Aristotle Meno

Aristotle on Platonic Recollection and the Paradox of Knowing Universals: "Prior Analytics"B.21 67a8-30Author(s): Mark GiffordSource: Phronesis, Vol. 44, No. 1 (Feb., 1999), pp. 1-29Published by: BRILLStable URL: http://www.jstor.org/stable/4182603 .

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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 in Prior Analytics B.21 where, in the course of solving a logical puzzle concerning our knowledge of universal statements, Aristotle offers his only explicit 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 reading I develop undermines the traditional view of the passage and lends fresh insight into Aristotle's conception of Plato's particular version of innatism; more specifically, when understood as I recommend, the passage strongly suggests that, on Aristotle's view, Plato's theory of Recollection is specifically designed to explain our apprehension of universal truths. The reading I propose also enables us to see how the allegedly non-standard use of the technical term rnEayon in B.21 can 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 Meno's 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 reflection 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 the rationalist 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 (E'nayyf). But although his empiricist response to the idea of innatism 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 XLIVII



2 MARK GIFFORD

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 Aristotle's conception of Plato's particular brand of rationalism as well as his attitude towards Plato's notorious account of knowledge-acquisition, this is a passage we will need to comprehend.

As things stand, however, Aristotle's treatment of Recollection in B.21, when not wholly ignored by scholars,' 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 Meno's Paradox found in the introductory chapter to the Posterior 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 Meno's 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 understanding 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 Aristotle's attempt to solve Meno's 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 something only half as ambitious as that: I will simply set aside the allegedly parallel passage in Posterior Analytics A. 1 - which is itself so crowded with difficulties as to be of dubious service, anyway - and attempt to understand 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 1998 ' The neglect this passage has suffered is well illustrated by Dominic Scott's recent

work on ancient innatism, Recollection and Experience: Plato's Theory of Learning and its Successors (Cambridge, 1995); for although Scott devotes considerable space to Aristotle's attitude towards innatism, he fails even to mention the explicit treatment of Recollection in An. Pr. B.21. The irony of this disregard is that the passage - one of the few places where Aristotle gives any indication of the specific form of innatism he saw himself up against - actually lends precious Aristotelian support to Scott's "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.



ARISTOTLE ON PLATONIC RECOLLECTION 3

through close commentary, when we situate Aristotle's 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 Aristotle's epistemology and its relationship to Platonic rationalism.

I. The Paradox of Knowing Universals

Let me begin by establishing the argumentative context in Prior Analytics B.21 within which Aristotle's 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 syllogistic 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 qualification, when those statements are transported into the psychological domain of knowledge-reports. The discussion 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 "Principle of 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 that c is A

Aristotle's strategy for exposing the fallaciousness of the UIK-Principle is to 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 67aI4, and "has 2R" abbre- viates the predicate of the angle-sum theorem for triangles, Aristotle's favorite illustration of an item of knowledge):

3 We cannot say who first fashioned the puzzle, but An. Post. A. 1 7 1a30-34 shows that "certain thinkers" advanced an alternative solution to Aristotle's - see further VII below.



4 MARK GIFFORD

1. Sappho knows that every triangle has 2R. [pI 2. t is a triangle. [p]

.-.3. Sappho knows that t has 2R. [1,2: UIK-Principle] 4. If S doesn't know that x exists,

then, for all F, S doesn't know that x is F. [pI 5. Sappho doesn't know that t exists. [p] 6. t has 2R, [p]

.-.7. Sappho doesn't know that t has 2R. [4,5,6]

.-.8. Sappho both knows and doesn't know that t has 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 doesn't know of the existence of certain subjects covered by the clause (PKU.5). In Aristotle's example, a person (whom I refer to as "Sappho") knows that every triangle has 2R but doesn't 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 doesn't know that t has 2R; and given the UIK-Principle, we can also infer the conclusion in PKU.3: that Sappho does know that t has 2R. Drawing both of these inferences, however, leaves us staring at the contradiction in PKU.8.

II. Aristotle's Solution to the Paradox of Knowing Universals

Aristotle offers his solution to PKU at 67al6-21 (call this "Section A"), the stretch of text which immediately precedes his treatment of Re- collection:

[AJ(1) <The puzzle fails> because "knowing that every triangle has 2R" is not univocal; (2)(a) rather, in one sense <it indicates knowing> by having universal knowledge, (b) and in another sense <knowing by having particular knowledge. (3)(a) In this way, then, he knows that <t> has 2R in the sense of <knowing> by universal knowledge, (b) but he doesn't know it in the sense of <knowing> by particular knowledge. (4) As a result, he will not occupy contrary states.

