[ANALYTICA PRIORA] GIFFORD (Aristotle on Platonic Recollection and the Paradox of Knowing...

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Aristotle on Platonic Recollection

and the Paradox of Knowing Universals:

Prior Analytics B.21 67a8-30

MARK GIFFORD

ABSTRACT

The paper provides close commentary on an important but generally neglected

passage inPrior Analytics B.21 where, in the course of solving a logical puzzle

concerning our knowledge of universal statements, Aristotle offers his only ex-

plicit treatment of the Platonic doctrine of Recollection. I show how Aristotle

defends his solution to the Paradox of Knowing Universals, as we might call

it, and why he introduces Recollection into his discussion of the puzzle. The read-

ing I develop undermines the traditional view of the passage and lends fresh in-

sight into Aristotles conception of Platos particular version of innatism; more

specically, when understood as I recommend, the passage strongly suggests that,

on Aristotles view, Platos theory of Recollection is specically designed to explainour apprehension of universal truths. The reading I propose also enables us to

see how the allegedly non-standard use of the technical term pagvg in B.21can be understood in a perfectly straightforward fashion to refer to an inductive

inference from singular statements to the universal truth they exemplify. Owing

to this last point in particular, the paper carries serious consequences for our

understanding of the purported doublet in the problematic opening chapter to the

Posterior Analytics where Aristotle offers his only explicit attempt to solve

Menos Paradox.

When Aristotle approached the study of human cognition, the question of

innate knowledge was waiting for him. Plato had placed the issue at the

forefront of epistemological reection by advancing a radical form of

innatism, and Aristotle could hardly have avoided declaring himself on so

famous an endoxon from so reputable a philosophical predecessor. As we

know from various passages scattered about the corpus the best known

of which is Posterior Analytics B.19 Aristotle went on to dismiss therationalist view that the mind is stocked from birth with unconscious

knowledge about the ultimate structure of reality, setting in its place an

empiricist account of knowledge-acquisition centered on the process of

induction (pagvg). But although his empiricist response to the idea ofinnatism makes an appearance in several places, only once in the surviv-

ing works does he expressly address the Platonic doctrine of Recollection

as such: in Prior Analytics B.21, while engaged in an attempt to solve a

Koninklijke Brill NV, Leiden, 1999 Phronesis XLIV/1


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logical puzzle about our knowledge of universal truths (The Paradox of

Knowing Universals, to give it a name), Aristotle explicitly introduces

into discussion the thesis that learning is Recollection. Naturally, then,

if we want to fully appreciate Aristotles conception of Platos particu-

lar brand of rationalism as well as his attitude towards Platos notorious

account of knowledge-acquisition, this is a passage we will need to

comprehend.

As things stand, however, Aristotles treatment of Recollection in B.21,

when not wholly ignored by scholars,1 is the object of serious misconception.

The reason this passage has long eluded proper appreciation, I suggest,

derives from the widespread belief that the discussion of Recollection in

B.21 all but duplicates the solution to Menos Paradox found in the intro-ductory chapter to thePosterior Analytics. Owing to this common assimi-

lation of the two passages, what scholarly accounts there are of the

remarks on Recollection in B.21 have been undertaken with at least one

eye on the supposedly parallel handling of Menos Paradox in Posterior

Analytics A.1.2 Unfortunately, such over-reliance on the relatively more

familiar passage in A.1 has served merely to discourage careful analysis

of the actual text in B.21 and, as a result, has prevented a proper under-standing of the remarks on Recollection to be found there; for, in reality,

the treatment of Recollection in B.21 has very little to do with Aristotles

attempt to solve Menos Paradox in A.1.

Of course, to make good on this larger claim about the relationship

between the two texts would require separate and careful investigation of

each. What I propose to do in the space of this essay, however, is some-

thing only half as ambitious as that: I will simply set aside the allegedlyparallel passage inPosterior Analytics A.1 which is itself so crowded with

difculties as to be of dubious service, anyway and attempt to under-

stand the treatment of Recollection in Prior Analytics B.21 in its own

terms and within its own argumentative environment. As I will try to show

Accepted May 19981 The neglect this passage has suffered is well illustrated by Dominic Scotts recent

work on ancient innatism, Recollection and Experience: Platos Theory of Learning

and its Successors (Cambridge, 1995); for although Scott devotes considerable space

to Aristotles attitude towards innatism, he fails even to mention the explicit treatment

of Recollection inAn. Pr. B.21. The irony of this disregard is that the passage one

of the few places where Aristotle gives any indication of the specic form of innatism

he saw himself up against actually lends precious Aristotelian support to Scotts

non-Kantian account of Platonic rationalism (see further n. 17 below).2 See e.g. the recent commentary of R. Smith, Aristotle: Prior Analytics (Indiana-

polis, 1989), ad loc.

2 MARK GIFFORD


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through close commentary, when we situate Aristotles remarks on Recol-

lection within their own dialectical setting, we are led to a reading of the

passage which both overturns traditional interpretations and furnishes valu-

able insight into Aristotles epistemology and its relationship to Platonic

rationalism.

I. The Paradox of Knowing Universals

Let me begin by establishing the argumentative context inPrior Analytics

B.21 within which Aristotles treatment of the theory of Recollection appears.

The chapter as a whole reveals Aristotle engaged in a further study of his

syllogistic system; the topic of concern in this case is the extension of syl-logistic into the territory of epistemic logic. His main aim in B.21 is to

establish that certain inference rules, valid for categorical statements, no

longer hold, or hold only under qualication, when those statements are

transported into the psychological domain of knowledge-reports. The dis-

cussion of Recollection is embedded within the central argument of the

chapter, at 67a8-30, where Aristotle is concerned to show, among other

things, the invalidity of a rule of inference that we might call the Principleof Universal Instantiation in Knowledge-Contexts (the UIK-Principle

for short). Aristotle himself articulates the principle at 67a9-12, and we

may set it out as the following argument-form (where c holds the place

of a singular term):

S knows that every B is A; c is in fact a B; \S knows thatc is A

Aristotles strategy for exposing the fallaciousness of the UIK-Principle isto dissolve a paradox which that principle generates. The puzzle, which

seems to have been in general philosophical circulation at the time,3 is the

one I have dubbed the Paradox of Knowing Universals (abbreviating to

PKU). Aristotle offers a version of it at 67a9-16, and we can formulate

the puzzle for our purposes in the following way (where t names the

particular, perceptible triangle introduced at 67a14, and has 2R abbre-

viates the predicate of the angle-sum theorem for triangles, Aristotlesfavorite illustration of an item of knowledge):

3 We cannot say who rst fashioned the puzzle, butAn. Post. A.1 71a30-34 shows

that certain thinkers advanced an alternative solution to Aristotles see further VII

below.

ARISTOTLE ON PLATONIC RECOLLECTION 3


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1. Sappho knows that every triangle has 2R. [p]

2. t is a triangle. [p]

\3. Sappho knows that thas 2R. [1,2: UIK-Principle]

4. IfS doesnt know thatxexists,

then, for all F, S doesnt know thatx is F. [p]

5. Sappho doesnt know that texists. [p]

6. thas 2R, [p]

\7. Sappho doesnt know that thas 2R. [4,5,6]

\8. Sappho both knows and doesnt know that thas 2R. [3,7]

The paradox threatens an epistemic commonplace: we ascribe knowledge

to someone by a knowledge-report having a universal content-clause(PKU.1), but that person doesnt know of the existence of certain subjects

covered by the clause (PKU.5). In Aristotles example, a person (whom I

refer to as Sappho) knows that every triangle has 2R but doesnt know

that t exists. Given this cognitive scenario, along with the principle in

PKU.4, which requires knowledge of the existence of a subject for any

other knowledge about that subject, we can infer the conclusion in PKU.7:

that Sappho doesnt know that thas 2R; and given the UIK-Principle, we

can also infer the conclusion in PKU.3: that Sappho does know that thas

2R. Drawing both of these inferences, however, leaves us staring at the

contradiction in PKU.8.

II. Aristotles Solution to the Paradox of Knowing Universals

Aristotle offers his solution to PKU at 67a16-21 (call this Section A),

the stretch of text which immediately precedes his treatment of Re-

collection:

[A](1) because knowing that every triangle has 2R is not

univocal; (2)(a) rather, in one sense by having universal

knowledge, (b) and in another sense particular knowledge.

(3)(a) In this way, then, he knows that < t> has 2R in the sense of

by universal knowledge, (b) but he doesnt know it in the sense of

by particular knowledge. (4) As a result, he will not occupy contrary states.

