word should be compared to God, of which it is the Word, as son to father.Compendium Theologiae 39

… the manner whereby God is in himself as beloved in lover is described by the terms breath or spirit.Compendium Theologiae 46

Since the Word is the Son when God understands and loves himself, which Word is uttered by the Father, we must infer that the Holy Ghost, who is of the love whereby God is in himself as th beloved in the lover, proceeds from the Father and the Son.

Compendium Theologiae 49

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