[A](1) rO yap 6i&8vxat nav TpiywVov Mxl 83o 6pOaci ox 6Xirxkoi5v icTtv, (2)(a) &XX TO gV Tv V 'v aOXoau ?Xetv atwlTv, (b) 6 & TO iv Kca zO' KaGtOV. (3)(a) oi3To pV oVv Xit m06 kou oloU TO F O"6t &Mo 4peal, (b) ( OE c Kas' trasxov oUa

o8F-v, (4) "T' oVX "4F?t Tatq ivavc'

This compact passage, in addition to containing Aristotle's solution to PKU, introduces the fundamental theses of the epistemic logic developed in B.21. It will reward close scrutiny.




In [A.1-2] Aristotle identifies the first premise of the puzzle as the source of the difficulty, 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 expressions, "universal knowledge" would refer to ordinary or explicit knowledge of a universal statement, while "particular knowledge" would indicate explicit knowledge of a singular statement. That PKU.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 of particular 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 of a string of singular statements - statements expressed by sentences of the form "x has 2R" 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.21 is that PKU.1 is ambiguous between ascriptions of universal and enumerative knowledge. And from this we see (ignoring the matter of existential import) that he is effectively noting the scope-ambiguity of the universal quantifier in knowledge-reports such as PKU.1:

(1) Sappho knows that (x)(x is a triangle -- x has 2R) (2) (x)(x is a triangle -> Sappho knows that x has 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 enumerative 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



6 MARK GIFFORD

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 doesn't 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 has 2R" 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 ouv, he draws two conclusions in the light of the distinction in [A.21: taking Sappho to have universal knowledge in the cognitive scenario under discussion, Aristotle infers in [A.3b] that she doesn't know that t has 2R "by particular knowledge", and in [A.3a] that she does know that t has 2R "by universal knowledge".

Now, the inference to [A.3b] presents no difficulty. In asserting that Sappho doesn't know that t has 2R by particular knowledge, Aristotle is simply 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 first 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 does after all know that t has 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 first of all that this fourth type of knowledge, knowing a singular statement by virtue of universal knowledge, cannot amount to having explicit knowledge of that singular statement; for that would be to have particular knowledge, and in the same breath Aristotle denies Sappho has that. Thus the form of knowledge ascribed in [A.3a] is going to have to be knowledge of a different order 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 Aristotle's actual solution to PKU "foists an utterly unnatural sense" on the knowledge-report in PKU.3.




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 singular statements (or subordinate universal statements) by virtue of knowing 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 &vvaiet with knowing evepyria; cf. Meta. A.1 982a21-23). But what are we to make of this idea of potential knowledge?

What we can say at least is that the inference drawn in [A.3a] betrays Aristotle's acceptance of a rule of inference for ascribing potential knowledge which turns out to be a variation on the specious form of the U1K- Principle: if you have explicit knowledge of a universal truth, then, by that very fact, you also have potential knowledge of each singular statement 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 introducing 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, Aristotle's 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 doesn't 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 Aristotle's 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:



8 MARK GIFFORD

(Ti) Knowledge-reports of the form "S knows that every B is A" are ambiguous 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 doesn't entail enumerative knowledge. (This represents Aristotle's 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.2 1, 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 puzzle, 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 universal content-clauses - opponents who would thus pose a threat not only to the epistemic logic of B.21 but to Aristotle's entire epistemology with its basic requirement that epist me 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 of episteme, namely, in the opening chapter to the Posterior Analytics. So let's consider which of the above statements in his solution to the puzzle Aristotle might feel the need to defend.

First of all, Ti 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 logical resources Aristotle does an adequate job of indicating the ambiguity in PKU.1 with his distinction between universal and enumerative knowledge. An opponent who continued to balk at Ti, then, would forfeit claim to linguistic competence and hence justly suffer the loss of dialectical standing.

Now, it might be thought that Aristotle's opponents would want him to justify his claim in T2, namely, his rejection of the UIK-Principle when




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 TI, Aristotle's dialectical 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 connection between two attributes. But in admitting that universal knowledge is an intelligible idea they would in fact be conceding T2, since the possibility of knowing a universal rule apart from knowledge of each of its instances is part of the very concept of universal knowledge. Aristotle's opponents would thus be faced with a dilemma: if they refuse to acknowledge the distinction between universal and enumerative knowledge in TI, then, as we've 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 Ti, then they would be forced by definitional necessity to concede the claim in T2 as well.5 We see, then, that Aristotle's rejection of the UIK-Principle in T2 requires no more defense than was needed for the conceptual distinction between universal and enumerative knowledge in Ti.