[A](1) t gr ednai pn trgvnon ti do ryaw ox plon stin , (2)(a) llt mn t tn kaylou xein pistmhn, (b) t d tn kay kaston. (3)(a) otvmn on w t kaylou ode t G ti do rya, (b) w d t kay kaston okoden, (4) st ox jei tw nantaw.

This compact passage, in addition to containing Aristotles solution to

PKU, introduces the fundamental theses of the epistemic logic developed

in B.21. It will reward close scrutiny.

4 MARK GIFFORD


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In [A.1-2] Aristotle identies the rst premise of the puzzle as the

source of the difculty, claiming that the knowledge-report in PKU.1 is

ambiguous between ascriptions of what he calls universal knowledge

and particular knowledge. On the most natural way of taking these ex-

pressions, universal knowledge would refer to ordinary or explicit knowl-

edge of a universal statement, while particular knowledge would indicate

explicit knowledge of a singular statement. ThatPKU.1 can be used to

ascribe universal knowledge in this sense is readily appreciated; but if, as

[A.2b] asserts, the sentence Sappho knows that every triangle has 2R

can also be used to indicate the possession ofparticular knowledge, then

knowing by particular knowledge, as Aristotle is thinking of it in here,

must involve a good deal more than knowledge of a solitary singular truth.What the claim in [A.2b] has to mean, of course, is that the knowledge-

report in PKU.1 can be taken as ascribing particular knowledge ofa string

of singular statements statements expressed by sentences of the form x

has2R whose singular subject terms are uniquely and exhaustively corre-

lated with each particular triangle that there is. If we call such a complex

epistemic state enumerative knowledge, then what Aristotle is saying

in [A.2] is thatPKU.1 is ambiguous between ascriptions of universal andenumerative knowledge. And from this we see (ignoring the matter of

existential import) that he is effectively noting the scope-ambiguity of the

universal quantier in knowledge-reports such as PKU.1:

(1) Sappho knows that (x)(x is a triangle xhas 2R)

(2) (x)(x is a triangle Sappho knows thatxhas 2R)

The narrow-scope reading in (1) gives us universal knowledge, while the

logically independent, broad-scope reading in (2) gives us enumerative

knowledge. And this distinction between the narrow- and broad-scope (or

intensional and extensional) readings of PKU.1 is just what Aristotle

needs to expose the faulty inference in PKU; for although the broad-scope

reading in (2) permits instantiation, this logical operation is blocked in (1)

by the intensional context within which the universal statement is there

embedded. Or, to put the point in more Aristotelian terms, while the UIK-Principle holds when its major premise is understood as ascribing enu-

merative knowledge, or knowledge of an exhaustive chain of singular

facts, it fails when that sentence is taken to ascribe universal knowledge

knowledge of a universal connection between two properties. Thus, having

drawn the distinction between universal and enumerative knowledge, and

thereby having exposed the equivocal major by which the UIK-Principle

gets its hold, Aristotle apparently could have completed his dissolution of



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the paradox at this point: all he needed to say was that in the cognitive

scenario under consideration Sappho has universal knowledge but not

enumerative knowledge that every triangle has 2R, and that when PKU.1

is read as ascribing universal knowledge the conclusion in PKU.3 fails to

go through.

To the consternation of some commentators,4 however, Aristotle doesnt

conclude his discussion of the paradox on that note. After drawing the

distinction between two types of knowledge that the sentence Sappho

knows that every triangle has2R could be used to ascribe, Aristotle goes

on for some reason to draw a corresponding distinction between two types

of knowledge that the sentence Sappho knows that t has 2R could be

used to ascribe. In [A.3], introduced by the inferential particle on, hedraws two conclusions in the light of the distinction in [A.2]: taking

Sappho to have universal knowledge in the cognitive scenario under dis-

cussion, Aristotle infers in [A.3b] that she doesnt know thatthas2R by

particular knowledge, and in [A.3a] that she does know thatthas2R by

universal knowledge.

Now, the inference to [A.3b] presents no difculty. In asserting that

Sappho doesnt know that thas 2R by particular knowledge, Aristotle issimply saying that she lacks explicit knowledge of that singular statement,

thereby making plain his rejection of the UIK-Principle when its major is

taken to ascribe universal knowledge. So this second half of the double-

assertion in [A.3] is expected and unexceptionable. But what are we to

make of the rst half? Instead of resting content with the claims that Sappho

has explicit knowledge of a universal truth but lacks explicit knowledge

of one of its instantiations, Aristotle infers in [A.3a] that Sappho doesafter all know that thas 2R, at least in a sense the sense in which one

knows a singular statement by virtue of knowing the universal truth under

which it falls. But what sense is that?

We can note rst of all that this fourth type of knowledge, knowing a

singular statement by virtue of universal knowledge, cannot amount to

having explicitknowledge of that singular statement; for that would be to

have particular knowledge, and in the same breath Aristotle denies Sapphohas that. Thus the form of knowledge ascribed in [A.3a] is going to have

to be knowledge of a differentorder than the other three cognitive states

Aristotle has noted i.e. universal, enumerative, and particular knowledge

4 See e.g. the complaint in J. Barnes,Aristotle: Posterior Analytics (Oxford, 1994),

88, that Aristotles actual solution to PKU foists an utterly unnatural sense on the

knowledge-report in PKU.3.

6 MARK GIFFORD


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all of which were forms of explicit knowledge, differentiated only with

respect to content. Furthermore, this is not the only occurrence in the

corpus of the idea that we have a kind of non-explicit knowledge of sin-

gular statements (or subordinate universal statements) by virtue of know-

ing the universal statement under which they fall. Elsewhere Aristotle

speaks of this sort of knowledge as potential knowledge (see e.g. An.

Post. A.24 86a22-29, where he contrasts knowing dunmei with knowingnerge&; cf.Meta. A.1 982a21-23). But what are we to make of this ideaof potential knowledge?

What we can say at least is that the inference drawn in [A.3a] betrays

Aristotles acceptance of a rule of inference for ascribing potential knowl-

edge which turns out to be a variation on the specious form of the UIK-Principle: if you have explicit knowledge of a universal truth, then, by

that very fact, you also have potential knowledge of each singular state-

ment falling under the universal truth. Call this the Potential Knowledge

Principle (or PK-Principle):

S has universal knowledge that every B is A; c is in fact a B;

\S has potential knowledge that c is A

The chief problem with this principle, though, is that, since PKU can

apparently be solved well enough in its absence, it appears to be intro-

ducing a thoroughly needless epistemic complexity. It might seem, then,

that the paradox has extracted a concession from Aristotle it has no right

to receive. Indeed, Aristotles acceptance of the PK-Principle could leave

one with the disappointing impression that he has not fully freed himself

from the fallacious grip of the UIK-Principle.But, however that may be, Aristotle doesnt wait to tell us why we

should accept this peculiar PK-Principle. After telling us that Sappho has

potential knowledge but lacks explicit knowledge of the fact that t has

2R, he concludes his solution to PKU in [A.4] by announcing that she is

therefore not in possession of incompatible states, and hence her cognitive

scenario is one that can actually occur.

III. Taking Stock of Aristotles Solution to the Paradox

Before proceeding to the ensuing remarks on Recollection, we would do

well to pause and take stock of the solution to PKU offered in [A]. In

attempting to solve the puzzle, Aristotle introduces, whether explicitly or

implicitly, the following key theses of his epistemic logic:



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(T1) Knowledge-reports of the form S knows that everyB isA are ambig-

uous between ascriptions of universal and enumerative knowledge.

(T2) Explicit knowledge of a universal truth does not entail explicit

knowledge of each singular statement falling under that truth; that

is, universal knowledge doesnt entail enumerative knowledge. (This

represents Aristotles rejection of the UIK-Principle when its major

is read as ascribing universal knowledge.)

(T3) Human beings can have explicit knowledge of universal statements;

that is, they can possess universal knowledge.

(T4) The PK-Principle: universal knowledge entails potential knowledge

of each singular statement falling under the known universal truth.

But in order to assess the strength of his proposed solution to the puzzle

and hence the strength of the overall argument in B.21, which depends

heavily on this solution we have to ask which of these four theses we

can reasonably demand that Aristotle defend. More to the point, which of

these claims should he defend against the original formulators of the puz-

zle, or other dialectical opponents, who would or at least could have taken

the paradox to be, not eloquent testimony against the UIK-Principle, but

a reductio ad absurdum of the idea of knowledge-ascriptions with uni-

versal content-clauses opponents who would thus pose a threat not only

to the epistemic logic of B.21 but to Aristotles entire epistemology with

its basic requirement thatepistm take the form of universal knowledge?

