‘Meno’s Paradox in Posterior Analytics 1.1’

July 15, 2017 | Autor: David Bronstein | Categoria: Epistemology, Aristotle, Ancient Greek Philosophy
Share Embed


Descrição do Produto

Created on 28 November 2009 at 22.10 hours page 115

M E N O ’ S PARA D OX IN PO S T E R I OR AN AL YTICS 1. 1 DAVI D BRO N ST EI N

M  ’s paradox is one of the most famous puzzles in the history of philosophy. Learning, or enquiry, is impossible, so the argument goes, for either you already know what you are searching for, in which case there is no need for you to search, or you do not already know, in which case there is no way for you to search. The solution Plato offers in the Meno is also widely known: learning consists in recollecting knowledge that the soul has acquired in a pre-incarnate state. Far less famous is Aristotle’s discussion of Meno’s paradox. This is at least partly because there is only one explicit reference to it in © David Bronstein  Earlier drafts of this paper were read at the meeting of the Western Canadian Philosophical Association in Winnipeg in , at the University of Oxford in , and at the APA in Chicago in . I would like to thank my commentators, Phil Corkum (at the WCPA) and Owen Goldin (at the APA), and the audience members for their helpful questions and comments on these occasions. Gail Fine generously provided me with written comments on an earlier draft and shared with me her forthcoming paper on the topic. This exchange did much to improve my interpretation. I would also like to thank Rachel Barney, David Charles, Lloyd Gerson, and Brad Inwood for their comments on previous drafts, and two anonymous readers for feedback on the penultimate version. Above all I owe a great debt to Jennifer Whiting for all her guidance and encouragement. I gratefully acknowledge the financial support of the Social Sciences and Humanities Research Council of Canada.  By ‘Meno’s paradox’ I mean the dilemma Socrates formulates at Meno   –, which amplifies a series of questions Meno raises at   –. The label is somewhat misleading because the words are put in Socrates’ mouth. But since Meno seems content with Socrates’ reformulation of his puzzle (  –), and since the label has entered popular philosophical discourse, I have opted to use it. Below I discuss some of the similarities and differences between Meno’s and Socrates’ formulations and their significance for Post. An. . . To avoid confusion, when I refer to Meno’s own formulation of the puzzle I do not use the expression ‘Meno’s paradox’.  This is a common interpretation of Plato’s solution (see e.g. N. P. White, ‘Inquiry’ [‘Inquiry’], in J. Day (ed.), Plato’s Meno in Focus [Focus] (London, ), –). However, some scholars disagree and downplay the extent to which recollection alone disarms the paradox (e.g. G. Fine, ‘Inquiry in the Meno’ [‘IM’], in R. Kraut (ed.), The Cambridge Companion to Plato (Cambridge, ), –; D. Scott, Plato’s Meno [PM] (Cambridge, ), –).

Created on 28 November 2009 at 22.10 hours page 116



David Bronstein

the whole extant Aristotelian corpus, in Posterior Analytics . , and it is a deeply enigmatic reference at that. For when Aristotle alludes to ‘the problem in the Meno’ at a it is not at all clear what argument he has in mind, and commentators are divided over how to interpret the reference. What are the argument’s premisses? What is its conclusion? How does Aristotle solve it? What is the connection to the puzzle in the Meno? My goal in this paper is to answer these questions. I shall argue that when Aristotle refers to Meno’s paradox in Post. An. .  he has in mind a specific version of the puzzle, one directed against the possibility of a specific type of learning—namely, a type of ‘simultaneous learning’ in which, starting from prior knowledge of a relevant universal, one learns at the same time that some object exists and that it has a certain property. Such learning, I shall suggest, is significantly different from the sort that provides the context for the version of Meno’s paradox in Plato’s dialogue. For that reason, readers who turn to Post. An. .  hoping to find the Aristotelian solution to the paradox from the Meno will be disappointed. There are several different versions of Meno’s paradox in the Posterior Analytics, only one of which is referred to and solved in its opening chapter—and it is not the version familiar from the Meno. At the same time, I shall try to show that there are important lessons for Aristotle’s theory of learning to be drawn from this chapter, as well as important lessons for our understanding of the differences and similarities between Plato’s and Aristotle’s accounts. My discussion will focus on the middle third of the chapter  For a range of different views see M. Ferejohn, ‘Meno’s Paradox and De Re Knowledge in Aristotle’s Theory of Demonstration’ [‘De Re’], History of Philosophy Quarterly,  (), –; G. Fine, ‘Aristotle and the Aporêma of the Meno’ [‘Aporêma’], in V. Harte, M. M. McCabe, R. W. Sharples, and A. Sheppard (eds.), Aristotle and the Stoics Reading Plato (London, ); S. LaBarge, ‘Aristotle on “Simultaneous Learning” in Posterior Analytics .  and Prior Analytics . ’ [‘Simultaneous’], Oxford Studies in Ancient Philosophy,  (), –; S. Mansion, ‘La signification de l’universel d’après An. Post. I ’ [‘Universel’], in E. Berti (ed.), Aristotle on Science: The Posterior Analytics [Science] (Padua, ), –. There is an interesting and unorthodox account of a closely related passage from Pr. An. .  in M. Gifford, ‘Aristotle on Platonic Recollection and the Paradox of Knowing Universals: Prior Analytics B.  a–’ [‘Paradox’], Phronesis,  (), –. Gifford’s interpretation is criticized in LaBarge, ‘Simultaneous’; see below, n. . I discuss the Prior Analytics passage below.  I owe the expression to LaBarge, ‘Simultaneous’.  For a different view see Ferejohn, ‘De Re’, , who argues that in Post. An. .  Aristotle intends to solve the same problem that Plato discusses in the Meno.