In conceding T2, however, Aristotle's opponents would not have to give up the field. For by granting T2 they have simply acknowledged that the possession of universal knowledge apart from enumerative knowledge 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 represent a real possibility - the human psuche must be capable, psychologically speaking, of entering into and occupying this state of universal knowledge. Thus Aristotle's opponents could grant what amounts to the conditional in T2 - if Sappho, say, has universal knowledge that every triangle has 2R, she need not have particular knowledge that t has 2R - but then dig in their heels and refuse to concede that the antecedent is ever satisfied. It would remain open to them to hold that the human mind is incapable of attaining to universal knowledge, being instead, like the souls of Aris- totelian beasts (NE VII.3 1 147b3-5 and Meta. A. 1 980b25 if.), 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,

' But see VII below for resistance to T2 from clever logicians hoping preserve a purely extensional system of inference rules.



10 MARK GIFFORD

in succinct Aristotelian terms, that there is no episte?met beyond empeiria.6 And given this dialectical possibility, if the effectively conditional statement 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 of T3 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 psychology. But the logical distinction in Tl can no more show the psychological reality of universal knowledge that every triangle has 2R than it can the psychological reality of enumerative knowledge that every triangle has 2R - a state whose real existence Aristotle himself denies. Thus it is not enough for Aristotle to look at the matter Xoytix, by simply marking a distinction in conceptual space; the real existence of universal knowledge must also be established quxmt-ce, by appeal to empirical fact.

And just as T3 remains in need of defense, so too does the independent 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 principle 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 that thought is nothing but perception (DA 111.3 427a21 ff.; cf. Meta. r.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, devil's advocates in an intramural dialectical moot, seeking an argument on this occasion for the reality of a psychological state so important for Aristotle's 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 [Al would have left them - something of which Aristotle himself was well aware (cf. e.g. Meta. B.4 999bl-4, where radical empiricism is mentioned as a possible response to the more familiar, metaphysical problem of universals).

I The talk of "potential knowledge" (as a first actuality) in passages such as DA II.5 417a21 ff. tends to conflate two notions that must be kept separate: (1) dispositional (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).



ARISTOTLE ON PLATONIC RECOLLECTION 1I1

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 first, 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 justification 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 that defense must be carried by his discussion of Recollection - a passage we are now in a position to examine.

IV. A Traditional View of Aristotle's Remarks on Recollection

Aristotle's 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. (Ooioi; 8&' xai o eV 'C Mivowl Myos, xTi h 11aNot; vRrst.

On the traditional view of this section, Aristotle announces in [B.1] that he plans to criticize Plato's theory of Recollection on grounds similar to those he has just advanced against PKU. But, standard translations notwithstanding, Aristotle doesn't actually assert this. As far as the language of [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 first glance - for what resemblance could Aristotle find 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 WMiep-clause in the subsequent sentence, which expands on the similarity noted 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 Aristotle's 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



12 MARK GIFFORD

though we were coming to know again. (3) For we know some things straight- away, e.g. that it has 2R, if we see that it is a triangle. (4) And likewise for other cases.

[BJ(2)(a) oUScagob ya&p augraxivEt ipoeicataiaOatO6 gcaK' EcLactov, (b) a&U' aFa Tm EInaywY( kaj36v tv Tiiv tv KaTa gpoq eictaTITiFv, (c) GoInFep &vacyvpiCovza;. (3) ?vta yap i65; (ogev, oIov 6-ri. &o 6pOai, i&v Nogev O6ri pitywvov. (4) 6goio) 8i KcX'I birt TV a&XXv.

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 conclusion 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 t has 2R at the same time as we are led to perform the syllogistic inference (&'ga mj icay i).9

Aristotle then suggests in [B.2c] that this syllogistic process of drawing out the logical consequences of acquired knowledge was mistaken by Plato for a process of recovering innate knowledge ((aIrCO p avaywpti-

ovtca;: "it's as though we were coming to know <these singular truths> for a second time").'0 Finally, in [B.3] he clarifies and illustrates the state-

8 Among commentators, W.D. Ross, Aristotle's Prior and Posterior Analytics (Oxford, 1949) 474, is nearest to the view I will sketch.

This is the reading of xnayo influentially advocated by Ross (Analytics, 476 and 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 ?inayoM', even more implausibly, to mark the process 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 of E'nay'yi in B.21; for the arguments in support of non-standard construals of the noun here rest almost entirely on the allegedly non-inductive use of the cognate verb E'naryEiv in A.1. For reasons mentioned at the start of this essay, I will not concern myself with such arguments on this occasion (but see further V below).