That Aristotle had some concern for critics of this kind is borne out by

the fact that he addresses opposition to the idea of universal knowledge,

along with PKU, at the very start of his principal investigation into the

nature ofepistm, namely, in the opening chapter to thePosterior Analytics.

So lets consider which of the above statements in his solution to the puz-

zle Aristotle might feel the need to defend.

First of all, T1 is a claim that neither needs nor even admits of elabo-

rate defense. The principal way we justify a claim that a certain sentence

is ambiguous is by teasing out the linguistic intuitions of competent speak-

ers of a language and helping them to see that a single sentence could be

used to express two very different logical possibilities. And given his log-ical resources Aristotle does an adequate job of indicating the ambiguity

in PKU.1with his distinction between universal and enumerative knowl-

edge. An opponent who continued to balk atT1, then, would forfeit claim

to linguistic competence and hence justly suffer the loss of dialectical

standing.

Now, it might be thought that Aristotles opponents would want him to

justify his claim in T2, namely, his rejection of the UIK-Principle when

8 MARK GIFFORD


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its major ascribes universal knowledge. But, actually, T2 could no longer

be a genuine point of contention. In view of the conceptual distinction

between universal and enumerative knowledge in T1, Aristotles dialecti-

cal adversaries would be obliged to concede that universal knowledge

represents a logical possibility. They would therefore have to admit the

intelligibility of the idea of a psychological state, irreducible to and not

entailing enumerative knowledge, in which one grasps a universal connec-

tion between two attributes. But in admitting that universal knowledge is

an intelligible idea they would in fact be conceding T2, since the possi-

bility of knowing a universal rule apart from knowledge of each of its

instances is part of the very concept of universal knowledge. Aristotles

opponents would thus be faced with a dilemma: if they refuse to acknowl-edge the distinction between universal and enumerative knowledge in T1,

then, as weve noted, they can be duly excluded from further discussion on

grounds of conceptual impairment; but if, on the other hand, they grant

the distinction in T1, then they would be forced by denitional necessity

to concede the claim in T2 as well.5 We see, then, that Aristotles rejection

of the UIK-Principle in T2 requires no more defense than was needed for

the conceptual distinction between universal and enumerative knowledgein T1.

In conceding T2, however, Aristotles opponents would not have to

give up the eld. For by granting T2 they have simply acknowledged that

the possession of universal knowledge apart from enumerative knowl-

edge represents a logical possibility and an intelligible idea. Yet disarming

the paradox and vindicating universal knowledge requires that universal

knowledge be more than merely a conceptual possibility; it must also rep-resent a real possibility the humanpsuch must be capable, psychologically

speaking, of entering into and occupying this state of universal knowledge.

Thus Aristotles opponents could grant what amounts to the conditional

in T2 ifSappho, say, has universal knowledge that every triangle has

2R, she need not have particular knowledge that thas 2R but then dig

in their heels and refuse to concede that the antecedent is ever satised.

It would remain open to them to hold that the human mind is incapable ofattaining to universal knowledge, being instead, like the souls of Aris-

totelian beasts (NE VII.3 1147b3-5 andMeta. A.1 980b25 ff.), forever con-

demned to the lowly task of recording the singular facts of experience. In

other words, they could adopt a stance of radical empiricism, declaring,

5 But see VII below for resistance to T2 from clever logicians hoping preserve a

purely extensional system of inference rules.



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10 MARK GIFFORD

in succinct Aristotelian terms, that there is no epistm beyond empeiria.6

And given this dialectical possibility, if the effectively conditional state-

ment in T2 is to play more than a hypothetical role in his solution to PKU,

Aristotle still needs to defend its antecedent, which is identical to the claim

in T3 that human beings actually do possess universal knowledge.

Defense ofT3 is all the more necessary in this context, since the real

existence of universal knowledge is essential to the overall project in B.21.

If the rules of epistemic logic that Aristotle is working out are to have

any actual application, they must be true to the facts of human psychol-

ogy. But the logical distinction in T1 can no more show the psychologi-

cal reality of universal knowledge that every triangle has 2R than it can

the psychological reality ofenumerative knowledge that every triangle has2R a state whose real existence Aristotle himself denies. Thus it is not

enough for Aristotle to look at the matter logikw, by simply marking adistinction in conceptual space; the real existence of universal knowledge

must also be established fusikw, by appeal to empirical fact.And just as T3 remains in need of defense, so too does the independ-

ent and effectively stronger claim in T4: the PK-Principle. Even if his

other three theses were conceded, Aristotle would still owe his opponents(and us) some reason for thinking that this unusual epistemological prin-

ciple is a rule of inference we should adopt. Indeed, before that, he should

give some indication of what his peculiar talk of knowing a particular by

virtue of universal knowledge, or potential knowledge, even means.7

6

Who would such opponents be? They could be opponents wedded to the idea thatthought is nothing but perception (DA III.3 427a21 ff.; cf. Meta. G.5 1009b12 ff.),thinkers of the knowing-is-seeing variety whom Plato was no doubt out to confront in

the Theaetetus; or they could even be friendly in-house critics, devils advocates in an

intramural dialectical moot, seeking an argument on this occasion for the reality of a

psychological state so important for Aristotles epistemology and epistemic logic as

that of universal knowledge. As far as I can see, naming names is impossible here (as

it is in the case of the authors of PKU itself); but the historical possibility of such

opponents is a genuine one, as is the dialectical opening the proposed solution in [A]

would have left them something of which Aristotle himself was well aware (cf. e.g.

Meta. B.4 999b1-4, where radical empiricism is mentioned as a possible response to

the more familiar, metaphysical problem of universals).7 The talk of potential knowledge (as a rst actuality) in passages such as DA

II.5 417a21 ff. tends to conate two notions that must be kept separate: (1) disposi-

tional (i.e. non-occurrent) explicit knowledge of a universal truth and (2) non-explicit

knowledge of the singular statements falling under a known universal truth. One could

readily acknowledge the existence of (1) and still question the meaning and legitimacy

of talk about (2).


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Thus, from this review of the principal claims that go into his solution

to PKU, we see that, before we can count that solution a success, Aristotle

must show there is good reason to accept the two theses in T3 and T4,

and especially the rst, more critical point. Nothing said in [A], however,

serves to defend either thesis against hostile reception. And if we leap

over the remarks on Recollection at 67a21-26 (Section B) for a moment,

neither is there anything in the conclusion Aristotle draws at 67a27-30

(Section C) that can be taken as justication for these claims: in bring-

ing his discussion of PKU to a close there, Aristotle basically reiterates

the solution proposed in [A], but advances no further arguments to support

his position. It appears, then, that if Aristotle does successfully defend the

two disputable theses in his solution to the paradox, the full burden of thatdefense must be carried by his discussion of Recollection a passage we

are now in a position to examine.

IV. A Traditional View of Aristotles Remarks on Recollection

Aristotles brief discussion of Recollection at 67a21-26 opens in charac-

teristically telegraphic fashion:

[B](1) Likewise the thesis in the Meno that learning is Recollection. (movw dka n t Mnvni lgow, ti myhsiw nmnhsiw.)

On the traditional view of this section, Aristotle announces in [B.1] that

he plans to criticize Platos theory of Recollection on grounds similar to

those he has just advanced against PKU. But, standard translations not-

withstanding, Aristotle doesnt actually assertthis. As far as the languageof [B.1] goes, he could equally well be claiming that the doctrine of

Recollection bears some resemblance to the position he himself has just

taken in [A]. And while this construction may seem implausible at rst

glance for what resemblance could Aristotle nd between Recollection

and his own empiricism? and even if there were some resemblance, why

would he call attention to it here? it should be observed that with the

sper-clause in the subsequent sentence, which expands on the similaritynoted in [B.1], Aristotle does actually liken the epistemological process he

describes to a case of Recollecting. At any rate, the wording of [B.1] by

itself cannot decide between these two readings of Aristotles intentions;

the decision between them will have to come from discovering what

exactly he goes on to say about Recollection:

[B](2)(a) For it never happens that we know a particular beforehand; (b) rather,

we acquire knowledge of the particulars at the same as the induction, (c) just as


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12 MARK GIFFORD

though we were coming to know again. (3) For we know some things straight-

away, e.g. that it has2R, if we see that it is a triangle. (4) And likewise for other

cases.