Created on 28 November 2009 at 22.10 hours page 117

Meno’s Paradox in Posterior Analytics . 



a

( –). Aristotle’s argument in this text unfolds in three stages. First he introduces an example of simultaneous learning (a– ). He then draws a distinction between two ways of knowing in order to explain it (‘knowing universally’ and ‘knowing without qualification’) (a–). And he concludes by suggesting that this distinction also solves a version of Meno’s paradox (a–). Commentators have had difficulty understanding the connection between the second and third stages of the argument. That is, it is not immediately clear how Aristotle’s distinction between knowing universally and without qualification is connected to his remark about Meno’s paradox in the lines that immediately follow. In addition, commentators have struggled to understand the connection between the puzzle Aristotle introduces and the one Plato presents in the Meno. My aim in this paper is to make these connections clear. . The prior knowledge requirement (a–) Post. An. .  begins with a general statement about one of the necessary conditions for teaching and learning—what I shall call ‘the prior knowledge requirement’. [] πᾶσα διδασκαλία καὶ πᾶσα µάθησις διανοητικὴ ἐκ προϋπαρχούσης γίνεται γνώσεως. (a–) All teaching and all intellectual learning come to be from pre-existing knowledge [γνώσεως].

This claim must play a significant role in any interpretation of  See M. Gifford, ‘Lexical Anomalies in the Introduction to the Posterior Analytics, Part ’ [‘Anomalies’], Oxford Studies in Ancient Philosophy,  (), –; LaBarge, ‘Simultaneous’.  See LaBarge, ‘Simultaneous’, whose interpretation I discuss below. Although I disagree with parts of his view, LaBarge’s paper is valuable for, among other things, its attempt to unpack the puzzle Aristotle introduces in Post. An. .  and explain its connection to the problem in the Meno. Such attempts are relatively rare. For example, in his commentary Ross simply quotes the relevant passage from the Meno, as though the connection to the Post. An. .  puzzle is obvious, which it is not (see Aristotle: Prior and Posterior Analytics [Analytics] (Oxford, ), ); Barnes has little more to say on the matter than Ross (see Aristotle: Posterior Analytics [Post. An.], nd edn. (Oxford, ), ); Pellegrin (Aristote: Seconds Analytiques (Paris, )) makes no comment at all. Aside from LaBarge, another notable exception is Fine, ‘Aporêma’.  Translations are my own, unless otherwise noted.