'0 avayvwpi ev and cognates are rare in Aristotle outside of their technical use in the 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 Aristotle's point on this timid construal. For this reason, and also because the iiirp-clause clearly furnishes a comparison with Platonic Recollection, avayvwpiCl~tv

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




ment in [B.21, 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 (eu66), that is, with no further mental act or empirical investigation intervening between the perceptual apprehension 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."

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 today take of the epideixis with the slave boy in Plato's Meno. What that epideixis 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 reasonable philosophical 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 Aristotle's remarks on Recollection. While this interpretation does give Aristotle a reasonable insight, I don't think this is quite the insight he wants to offer here. And to see why this interpretation cannot be sustained, let me note a few of the serious difficulties facing the preceding account of [B].

to know" (yvopi'v.v) "again" (ava-) - as one would do in Recollecting. The term here, then, serves as shorthand for avakxo&i3vrtv eintarfv "v npoTrepov JIXEv, the standard definition of 6vaiivmltc; in Plato and Aristotle - see Meno 85d, Phaedo 75e, and Mem. 2 451b3-6.

I 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 definitions, we can characterize innate knowledge in Plato, on Aristotle's view, as knowledge that is explicit but not conscious - see An. Post. B. 19 99b25-27 and Meta. A.9 993al-2.



14 MARK GIFFORD

On that account, Aristotle is supposed to be describing in [B.2], as he clearly is in [B.31, a process of knowledge-acquisition that occurs by means of a syllogistic inference. Yet the term he uses to refer to the inferential process he has in mind in [B.2] is not avkXoyiai6,"2 but E'nayy; and ?iay is Aristotle's technical term for marking not a syllogistic or deductive 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 E'nay to pick out an inferential process that is for Aristotle diametrically opposed to the standard, technical referent of the term.

Moreover, as a second problem for available readings of iC'ayoy in [B.2], it should be remarked that these readings frustrate our philosophical 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 significant exception is DA III.4 429a27-29; cf. IH.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 Posterior Analytics 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 fires at innatism in Metaphysics A.9 (992b34- 993a2) - which reiterates the objection of An. Post. B.19 (99b26-27) that a theory postulating innate, unconscious knowledge of high-level scientific truths presents us with an unacceptable view of the mind - follows immediately upon mention of his own account of knowledge-acquisition through induction (992b34). And, finally, we can also adduce here Aristotle's well-known remarks in Metaphysics M.4 (1078bl7-31) on Socrates' two claims to philosophical fame: his concern with defining (non-separated) universals and his employment of inductive arguments (inaKttcKoi X6yot). Coming at the start of a critical review of the original theory of Forms, Aristotle's mention of the latter activity might seem puzzling; for while Socrates' interest in defining universals clearly merits a central place in an

12 Nor, apropos of readings in which einayoi marks the process of appre- hending the minor, is the term used here aGa&c t;, as we would have expected were Aristotle referring to the process by which we recognize a perceptible triangle (aiatrbov tpiyovov, 67a14) as a triangle - see also NE VI.8 1142a25-30, and note Y'&ogev in [B.3].




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 separation, 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, Aristotle's almost reflexive response is: "No, induction." And so when he explicitly refers to the theory of Recollection in Prior Analytics B.21, and then immediately tosses the term ixayorr' into the 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 E'nay ', rudely fail to satisfy our strong philosophical expectations in this regard.

So much for the first two difficulties 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 Aristotle's 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 specifically, we must ask whether this reading of the text gives Aristotle any argument for the two 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 discussion 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 doesn't carry with it explicit knowledge of the singular statements that exemplify the known universal truth. To paraphrase [B.2a-b] on this reading, "<Even though we have explicit knowledge of the universal truth under which they fall>, we don't have explicit knowledge of the particulars before we encounter



16 MARK GIFFORD

them; rather, we gain explicit knowledge of them at the same time as the syllogistic inference."'3 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., if we have knowledge of a universal truth, it doesn't 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 find the idea of potential knowledge in [B.2b-3J, and hence would allow us to reconstruct an im- plicit argument for T4, Aristotle's 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 [Al. His main concern would be to make clear, not that explicit knowledge of a universal truth does give us potential knowledge of its singular instantiations (T4), but that it doesn't give us explicit knowledge of those instantiations (T2); and the latter claim hardly suffices to establish the former. Thus, on standard interpretations, Aristotle would offer no explicit justification for introducing the unusual PK-Principle into his solution to PKU and thereby into the system of epistemic logic developed in B.21 as a whole.