[B](2)(a) odamo gr sumbanei proepstasyai t kay kaston, (b) ll ma

t pagvg lambnein tn tn kat mrow pistmhn , (c) sper nagnvrzontaw.(3) nia gr eyw smen, oon ti do ryaw, n dvmen ti trgvnon. (4) movwd ka p tn llvn.

Before unveiling my own reading of these succinct remarks, let me set

out what I think is the least implausible interpretation that one can offer

from within the framework of traditional views of this passage. 8 On this

reading, Aristotle is contemplating a simple syllogistic inference from the

known universal major that every triangle has 2R to the singular conclu-sion that t, say, has 2R. He asserts in [B.2a] that we never know such

conclusions beforehand (that is, before we perform the corresponding

syllogistic inferences, or perhaps before we encounter the particulars in

experience); rather, [B.2b], we gain knowledge that thas 2R at the same

time as we are led to perform the syllogistic inference (ma t pagvg).9

Aristotle then suggests in [B.2c] that this syllogistic process of drawing

out the logical consequences of acquired knowledge was mistaken byPlato for a process of recovering innate knowledge (sper nagnvrz-ontaw: its as though we were coming to know for a second time).10 Finally, in [B.3] he claries and illustrates the state-

8 Among commentators, W.D. Ross, Aristotles Prior and Posterior Analytics

(Oxford, 1949) 474, is nearest to the view I will sketch.

9 This is the reading of pagvg inuentially advocated by Ross (Analytics, 476and 481-483), who argues that the term is sometimes used non-technically to refer

to any process of being led from one statement to another, even a syllogistic process,

as he claims it does here. Others take pagvg, even more implausibly, to mark theprocess by which we come to know the singular minor that t is a triangle see e.g.

R. McKirahan, Aristotelian Epagoge in Prior Analytics 2.21 and Posterior Analytics

I.1,Journal of the History of Philosophy 21 (1983) 1-13. Scholarly over-reliance on

the purported doublet in Posterior Analytics A.1 is no more in evidence than in the

interpretation ofpagvg in B.21; for the arguments in support of non-standard con-struals of the noun here rest almost entirely on the allegedly non-inductive use of the

cognate verb pgein in A.1. For reasons mentioned at the start of this essay, I willnot concern myself with such arguments on this occasion (but see further V below).

10 nagnvrzein and cognates are rare in Aristotle outside of their technical use inthe Poetics for indicating dramatic recognition (see Bonitz 43b46-44a3), and the

term here in B.21 is likewise often rendered by recognize. But it is not easy to make

out Aristotles point on this timid construal. For this reason, and also because the

sper-clause clearly furnishes a comparison with Platonic Recollection, nagnvrzein

in this occurrence is actually better read as meaning to re-cognize that is, to come


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ment in [B.2], explaining that, if we know the universal major of a simple

syllogism and then apprehend the singular minor, we can come to know

the singular conclusion straight-away (eyw), that is, with no further men-tal act or empirical investigation intervening between the perceptual appre-

hension of the minor and the syllogistic inference to the conclusion. The

main point behind this remark, and behind the discussion of Recollection

as a whole, would then be this: Aristotle is faulting Plato for failing to

recognize the distinction between explicit and potential knowledge and for

thus misconstruing the immediacy of syllogistic knowledge-acquisition as

a sign of our recovering explicit knowledge innately stored in the mind. 11

And this, it must be admitted, would be a sensible point to ascribe to

Aristotle. It is at least a point that comes close to the view many todaytake of the epideixis with the slave boy in Platos Meno. What that epi-

deixis shows on this view is not that the slave has retrieved an explicit

truth from a secret cognitive storehouse built into the human mind, but

merely that, given a stock of information previously acquired, he has the

native deductive capacity to expand this store of explicit knowledge by

extracting the logical consequences implicitly contained within it. The

above reading of[B], then, allows us to attribute to Aristotle a reasonablephilosophical insight.

V. Problems for a Traditional View

But that is about all one can say for even the best version of a traditional

reading of Aristotles remarks on Recollection. While this interpretation

does give Aristotle a reasonable insight, I dont think this is quite theinsight he wants to offer here. And to see why this interpretation cannot

be sustained, let me note a few of the serious di fculties facing the pre-

ceding account of [B].

to know (gnvrzein) again (n-) as one would do in Recollecting. The term here,then, serves as shorthand fornalambnein pistmhn n prteron exen, the stand-ard denition ofnmnhsiw in Plato and Aristotle see Meno 85d,Phaedo 75e, and

Mem. 2 451b3-6.11 By explicit knowledge I mean knowledge whose object is actually represented

in the mind. Explicit knowledge in this sense can be distinguished from what we

might call conscious knowledge, or knowledge which (if one is not already enter-

taining it) one can retrieve from memory and entertain at will. Given these rough

denitions, we can characterize innate knowledge in Plato, on Aristotles view, as

knowledge that is explicit but not conscious seeAn. Post. B.19 99b25-27 andMeta.

A.9 993a1-2.


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14 MARK GIFFORD

On that account, Aristotle is supposed to be describing in [B.2], as he

clearly is in [B.3], a process of knowledge-acquisition that occurs by

means of a syllogistic inference. Yet the term he uses to refer to the infer-

ential process he has in mind in [B.2] is notsullogismw,12 but pagvg;

and pagvg is Aristotles technical term for marking not a syllogistic ordeductive inference, but an inductive one a movement of thought from

singular statements (or subordinate universal statements) to the universal

statement under which they fall. To its demerit, then, the above reading

of[B] forces pagvg to pick out an inferential process that is for Aristotlediametrically opposed to the standard, technical referent of the term.

Moreover, as a second problem for available readings of pagvg in

[B.2], it should be remarked that these readings frustrate our philosophi-cal as well as our linguistic expectations. For induction plainly furnishes

Aristotle with his primary response to Platonic Recollection. In virtually

every other context in which the issues of empiricism and innatism are

raised (a signicant exception is DA III.4 429a27-29; cf. III.8 432a3-8),

Aristotle advances or at least calls attention to his empiricist doctrine that

induction is the way by which we come to know universal truths. This he

does most famously in the response to innatism that is found in PosteriorAnalytics B.19. But in his defense of empiricism in Posterior Analytics

A.18 (81a38-b9), Aristotle likewise places induction at center stage.

Further, the passing shot he res at innatism inMetaphysics A.9 (992b34-

993a2) which reiterates the objection ofAn. Post. B.19 (99b26-27) that

a theory postulating innate, unconscious knowledge of high-level scien-

tic truths presents us with an unacceptable view of the mind follows

immediately upon mention of his own account of knowledge-acquisitionthrough induction (992b34). And, nally, we can also adduce here Aristotles

well-known remarks in Metaphysics M.4 (1078b17-31) on Socrates two

claims to philosophical fame: his concern with dening (non-separated)

universals and his employment of inductive arguments (paktiko lgoi).Coming at the start of a critical review of the original theory of Forms,

Aristotles mention of the latter activity might seem puzzling; for while

Socrates interest in dening universals clearly merits a central place in an

12 Nor, apropos of readings in which pagvg marks the process of appre-hending the minor, is the term used here asyhsiw, as we would have expected wereAristotle referring to the process by which we recognize a perceptible triangle

(asyhtn trgvnon, 67a14) as a triangle see also NE VI.8 1142a25-30, and notedvmen in [B.3].


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account of the development of the theory of Forms, his employment of

inductive arguments seems tangential to that story. Puzzlement vanishes,

however, when we recall that Aristotelian historiography typically serves

a dialectical agenda; for we can then see that Aristotle here is actually

appealing to Socrates for endoxic support, not only against Platonic sep-

aration, but against its attendant epistemology as well. That is, the reason

he notes Socrates use of inductive arguments is that he is endorsing

induction as a procedure for arriving at universal truths which, unlike

Platonic Recollection, is free of the epistemological embarrassments that

accompany separation (cf.Meta. M.9 1086b2-7). So understood, then, this

passage from M.4 likewise helps us to see that, when the idea of innatism

is broached in the corpus, Aristotles almost reexive response is: No,induction. And so when he explicitly refers to the theory of Recollection

inPrior Analytics B.21, and then immediately tosses the term pagvg intothe bargain, there is a powerful presumption that Aristotle is referring to

his own empiricist account of knowledge-acquisition through induction

the inferential process by which we apprehend universal statements from

the information of perception. Yet going readings of [B], with their non-

inductive construals of pagvg, rudely fail to satisfy our strong philo-sophical expectations in this regard.