For these reasons, then, if we accept a traditional account of the discussion in [B], we seem forced to conclude that Aristotle has not explicitly and adequately justified the claims in T3 and T4, and hence that - to

'^ Notice that standard readings also seem to generate an untoward consequence for Aristotle's conception of Platonic Recollection: since [B.2] is supposed to be describing a process by which we acquire knowledge of singular statements, 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 possess, 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 Aristotle's behalf two arguments against the pre- natal acquisition of particular knowledge: (1) knowledge of particulars requires perception and hence the bodily organs of perception, and (2) many particulars would have come into existence after I was born. But the unbearable obviousness of those points speaks rather against the imputation, and thus against standard readings. Indeed, on Aristotle's own account, Plato separated universals in order to secure stable objects of knowledge owing to his belief that fluctuating particulars cannot be known at all (Meta. M.4 1078bl2-17; cf. A.6 987a32 ff.).




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 final problem I want to mention, a problem concerning the rationale behind Aristotle's 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 reasonable point against the epideixis in the Meno, there doesn't appear to be any pressing need for him to make that point in connection with PKU.'4 Since on standard readings Aristotle wouldn't be advancing the cause of his solution much beyond what was already said in [A], and since whatever advance there might be could have been achieved seemingly just as well without the mention of Plato, the treatment of Recollection has generally given the appearance of being a sort of mini-digression - a digressiuncula as Pacius called it - with Aristotle turning aside from the matter at hand to take a quick poke at Plato. But, other things being equal, a reading of [B] that makes this section an integral component in Aristotle's discussion 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 interpretations of [B], we can conclude that, in the four short sentences that com- prise Aristotle's discussion of Recollection, these readings generate at least four majors problems (see n. 13 for a fifth): (1) they construe Aristotle's technical term tiay y in rather improbable ways; (2) they disappoint our strong expectation that, given the use of inayom' in the context of remarks on Recollection, Aristotle would be opposing to innatism his own empiricist theory of induction; (3) in connection with his solution to PKU, they have Aristotle, as far his explicit argument goes, assuming the controver-

'4 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, however, and ask after which specific thesis in his solution he is concerned to support, we are led back to the result just mentioned as the third difficulty for traditional views: that Aristotle is unduly occupied with T2 to the disadvantage of T3 and T4.



18 MARK GIFFORD

sial and defending the obvious; and, finally, (4) they turn Aristotle's remarks 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 Meno's Paradox.

VI. An Alternative Interpretation of [B]

In view of the philological and philosophical difficulties to which a traditional interpretation of [B] gives rise, we should now be open to an alternative reading that can avoid them. Let's see what happens to Aristotle's discussion of Recollection, then, when we allow inayom' its standard reference to an inductive process of arriving at universal truths, thereby elim- inating the first two of the four major difficulties canvassed above.

Consider first how [B.2] comes out on this reading. Aristotle would be saying that we don't know the particulars beforehand ([B.2a]: o68aiio yap 01)laivat npoEnriataaOOatt ica0' EKaatov), that is, before the induction, or perhaps before we encounter particulars of the given type in experience; rather, we gain knowledge of the particulars at the very moment we perform the inductive inference ([B.2b]: kXX' i`Cga tn Exyo4y Xaivetv Trnv

t)v gcara gpo; ?uo"niv), namely, the inductive inference to the universal statement under which these particulars fall.

Far from being an impossible interpretation of eiaywyi here, this construal yields a reading of [B.2] that is actually quite promising; for an inductive inference, which furnishes explicit knowledge of a universal truth, could provide us with knowledge of a plurality of particulars or singular statements only if Aristotle were talking about the acquisition of potential knowledge of those statements."5 Thus, on the reading now

'5 It cannot be objected that in [B.2b] Aristotle is expressly referring to the acquisition of explicit knowledge of singular statements, for the nominalizing article immediately before icar&a gipo; shows that the phrase yv rdv Kcxa ju'po; etnicrtv is not being used as a name for particular knowledge. When he names the state of particular knowledge, Aristotle omits the internal article before the expressions ax0' 'EcKOcOV

and icczr& pEpO; - see 67al8-19, a20, and a30 - in which cases these expressions func- tion as attributive adjectives, whereas icaax pi'po; in [B.2b] plainly serves as a noun. Thus Aristotle is simply describing a way in which we acquire knowledge of particulars; 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 KcxT'a

pipo; shows that Aristotle was not especially interested here in conveying the idea of particular knowledge, something he could have done more simply and effectively without the extra article.)




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 singular statements falling under a universal truth at the very moment (&aia) we draw the inductive inference'6 - 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 knowledge (T3), [B.2b] on this reading contains both of the claims from his solution to PKU that are still in need of support.

Let's now see whether Aristotle offers any sort of justification for these claims. And, setting aside the comparison with Recollection in [B.2c] for the moment, let's first focus our attention on [B.3], which, introduced by the particle yap, 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 icayom to indicate the process by which we gain this knowledge had made it sufficiently 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 iiayoj. Knowledge of particulars acquired in this way could only be potential knowledge. Note further the (apparently non-generic) definite article before Exyoayf and the plural article before Kaccxt gipoq: Aristotle is saying we gain knowledge of a plurality of singular statements (rGv KcaLac gipo;) by a single cognitive act (rj, kayoy). It is only the inferential movement to the universal truth under which those statements fall - in this case, the angle-sum theorem - that could accomplish this remarkably prolific epistemic 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 certain moment, its antithesis in [B.2a] should be telling us that we lack potential knowledge 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 significance of the obser- vation in [B.2a] will be discussed shortly, but we can see already that the present reading 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 actually 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 particular diagramma.



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 singular statements falling under the universal truth?", Aristotle's response in [B.3] would be, "Because we come to know certain singular statements (E"vta) immediately after (e?0{5) we identify their subjects." But how exactly is 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 first she comes to the task merely with an ability to recognize frogs, but with no knowledge of their anatomy. She encounters Tom for the first time and correctly identifies him as a frog. At this point, she is in no position to infer that Tom has a heart. If she wishes to gain that information she has to do some dissecting first. (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.) So she proceeds to cut Tom up, and then does the same for a number of other frogs, thereby entering into the state of empeiria - 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 finds that there is good reason to think she has hit upon a universal fact of nature, and so she inductively infers and comes to have explicit 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 doesn't have to carve the poor devil up; on the basis of her universal knowledge she can infer that Atom has a heart straight-away (F-601) - no intervening process, such as dissection, need occur between her identification of Atom as a frog and her syllogistic acquisition of the knowledge 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 Sappho's cognitive behavior: at one point she had to dis- sect frogs in order to discover that each had a heart (Stage 1: [B.2a]),




while at a later point a simple movement of thought sufficed (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 Sappho's cognitive behavior?

The difference - and this is the point Aristotle is arguing in [B.2-31 - is best explained on the hypothesis that human beings actually do acquire and do possess knowledge of universal truths (Stage 2: [B.2b]). The earlier 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 simple syllogistic inferences; this is what accounts for her subsequent cognitive ability to know facts about previously unknown frogs euO{s, immediately after she identifies 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 confines cognition to the level of empeiria, Sappho's knowledge that Atom has a heart could have come about 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 talking the talk of potential knowledge and for accepting the PK-Principle in T4. For if we were interested in calling attention to the significantly 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 you're 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



22 MARK GIFFORD

also in order to incorporate into your own view as much truth as there is in the opposition's UIK-principle, which is what Aristotle's 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 (ei6i) we identify the subjects 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 (a`ga) we inductively acquire knowledge of universal truths and, indeed, is actually constituted by our explicit knowledge of those truths, potential knowledge of 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 solution to PKU in [A]. And we can now also address the final point that proved troublesome 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 Aristotle's defense of his solution 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, consider first what happens when we perform an inductive inference and acquire universal knowledge. On Aristotle's view, in acquiring 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 disqualified as possible objects of perception by the fact that they are eternally and ubiquitously true). Our knowledge 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 finite string of singular statements. The epistemic surplus over and above empeiria must then, at least in a sense, have comefrom within. It's as though these super-experiential, universal truths were lurking in our minds somewhere and we merely retrieved them from storage. That is, in




acquiring knowledge of a universal truth by means of induction ([B.2b]), it's as though we were Recollecting - which is precisely the force of Ot)onep

mvayvcopiCovx;a in [B.2c].'7 Aristotle and Plato are of one mind on the point that human beings

have access to knowledge which transcends the mere recording of the singular 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 episteme to mere empeiria, would deny the thesis in T3 that human beings are capable of universal knowledge. Now, while it's true that Plato (for his own unique reasons) would join hands with the radical empiricists on the question of our ability to arrive at universal truths from the world of sense perception, nevertheless, the question of how we acquire universal knowledge - 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