So much for the rst two difculties facing received opinion on [B]. As

for the third, recall that this passage occurs in the context of an attempt

to solve PKU. So we have to ask how Aristotles treatment of Recollec-

tion, on the reading of[B] sketched above, advances his solution from the

stage at which we left it at the end of [A]. More specically, we must

ask whether this reading of the text gives Aristotle any argument for thetwo claims we found he still needs to justify: that human beings actually

do possess knowledge of universal truths (T3) and that this universal

knowledge entails potential knowledge of singular statements the PK-

Principle (T4).

But our answer to this question, particularly as regards the all-important

claim in T3, must be a negative one. On the reading of[B] under discus-

sion Aristotle merely assumes that human beings know universal truths.In connection with his solution to the paradox, what he would be trying

to make clear, evidently, is that universal knowledge doesnt carry with it

explicit knowledge of the singular statements that exemplify the known

universal truth. To paraphrase [B.2a-b] on this reading, ,

we dont have explicit knowledge of the particulars before we encounter


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16 MARK GIFFORD

them; rather, we gain explicit knowledge of them at the same time as the

syllogistic inference.13 Thus, rather than arguing for the crucial and con-

troversial claim in T3, Aristotle would be presupposing it and concen-

trating instead on his rejection of the UIK-Principle in T2. In the eyes of

his opponents, he would therefore be making an uncontroversial and,

indeed, quite obvious conditional claim i.e., ifwe have knowledge of a

universal truth, it doesnt follow that we have explicit knowledge of the

singular statements falling under that truth while curiously neglecting

to say anything in favor of its disputable antecedent. Given available

views of [B], then, Aristotle would stand convicted of ignoratio elenchi.

The situation is better in connection with T4, but only slightly so. For

although a traditional reading can manage to nd the idea of potentialknowledge in [B.2b-3], and hence would allow us to reconstruct an im-

plicit argument forT4, Aristotles focus would nonetheless not be on a

defense of the PK-Principle which, indeed, would pass without explicit

mention in [B], as it did also in [A]. His main concern would be to make

clear, not that explicit knowledge of a universal truth does give us poten-

tial knowledge of its singular instantiations (T4), but that it doesntgive

us explicit knowledge of those instantiations (T2); and the latter claimhardly sufces to establish the former. Thus, on standard interpretations,

Aristotle would offer no explicit justication for introducing the unusual

PK-Principle into his solution to PKU and thereby into the system of epis-

temic logic developed in B.21 as a whole.

For these reasons, then, if we accept a traditional account of the dis-

cussion in [B], we seem forced to conclude that Aristotle has not explic-

itly and adequately justied the claims in T3 and T4, and hence that to

13 Notice that standard readings also seem to generate an untoward consequence for

Aristotles conception of Platonic Recollection: since [B.2] is supposed to be describ-

ing a process by which we acquire knowledge ofsingularstatements, and since this

is the process Aristotle is supposed to be claiming Plato mistook for Recollection,

Aristotle would apparently be imputing to Plato the preposterous notion that we pos-

sess, as part of our unconscious cognitive birthright, explicit knowledge of perceptible

and ephemeral particulars. Pacius acknowledges the consequence in his commentary

(ad loc.) and proceeds to supply on Aristotles behalf two arguments against the pre-

natal acquisition of particular knowledge: (1) knowledge of particulars requires per-

ception and hence the bodily organs of perception, and (2) many particulars would

have come into existence afterI was born. But the unbearable obviousness of those

points speaks rather against the imputation, and thus against standard readings. Indeed,

on Aristotles own account, Plato separated universals in order to secure stable objects

of knowledge owing to his belief thatuctuating particulars cannot be known at all

(Meta. M.4 1078b12-17; cf. A.6 987a32 ff.).


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the detriment of the epistemic logic of B.21 he has not satisfactorily

defended his proposed solution to PKU. At the very least, it will have to

be admitted that a reading of[B] in which Aristotle does offer some pro-

tection to T3 and T4 is to be favored on grounds of philosophical charity

over interpretations in which these two theses are left exposed to rough

handling.

Which brings us to a nal problem I want to mention, a problem con-

cerning the rationale behind Aristotles inclusion of a discussion of Re-

collection in the course of his treatment of PKU. While it is true that, as

noted earlier, a traditional reading of[B] allows Aristotle to present a rea-

sonable point against the epideixis in the Meno, there doesnt appear to

be any pressing need for him to make that point in connection with PKU.14

Since on standard readings Aristotle wouldnt be advancing the cause of

his solution much beyond what was already said in [A], and since what-

ever advance there might be could have been achieved seemingly just as

well without the mention of Plato, the treatment of Recollection has gen-

erally given the appearance of being a sort of mini-digression a digres-

siuncula as Pacius called itwith Aristotle turning aside from the matter

at hand to take a quick poke at Plato. But, other things being equal, a read-ing of[B] that makes this section an integral component in Aristotles dis-

cussion of PKU a discussion which itself constitutes the decisive moment

in the undertaking of B.21 as a whole is much to be preferred to one

which is forced to hypothesize a brief departure from the main course of

the argument.

So, to summarize the preceding examination of traditional interpreta-

tions of [B], we can conclude that, in the four short sentences that com-prise Aristotles discussion of Recollection, these readings generate at least

four majors problems (see n. 13 for a fth): (1) they construe Aristotles

technical term pagvg in rather improbable ways; (2) they disappoint ourstrong expectation that, given the use ofpagvg in the context of remarkson Recollection, Aristotle would be opposing to innatism his own empiri-

cist theory of induction; (3) in connection with his solution to PKU, they

have Aristotle, as far his explicit argument goes, assuming the controver-

14 The best I think an advocate of available readings can say by way of explaining

the appearance of Recollection in this context is that Aristotle is supporting his solution

to PKU by revealing its power showing how it provides the resources to undermine

yet another problematic epistemological argument. When we follow this line out, how-

ever, and ask after which specic thesis in his solution he is concerned to support, we

are led back to the result just mentioned as the third difculty for traditional views:

that Aristotle is unduly occupied with T2 to the disadvantage ofT3 and T4.


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18 MARK GIFFORD

sial and defending the obvious; and, nally, (4) they turn Aristotles re-

marks on Recollection into a largely idle aside in the overall argument of

B.21. This, I think, is a fairly high price to pay for a sensible complaint

against the epideixis with the slave boy let alone for a regrettable

attempt to solve Menos Paradox.

VI. An Alternative Interpretation of [B]

In view of the philological and philosophical difculties to which a tradi-

tional interpretation of[B] gives rise, we should now be open to an alter-

native reading that can avoid them. Lets see what happens to Aristotles

discussion of Recollection, then, when we allow pagvg its standard ref-erence to an inductive process of arriving at universal truths, thereby elim-

inating the rst two of the four major difculties canvassed above.

Considerrst how [B.2] comes out on this reading. Aristotle would be

saying that we dont know the particulars beforehand ([B.2a]: odamo grsumbanei proepstasyai t kay kaston), that is, before the induction, orperhaps before we encounter particulars of the given type in experience;

rather, we gain knowledge of the particulars at the very moment we per-form the inductive inference ([B.2b]: ll ma t pagvg lambnein tntn kat mrow pistmhn), namely, the inductive inference to the universalstatement under which these particulars fall.

Far from being an impossible interpretation of pagvg here, thisconstrual yields a reading of[B.2] that is actually quite promising; for an

inductive inference, which furnishes explicit knowledge of a univer-

sal truth, could provide us with knowledge of a plurality of particulars orsingular statements only if Aristotle were talking about the acquisition

ofpotential knowledge of those statements.15 Thus, on the reading now

15 It cannot be objected that in [B.2b] Aristotle is expressly referring to the acqui-

sition ofexplicit knowledge of singular statements, for the nominalizing article imme-

diately before kat mrow shows that the phrase tn tn kat mrow pistmhn is notbeing used as a name for particular knowledge. When he names the state of particu-

lar knowledge, Aristotle omits the internal article before the expressions kay kastonand kat mrow see 67a18-19, a20, and a30 in which cases these expressions func-tion as attributive adjectives, whereas kat mrow in [B.2b] plainly serves as a noun.Thus Aristotle is simply describing a way in which we acquire knowledge of partic-

ulars; his language leaves open the question whether the form of knowledge we are

gaining is explicit or potential. (If anything, the addition of the article before katmrow shows that Aristotle was not especially interested here in conveying the idea ofparticular knowledge, something he could have done more simply and effectively with-

out the extra article.)