In the developmental account of our knowledge of first principles that serves as Aristotle's empiricist response to Platonic innatism in An. 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 final stage where we attain knowledge of first 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 (,roi ?vO; icapa xra lcokkXX), whatever is one and the same in all those <singular statements of empeiria>" (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 of universal truths. Once he has furnished an empiricist process to answer this question, the answer to the question of whether our knowledge of first principles is acquired or innate follows as a matter of course - as is reflected in the conclusion at 100b3-5, where Aristotle rests his case for the role of induction in acquiring first principles from subordinate 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 and An. Post. B.19 lend some support (and precision) to the suggestion in Scott (Recollection, esp. secs. I-H, 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 of empeiria and apprehend the universal truths that constitute the eternal structure of reality. (I cannot discuss here the merits of Aristotle's conception of Recollection, though I do think that Aristotle basically gets Plato's theory right.)



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. (In An. 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 cognition that transcends the realm of fluctuating particulars, and he thereby strengthens his own position against radical empiricism on the reality of universal knowledge. In the final analysis, then, this is why Aristotle invokes Plato in the discussion of PKU: to serve less as a philosophical foe than as a dialectical ally.

And, in that case, what we find in the discussion of PKU at Prior Ana- lytics 67a8-30 is an exemplary specimen of Aristotle's "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 (1 145b2-7). In our passage from B.2 1, Aristotle has addressed the notable views 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 difficulties sur- rounding this question (PKU and, implicitly, the unpalatable features of Platonic innatism), while at the same time finding 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 the reality 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, satisfied that his position had been sufficiently established.

VII. Additional Support for the Proposed Reading

But given the importance of the passage on Recollection in B.21 and the heterodox 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 proposed reading of [B]:

[CJ(1)(a) Thus we 8eXpOi?v the particulars by universal knowledge (4f gThV "OV

Kca0O64o- OFo pObgIEV lac ?V ?pet), (b) but we don't know them by specific knowledge (rj &? oiIcEi4 OV iFgv)....




Notice first that [C.1] is introduced by the inferential particle ovv, which shows that Aristotle is drawing a conclusion from the discussion in [B].'8 Now consider what that conclusion is: Aristotle says in [C.la] that we OrwpoiiEv the particulars by virtue of universal knowledge. But what does he mean here by OEtpetv? The basic meaning of 0ewpeiv is "to look at" or "to see", and Aristotle also uses the term by extension to indicate a number 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.'9 So to which of these cognitive processes is Aristotle referring in [C.la]?

First of all, reference to contemplation is clearly out of the question here. If Aristotle has committed himself to anything in his solution to PKU, it is to the view that universal knowledge doesn't 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 finished informing us that universal knowledge enables us to come to know particulars straight-away. The absence of any sort of durational process of knowledge-acquisition - vital to Aristotle's point, however understood - is precisely what he wants to signal through the use of r-k'3; in [B.31. Thus there is simply no time available for the transpiring of anything that might justly be characterized as study or investigation. And so a quick argument from elimination reveals that Orxpeiv here has to be indicating the process of entering into the state of knowing. As a result, Aristotle's conclusion in [C.la] must be understood as making a

8 In the OCT (followed by the Oxford Translation) Ross evidently takes psEv o"v as resumptive, for he begins a new paragraph at the start of [C]; in doing so, however, 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].

'9 This third use of Oeppeitv is more common in the ingressive aorist, which indicates entry into the state of knowing (see e.g. the occurrence of Oropifioat at 81b2 in Aristotle's defense of empiricism in An. Post. A.18, where "to come to know" is the only rendering suitable to the argumentative context; cf. Pol. 1.5 1254a20-21, where Oeopfiiat is matched by KaTaga6Eiv). But as is shown by the well-known remark on the acquisition of first principles at NE I.7 1098b3-4, even in its present aspect Oope?iv can indicate the process of coming to know. (Note, moreover, that in both An. Post. A.18 and NE 1.7 Oeepeiv is used specifically in connection with the process of coming to know universal truths by means of incay i.)



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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 termns of the acquisition of potential knowledge of singular statements; for only on this reading does ?Cay ' in [B.2] indicate the inferential process by which we acquire explicit knowledge of a universal 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.la], tm~ 1ca06Xov Oeopogv Ta Etv ?i'pct, and the original thesis stated in [B.2b1, (orugoaivet) Ta rn inaywyf Xag6vtv etv Xwv xaraT& gpoq ntaITi.riv,

separated as they are primarily by the clause in [B.3] that justifies 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 universal knowledge which I have attributed to Aristotle is a kind of argument that finds several parallels in the corpus. In situations relevantly similar to those in which he finds himself in B.21, where questions about the 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 1147al8-24, 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 disown provides the best explanation for their behavior - see e.g. Meta. r.4 1008b1 2- 26 against "Heracliteans" who claim not to accept the Law of Noncontra- diction (cf. r.3 1005b23-26, as well as An. Post. A.10 76a23-27) and r.5 1010b3-11 against skeptics who claim not to know, among other things, whether or not they are dreaming (cf. r.6 101 la3-1 1).

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 in Posterior Analytics A. 1 (71 a30-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 logical system, as it seems) - take the paradox to be a reductio of knowledge- reports with unqualifiedly universal content-clauses. Unlike the radical empiricists of concern to Aristotle in B.21, however, they don't deny that




we can know universal truths of any sort; rather, they cleverly suggest that we know qualified 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.1 with a knowledge-report in this form, we would be explicitly barred from instantiating unknown particulars. What's 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 appealed to in [B.31 in order to establish the psychological reality of universal knowledge.

But although this argument to the best explanation of cognitive behavior is neutralized by the alternative solution, Aristotle resorts to another argument of the selfsame type:

Yet they know (Zaccat) precisely those things about which they have (EXoOto) a demonstration and about which they laid down their premises (EXAaov), and they laid down their premises (?5Xaov) not about everything which they happen to know (ei&I'MV) to be a triangle or a number, but about every triangle or number without qualification; for no one lays down premises in this form - what you know to be a number <is F> or what you know to be a rectilinear figure <is G> - but <simply> about everything <of these kinds>. (7 1a34-b5)

As is shown by the recurrence of verbs in the third-person plural, Aristotle counters the alternative solution by appeal to cognitive behavior which his 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 unqualifiedly 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 cognitive states than do the epistemic avowals they offer in a dialectical arena. Those avowals notwithstanding, then, even his opponents themselves possess knowledge of universal statements in unqualifiedly universal form. And, whatever one may think of its power, the character of Aristotle's 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, L'Argomentazione dimonstrativa in Aristotele (Padua, 1975), 15. Aristotle is not merely appealing to conventional scientific practice



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nitive behavior in order to establish the existence of universal knowledge, arguing that knowledge with propositional content of unqualifiedly universal 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 specific kind of explanatory inference I have suggested finds powerful corroboration in the strikingly similar argument with which he rebuts the Megarian denial of cognitive potentialities:

The absurd consequences of this view2' are not hard to see. For, obviously, someone will not even be a house-builder unless he's 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 ... it's impossible to possess these sorts of technai save by learning and by having acquired them at some point. .., <and on their view> whenever the builder stops building he will no longer possess the techne. But if he then starts building again straight-away (6rXO(6), how will he have acquired the techne? (Meta. 0.3 1046b29-47a3)

Aristotle here argues for the existence of unactualized cognitive potentialities by appealing to otherwise inexplicable facts about our cognitive performance. The facts are these: people possessing a technel 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 (ei06%g), that is, without 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 (E6O{';) - without dissection or any other process of investigation intervening between her 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 unqualifiedly 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 solution to be one belonging primarily to the psychology of cognition, his criticism cannot be counted a misfire. (Notice also that, although earlier in A. I Aristotle had solved PKU on conceptual grounds - that is, by arguing XoyticK - he here supports his solution against opposition by arguing (puatoKix, 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 builder S is idle. If so, then Aristotle knows how to undermine this argument by arguing Xoy1ick (see Soph. El. 177b22-26). Here, though, in order to secure the real existence of unactualized potentiality, he feels the need to attack the Megarian position by arguing 9pY1KGiOq.




techne is typically a matter of subsuming particular facts under the universal rules that constitute the techne, the argument here in 0.3 emerges as 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 techne, 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 at Prior Analytics B.21 67a8-30 that scholars have long overlooked or misconstrued. In the course of my discussion I have shown, first, what Aristotle's solution to Paradox of Knowing Universals is and how he defends that solution; second, what his remarks on the theory of Recollec- tion amount to and why they appear where they do; and, finally, I have shown what meaning we need to attach to the allegedly non-standard occurrence of Finayyi in Prior Analytics B.21. If my arguments about this passage in B.21 have been successful, then, as I can only suggest in clos- ing, the present study also carries serious implications for our understanding of the purported doublet in Posterior Analytics A.1 where Aristotle showcases his only explicit attempt to solve Meno's Paradox.22

Virginia Polytechnic Institute and State University

22 My thanks to Paul Woodruff, Jacques Brunschwig, and Jim Hankinson for help- ful criticism of an early version of the argument.



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Aristotle Meno