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being proposed, Aristotle is saying more about potential knowledge, as he

should. Indeed, on this reading he is actually articulating the PK-Principle;

for an induction yields explicit knowledge of a universal truth, and Aris-

totle is saying in [B.2b] that we acquire potential knowledge of the sin-

gular statements falling under a universal truth at the very moment (ma)we draw the inductive inference16 in other words, universal knowledge

entails potential knowledge (T4). And since, moreover, the reference to

induction plainly commits Aristotle to the real existence of universal knowl-

edge (T3), [B.2b] on this reading contains both of the claims from his

solution to PKU that are still in need of support.

Lets now see whether Aristotle offers any sort of justication for these

claims. And, setting aside the comparison with Recollection in [B.2c] forthe moment, lets rst focus our attention on [B.3], which, introduced by

the particle gr, could be adducing independent evidence in support of[B.2b]. If a radical empiricist were to demand, Why should I accept your

Now, it might be thought that since the form of coming to know in question is pre-

sented without insignia (e.g. by virtue of universal knowledge), it must by default

constitute the acquisition of ordinary, explicit knowledge of particulars. But Aristotle

could well think that his use of pagvg to indicate the process by which we gainthis knowledge had made it sufciently plain what sort of knowledge he intends:

knowledge of singular statements gained through an inference to a universal truth the

inferential process unambiguously designated by his terminus technicus pagvg.Knowledge of particulars acquired in this way could only be potential knowledge.

Note further the (apparently non-generic) denite article before pagvg and the pluralarticle before kat mrow: Aristotle is saying we gain knowledge of a plurality ofsingular statements (tn kat mrow) by a single cognitive act (t pagvg). It is only

the inferential movement to the universal truth under which those statements fall inthis case, the angle-sum theorem that could accomplish this remarkably prolic epis-

temic feat.

We see, then, that the linguistic evidence decidedly favors the idea that in [B.2b]

Aristotle is describing the acquisition of potential knowledge of particulars. And since

the adversative clause in [B.2b] tells us that we acquire potential knowledge at a cer-

tain moment, its antithesis in [B.2a] should be telling us that we lack potential knowl-

edge before that moment. Thus, although it too appears without special markings, the

knowledge Aristotle denies us in [B.2a], like the knowledge he accords us in [B.2b],

is potential and not explicit knowledge of particulars. The signicance of the obser-

vation in [B.2a]will be discussed shortly, but we can see already that the present read-

ing of the clause emancipates Aristotle from the undue concern which he displays on

standard readings with the virtually self-evident thesis in T2.16 It should occasion no surprise that Aristotle would be speaking of induction in

connection with our apprehension of a universal truth that, in his illustration, is actu-

ally a mathematical theorem see e.g. An. Post. A.18 81b2-5. The process of uni-

versalization at work in such a case can be thought of as an intuitive induction from

a particulardiagramma.


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20 MARK GIFFORD

claims that human beings have explicit knowledge of universal truths and

that this explicit knowledge carries with it potential knowledge of the sin-

gular statements falling under the universal truth?, Aristotles response

in [B.3]would be, Because we come to know certain singular statements

(nia) immediately after (eyw) we identify their subjects. But how exactlyis this point supposed to support the claims in T3 and T4?

To see what Aristotle has in mind, consider the following three-stage

Aristotelian story about the empirical process by which Sappho comes to

know a universal truth like all frogs have hearts. Stage 1: At rst she

comes to the task merely with an ability to recognize frogs, but with no

knowledge of their anatomy. She encounters Tom for the rst time and

correctly identies him as a frog. At this point, she is in no position toinfer that Tom has a heart. If she wishes to gain that information she

has to do some dissecting rst. (This is the point of [B.2a], where Aris-

totle denies that we bring potential knowledge with us to our early, pre-

induction encounters with particulars of a given type; he takes it to be

plain from experience that we lack potential knowledge at this stage, for

if we were already endowed with potential knowledge, then, in order to

discover that Tom has a heart, there would be no need for dissection.) Soshe proceeds to cut Tom up, and then does the same for a number of other

frogs, thereby entering into the state ofempeiria the state of knowing a

string of singular statements about the heartedness of these particular frogs.

Stage 2: Having discovered that each of the dissected frogs has a heart,

Sappho nds that there is good reason to think she has hit upon a uni-

versal fact of nature, and so she inductively infers and comes to have ex-

plicit knowledge of the universal truth that all frogs have hearts. Stage 3:After this, bearing her newly acquired knowledge around with her, she

comes across Atom, another frog previously unknown to her, and wishes

to know whether he has a heart. Well, in order to get this information,

thankfully, she doesnt have to carve the poor devil up; on the basis of

her universal knowledge she can infer that Atom has a heart straight-away

(eyw) no intervening process, such as dissection, need occur between

her identication of Atom as a frog and her syllogistic acquisition of theknowledge that he has a heart. (This is the point of [B.3].)

Now, if we subtract from the preceding narrative those elements that

are owed to interpretation through Aristotelian cognitive psychology with

its inferential mechanisms of inductive and syllogistic inference and its

consequent commitment to the reality of universal knowledge, what would

remain would be Sapphos cognitive behavior: at one point she had to dis-

sect frogs in order to discover that each had a heart (Stage 1: [B.2a]),


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while at a later point a simple movement of thought sufced (Stage 3:

[B.3]). Aristotle could justly assume that even stubborn critics would have

to acknowledge these evident facts about our cognitive life. But then the

crucial question arises: what explains the difference in Sapphos cognitive

behavior?

The difference and this is the point Aristotle is arguing in [B.2-3]

is best explained on the hypothesis that human beings actually do acquire

and do possess knowledge of universal truths (Stage 2: [B.2b]). The ear-

lier and later Sappho exhibited different cognitive behavior with respect

to frog hearts because in the interim she had inductively acquired explicit

knowledge of a universal truth that permits and disposes her to gain

knowledge about the heartedness of particular frogs by means of simplesyllogistic inferences; this is what accounts for her subsequent cognitive

ability to know facts about previously unknown frogs eyw, immediatelyafter she identies them as frogs. Were the human mind limited to transcrib-

ing the singular facts of experience, as the radical empiricist maintains,

this type of knowledge-acquisition would remain a mystery; for on that

hypothesis, which denies Stage 2 and thus connes cognition to the level

ofempeiria, Sapphos knowledge that Atom has a heart could have comeabout only through the untimely demise of yet another hapless amphibian.

On the reading here proposed, then, Aristotle does after all defend the

claim in T3 that humans beings are psychologically capable of universal

knowledge; and how he defends this vital thesis in his solution to PKU

is by an inference to the best psychological explanation of our cognitive

behavior.

Moreover, on this reading, [B] would also contain reason for talkingthe talk of potential knowledge and for accepting the PK-Principle in T4.

For if we were interested in calling attention to the signicantly different

cognitive relations Sappho stands in towards the hearts of unknown frogs

before and after she inductively infers the universal truth that all frogs

have hearts, just as Aristotle was interested in noting this before-and-after

contrast in order to establish the existence of universal knowledge, then

we might well speak of the post-induction relation as a matter of Sappho,prior to her encounter with Atom, having potential knowledge that he has

a heart. By speaking in this fashion, we commit no error of logic; the only

objection could be that the new language seems a needless addition to our

epistemological vocabulary. But if youre Aristotle, with opponents giving

you trouble about knowing universal truths, you might well feel the need

to introduce an entry on potential knowledge into your philosophical

lexicon not only for the general purpose of epistemological clarity, but


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22 MARK GIFFORD

also in order to incorporate into your own view as much truth as there is

in the oppositions UIK-principle, which is what Aristotles dialectical or

endoxic style of philosophical argumentation requires, and which Aristotle

himself accomplishes through his adoption of the PK-Principle. Potential

knowledge, then, would represent a cognitive disposition to infer syllogis-

tically and to come to know explicitly any of the singular statements that

fall under a universal truth immediately after (eyw) we identify the sub-jects of those statements as members of the kind to which the universal

truth pertains. And since this disposition to know (to be distinguished from

dispositional knowledge) is acquired at the very same time as (ma) weinductively acquire knowledge of universal truths and, indeed, is actually

constituted by our explicit knowledge of those truths, potential knowledgeof singular statements and universal knowledge of the universal truth

under which those statements fall are merely two ways of describing one

and the same cognitive state. For this reason, then, universal knowledge

entails potential knowledge hence the PK-Principle.

Thus, if we accept the present reading of[B], Aristotle does effectively

discharge the argumentative obligations imposed upon him by his solu-

tion to PKU in [A]. And we can now also address the nal point that provedtroublesome for standard readings: the reason why Aristotle introduces

the Platonic doctrine of Recollection into his discussion of the paradox.

The remarks on Recollection are, I submit, no digressiuncula ; they do in

fact have a quite important role to play in Aristotles defense of his solu-

tion to PKU. For the reason Aristotle invokes Recollection in this context

is not so much to criticize that doctrine as to garner its support for the

crucial thesis in T3.To see this, considerrst what happens when we perform an inductive

inference and acquire universal knowledge. On Aristotles view, in ac-

quiring knowledge of a universal connection between two properties, we

obtain information that holds for all of the particulars of a given sort at all

times and in all places (see e.g. An. Post. A.31 87b28-33, where Aristotle

stresses that universal truths are disqualied as possible objects of percep-

tion by the fact that they are eternally and ubiquitously true). Our knowl-edge of a universal truth thus provides an epistemic surplus far exceeding

the comparatively meager information of experience. So where did this

surplus come from? Again, not from without, for experience gave us only

a radically nite string of singular statements. The epistemic surplus over

and above empeiria must then, at least in a sense, have come from within.

Its as though these super-experiential, universal truths were lurking in our

minds somewhere and we merely retrieved them from storage. That is, in


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acquiring knowledge of a universal truth by means of induction ([B.2b]),

its as though we were Recollecting which is precisely the force ofspernagnvrzontaw in [B.2c].17

Aristotle and Plato are of one mind on the point that human beings

have access to knowledge which transcends the mere recording of the sin-

gular truths of experience. For Plato these supersensible, universal truths

are innate and Recollected, while for Aristotle they are acquired from

experience via our native inferential capacity of induction. But the two

stand as one against any radical empiricist who, wishing to reduce epistm

to mere empeiria, would deny the thesis in T3 that human beings are cap-

able of universal knowledge. Now, while its true that Plato (for his own

unique reasons) would join hands with the radical empiricists on the ques-tion of our ability to arrive at universal truths from the world of sense

perception, nevertheless, the question ofhow we acquire universal knowl-

edge induction or Recollection? is not so important to the solution to

PKU and the overall project of B.21 as is the question of whether or not

17 In the developmental account of our knowledge ofrst principles that serves as

Aristotles empiricist response to Platonic innatism inAn. Post. B.19 (99b32-100a14),

notice that it is the point at which we acquire knowledge of universal truths that marks

the true climax of the story. It is at this penultimate stage not at the nal stage where

we attain knowledge of rst principles, which in this tale represents a mere denoue-

ment that Aristotle breaks out into language resounding with Platonism, celebrating

the entire universal that has come to rest in the soul, the one besides the many (tonw par t poll), whatever is one and the same in all those (100a6-8). From this it appears that Aristotle saw the crucial issue divid-

ing himself and Plato to be the question of the origin of our knowledge ofuniversaltruths. Once he has furnished an empiricist process to answer this question, the answer

to the question of whether our knowledge of rst principles is acquired or innate fol-

lows as a matter of course as is reected in the conclusion at 100b3-5, where

Aristotle rests his case for the role of induction in acquiring rst principles from sub-

ordinate universals on the part he had previously established for induction in leading

us to universal truths from the singular statements of perception.

Understood as I am suggesting, then, the passages on Recollection and innatism in

An. Pr. B.21 andAn. Post. B.19 lend some support (and precision) to the suggestion

in Scott (Recollection, esp. secs. I-II, passim) that the debate over innatism in the clas-

sical period represents a dispute about the source of higher rather than ordinary

forms of learning. In these passages at least, Aristotle views the Platonic challenge

not so much as calling for an account of how we work up the raw data of sensation

so that we can recognize particulars as instances of a certain kind; rather, as he sees

it, the issue is more one of explaining our ability to transcend the singular perceptual

judgements ofempeiria and apprehend the universal truths that constitute the eternal

structure of reality. (I cannot discuss here the merits of Aristotles conception of

Recollection, though I do think that Aristotle basically gets Platos theory right.)


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24 MARK GIFFORD

we possess universal knowledge. Thus, for the purposes of the epistemic

logic in B.21, Aristotle emphasizes that aspect of the doctrine of Recollec-

tion which is sound and merely notes his alternative, inductive account of

the source of universal knowledge. (InAn. Post. B.19 the priority of these

questions is reversed, leading Aristotle to adopt a less congenial attitude

towards Platonic rationalism.) Hence, by showing that he preserves what

truth there is in the endoxon of Recollection, Aristotle is able to co-

opt the legitimate considerations that led Plato to posit a kind of cogni-

tion that transcends the realm of uctuating particulars, and he thereby

strengthens his own position against radical empiricism on the reality of

universal knowledge. In the nal analysis, then, this is why Aristotle

invokes Plato in the discussion of PKU: to serve less as a philosophicalfoe than as a dialectical ally.

And, in that case, what we nd in the discussion of PKU atPrior Ana-

lytics 67a8-30 is an exemplary specimen of Aristotles dialectical approach

to philosophical problems, the method of solving puzzles while saving

phainomena which he famously describes in Nicomachean Ethics VII.1,

at the start of his discussion of another puzzling psychological condition

(1145b2-7). In our passage from B.21, Aristotle has addressed the notableviews on the question of whether human beings know universal truths

(that we are wholly incapable of universal knowledge and that we are

born knowing universal truths), and he has eliminated the difculties sur-

rounding this question (PKU and, implicitly, the unpalatable features of

Platonic innatism), while at the same time nding as much truth in the

endoxa as he could (by turning the specious form of his opponents UIK-

Principle into his own PK-Principle, T4, and by accepting with Plato thereality of universal knowledge, T3, without going all the way with Re-

collection). He therefore had every reason to proceed to his conclusion at

67a27-30, satised that his position had been sufciently established.

VII. Additional Support for the Proposed Reading

But given the importance of the passage on Recollection in B.21 and theheterodox interpretation I am recommending, further argumentation may

be in order.

First of all, consideration of the subsequent passage at 67a27-30, where

Aristotle wraps up his discussion of PKU, lends strong support to the pro-

posed reading of [B]:

[C](1)(a) Thus we yevromen the particulars by universal knowledge (t mn on

kaylou yevromen t n mrei), (b) but we dont know them by specic knowl-edge (t d oke& ok smen). . . .


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Notice rst that [C.1] is introduced by the inferential particle on, whichshows that Aristotle is drawing a conclusion from the discussion in [B].18

Now consider what that conclusion is: Aristotle says in [C.1a] that we

yevromen the particulars by virtue of universal knowledge. But what does

he mean here by yevren? The basic meaning ofyevren is to look at orto see, and Aristotle also uses the term by extension to indicate a num-

ber of cognitive processes: (1) to contemplate or to attend to some item of

knowledge already possessed, (2) to investigate or study some matter in

order to acquire knowledge, and (3) to actually acquire that knowledge,

to come to know some fact.19 So to which of these cognitive processes is

Aristotle referring in [C.1a]?

First of all, reference to contemplation is clearly out of the questionhere. If Aristotle has committed himself to anything in his solution to

PKU, it is to the view that universal knowledge doesnt impart awareness

of the particulars falling under the known universal truth; yet awareness

of the particulars is clearly implied by the idea of contemplating them.

To contemplate the particulars by universal knowledge, then, is non-

sense. Nor will a reference to study or investigation work in this context.

Aristotle has just nished informing us that universal knowledge enablesus to come to know particulars straight-away . The absence of any sort of

durational process of knowledge-acquisition vital to Aristotles point,

however understood is precisely what he wants to signal through the use

ofeyw in [B.3]. Thus there is simply no time available for the transpiringof anything that might justly be characterized as study or investigation .

And so a quick argument from elimination reveals that yevren here has

to be indicating the process of entering into the state of knowing. As aresult, Aristotles conclusion in [C.1a] must be understood as making a

18 In the OCT (followed by the Oxford Translation) Ross evidently takes mn onas resumptive, for he begins a new paragraph at the start of [C]; in doing so, how-

ever, he unhelpfully divides the continuous argument at 67a5-33 between two para-

graphs. Better would be simply to parenthesize the whole of [B] if, that is, one

subscribes to the digressiuncula hypothesis that is implicated in a resumptive reading

of the introductory particle to [C].19 This third use ofyevren is more common in the ingressive aorist, which indi-

cates entry into the state of knowing (see e.g. the occurrence of yevrsai at 81b2 inAristotles defense of empiricism in An. Post. A.18, where to come to know is the

only rendering suitable to the argumentative context; cf. Pol. I.5 1254a20-21, where

yevrsai is matched by katamayen). But as is shown by the well-known remark onthe acquisition ofrst principles atNE I.7 1098b3-4, even in its present aspectyevrencan indicate the process of coming to know. (Note, moreover, that in both An. Post.

A.18 and NE I.7 yevren is used specically in connection with the process of com-ing to know universal truths by means ofpagvg.)



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point about coming to know particulars by virtue of coming to know the

universal they instantiate; that is, his conclusion concerns the acquisition

of potential knowledge. But only on the reading that I am proposing does

Aristotle present an argument in [B] for a conclusion in [C] that is suit-

ably couched in terms of the acquisition of potential knowledge of sin-

gular statements; for only on this reading does pagvg in [B.2] indicatethe inferential process by which we acquire explicit knowledge of a uni-

versal truth, and thus, thanks to the PK-Principle, the inferential process

by which we acquire potential knowledge of the singular statements

falling under that universal truth. We see, then, that the conclusion drawn

in [C.1a], t kaylou yevromen t n mrei, and the original thesis stated

in [B.2b], ma t pagvg lambnein tn tn kat mrow pistmhn,separated as they are primarily by the clause in [B.3] that justies them,

are making precisely the same point.

Turning now to considerations of the style of argument employed in

[B], I should remark that the inference to the psychological reality of uni-

versal knowledge which I have attributed to Aristotle is a kind of argu-

ment that nds several parallels in the corpus. In situations relevantly

similar to those in which he nds himself in B.21, where questions aboutthe existence of certain epistemic or doxastic states arise, Aristotle will

often point to observable behavior in order to resolve the matter see

e.g. NE X.1 1172a34-b7 on believing that pleasure is bad; cf. NE VII.3

1147a18-24, where action is favored over utterance as an indication of the

belief-state of the akratic. Indeed, in such situations Aristotle will even

appeal to his opponents own behavior in attempting to undermine their

claims, arguing that their possession of the very mental state they disownprovides the best explanation for their behavior see e.g.Meta. G.4 1008b12-26 against Heracliteans who claim not to accept the Law of Noncontra-

diction (cf. G.3 1005b23-26, as well as An. Post. A.10 76a23-27) and G.51010b3-11 against skeptics who claim not to know, among other things,

whether or not they are dreaming (cf. G.6 1011a3-11).And so it is in another passage where the doubts about the reality of

universal knowledge are raised. Consider the way in which Aristotle criti-cizes an alternative solution to PKU inPosterior Analytics A.1 (71a30-b5).

The nameless sponsors of this proposed solution who evidently want to

keep to an exclusively extensional construction of knowledge-reports with

universal content-clauses (purely in behalf of a more parsimonious logi-

cal system, as it seems) take the paradox to be a reductio of knowledge-

reports with unquali edly universal content-clauses. Unlike the radical

empiricists of concern to Aristotle in B.21, however, they dont deny that

26 MARK GIFFORD


27/29

we can know universal truths of any sort; rather, they cleverly suggest

that we know qualied universal statements ascribed by knowledge-

reports taking the form: S knows that everything S knows to be A is B.

This proposal, if otherwise defensible, would certainly defuse the paradox;

for if we were to replace PKU.1with a knowledge-report in this form, we

would be explicitly barred from instantiating unknown particulars. Whats

more, if Sappho were psychologically equipped with the convoluted state

of knowing that everything she knows to be a frog has a heart, then, once

she came to know that Atom is a frog, she could instantiate this known

particular into the peculiar universal she knows, and she could thus infer

that Atom has a heart straight-away. So the alternative solution could

account for the very same cognitive performance that Aristotle appealedto in [B.3] in order to establish the psychological reality of universal

knowledge.

But although this argument to the best explanation of cognitive behav-

ior is neutralized by the alternative solution, Aristotle resorts to another

argument of the selfsame type:

Yet they know (sasi) precisely those things about which they have (xousi) ademonstration and about which they laid down their premises (labon), and theylaid down their premises (labon) not about everything which they happen toknow (edsin) to be a triangle or a number, but aboutevery triangle or numberwithout qualication; for no one lays down premises in this form whatyou

know to be a number or whatyou know to be a rectilineargure

but about everything . (71a34-b5)

As is shown by the recurrence of verbs in the third-person plural, Aristotle

counters the alternative solution by appeal to cognitive behavior whichhis opponents themselves engage in. He points to the fact that when his

opponents set about constructing mathematical proofs they, like everyone

else, lay down premises in unqualiedly universal form (and hence are en-

titled to conclusions in that form, as well). This premise-laying behavior,

Aristotle thinks, provides a better indication of the content of their cog-

nitive states than do the epistemic avowals they offer in a dialectical arena.

Those avowals notwithstanding, then, even his opponents themselves pos-sess knowledge of universal statements in unqualiedly universal form.

And, whatever one may think of its power, the character of Aristotles

argument is plain.20 Just as he did in [B] of B.21, Aristotle appeals to cog-

20 The argument has greater force than commentators give it credit for see e.g.

Barnes (Posterior, 89) and M. Mignucci,LArgomentazione dimonstrativa in Aristotele

(Padua, 1975), 15. Aristotle is not merely appealing to conventional scientic practice



28/29

nitive behavior in order to establish the existence of universal knowledge,

arguing that knowledge with propositional content of unqualiedly uni-

versal form provides the best psychological explanation for that cognitive

behavior.

Finally, that Aristotle defends his conception of universal-cum-potential

knowledge in B.21 by the specic kind of explanatory inference I have

suggested nds powerful corroboration in the strikingly similar argument

with which he rebuts the Megarian denial of cognitive potentialities:

The absurd consequences of this view21 are not hard to see. For, obviously, some-

one will not even be a house-builder unless hes actually building a house, since

to be a house-builder just is to have the potentiality to build a house; and likewise

for the other technai. Now . . . its impossible to possess these sorts oftechnaisave by learning and by having acquired them at some point . . ., whenever the builder stops building he will no longer possess the techn.

But if he then starts building again straight-away (eyw), how will he haveacquired the techn? (Meta. Y.3 1046b29-47a3)

Aristotle here argues for the existence of unactualized cognitive poten-

tialities by appealing to otherwise inexplicable facts about our cognitive

performance. The facts are these: people possessing a techn need not re-learn their cognitive skill each time they want to put it to use; rather, they

can actualize this cognitive potentiality straight-away (eyw), that is, with-out a refresher course or any other process of learning intervening between

their inactivity and the resumption of their work. Likewise, Sappho, by

virtue of the cognitive potentiality generated by her universal knowledge,

could come to know that Atom has a heart straight-away (eyw) with-

out dissection or any other process of investigation intervening betweenher perception of Atom as a frog and her syllogistic inference to the fact

of his having a heart. And when we recall that, for Aristotle, activating a

of laying down premises in unqualiedly universal form, but to the fact that, in unguarded

moments away from the dialectical lists, his opponents themselves conform to this

practice. And insofar as he regards the decisive issue raised by the alternative solu-

tion to be one belonging primarily to the psychology of cognition, his criticism can-

not be counted a misre. (Notice also that, although earlier in A.1 Aristotle had solved

PKU on conceptual grounds that is, by arguing logikw he here supports his solu-tion against opposition by arguing fusikw, just as we saw him doing in B.21.)

21 The Megarian thesis seems to depend on a slide from (1) S lacks the ability to

build-at-t to (2) At t, S lacks the ability to build, where t is a particular moment

at which the builderS is idle. If so, then Aristotle knows how to undermine this argu-

ment by arguing logikw (see Soph. El. 177b22-26). Here, though, in order to securethe real existence of unactualized potentiality, he feels the need to attack the Megarian

position by arguing fusikw.

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techn is typically a matter of subsuming particular facts under the uni-

versal rules that constitute the techn, the argument here in Y.3 emergesas a close associate of the argument for universal knowledge and its ac-

companying potential knowledge that I am ascribing to him in B.21.

Just as we can explain how the house-builder is able to begin constructing

immediately after a short break only by positing an enduring cognitive

potentiality that is constituted by his mastery of the universal rules of his

techn, so too we can explain how Sappho was able to come know that

Atom has a heart immediately after identifying him as a frog only by

positing a kind of potential knowledge that is constituted by her explicit

knowledge of a universal truth.

Conclusion

In this paper I have attempted to remedy an unfortunate defect in our

understanding of Aristotelian epistemology and its relationship to Platonic

rationalism by providing a detailed commentary on the important passage

atPrior Analytics B.21 67a8-30 that scholars have long overlooked or

misconstrued. In the course of my discussion I have s

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