Created on 28 November 2009 at 22.10 hours page 118



David Bronstein

Meno’s paradox in Post. An. . , so we would do well to spend some time examining it. Gnōsis (‘knowledge’ in my rendering) is a difficult word to translate in this context. It is an extremely broad term in Aristotle, covering a wide range of cognitive states, from our perceptual awareness of contingent facts to our intellectual grasp (i.e. nous) of the necessary and eternal first principles. This would seem to tell against my translation, for it is not clear that we would be comfortable calling ‘knowledge’ everything Aristotle calls gnōsis. None the less, of the available catch-all terms ‘knowledge’ seems to me the most preferable. Although some of Aristotle’s uses of gnōsis may be inconsistent with some modern philosophical conceptions of knowledge, there is also significant overlap—enough, I think, to warrant my translation. So long as we do not cling too rigidly to a single conception of knowledge (as, for instance, justified true belief) we shall not be misled. Learning requires prior knowledge—but of what? The evidence in the Posterior Analytics suggests that there are two general possibilities. In some cases learning x requires (some sort of) prior knowledge of x itself; in other cases it requires prior knowledge of something else, say y, where x and y stand in some appropri For perception as a type of γνῶσις see e.g. Post. An. . , b–, GA . , a– (for additional references see M. F. Burnyeat, ‘Aristotle on Understanding Knowledge’ [‘Understanding’], in Berti (ed.), Science, – at ). For νοῦς as a type of γνῶσις see e.g. Post. An. . , b– and b. In the .  passages Aristotle speaks of γνῶσις of the principles (ἀρχῶν, b) and immediates (ἀµέσων, b) and later in the chapter he says that νοῦς is of the principles (b)—hence νοῦς is a type of γνῶσις.  For further discussion of this issue see the useful account in Fine, ‘Aporêma’, who translates γνῶσις as ‘cognition’.  Aristotle says that teaching (διδασκαλία) and learning (µάθησις) require prior knowledge, but he does not mean to restrict the requirement to learning brought about by teaching—i.e. didactic learning. For as we are about to see, he also recognizes the existence of learning that occurs in the absence of a teacher, and such non-didactic learning is also dependent on prior knowledge. (My discussion focuses on non-didactic learning.) In some such cases the learning occurs as the result of a successful ζήτησις (an enquiry, a search), and is in that sense identical to discovery (εὕρεσις) (learning and discovery are paired in DA . , b). In other cases, such as the one we shall examine, the learning is not preceded by a deliberate search. For ζήτησις and learning see Post. An. . – and . Aristotle does not use the terms µάθησις or µανθάνειν in these chapters. However, he often employs terms for searching (e.g. ζητοῦµεν, b, a, a, etc.), discovering (e.g. εὑρόντες, b; εὕρωµεν, a), and getting to know (e.g. γίνεται γνώριµον, b–; γνῶναι, b), some of which are synonymous with learning. ζήτησις, whether successful or not, requires prior knowledge. For example, in Post. An. . – and , Aristotle’s most extended discussion of ζήτησις, he says repeatedly that to enquire about something’s essence one must first know that the thing exists.

Created on 28 November 2009 at 22.10 hours page 119

Meno’s Paradox in Posterior Analytics . 





ate relation. In Post. An. .  Aristotle gives us an example of the second sort of learning (a–b). A novice astronomer is enquiring about eclipses. At the start of her search she does not know what the essence of eclipse is, nor does she know whether such a thing even exists. What she does know is that eclipse, if it exists, is the full and unobstructed moon’s inability to cast shadows on earth. Armed with this knowledge she discovers, first, that eclipse does in fact exist and, second, what its essence is: loss of light from the moon caused by screening by the earth. She learns by reasoning from effect to cause: the absence of shadows is explained by the moon’s loss of light, which in turn is explained by its being screened from the sun by the earth. She learns the essence starting from prior knowledge, not of the essence itself, but of something appropriately connected: one of its effects (which in this case is a per se accident). Post. An. .  seems to contain another example of this general type of learning: we acquire knowledge of first principles starting from prior perceptual knowledge of sensible particulars (b–b). In Post. An. .  by contrast, in a passage we are about to examine (a–), Aristotle gives an example of the type of learning that depends on (some sort of) prior knowledge of the object itself. A geometer knows the universal ‘all As are Bs’, but is ignorant that this particular A exists. He then goes on to learn that this A exists and that it is B. For Aristotle, although there is a clear way in which, prior to learning, the geometer does not know that this A is B (because he does not know that this A exists), there is another way in which he does know it (because he knows the relevant universal). In all cases of this general sort, Aristotle’s view is that prior to learning x one does not know x in the very same way one will know it as a result of learning it; rather, one knows it in a different way (Post.  I am grateful to Lesley Brown and Gail Fine for calling my attention to this issue. Brown discusses the distinction, as it applies to the Meno, in her ‘Review of Dominic Scott’s Plato’s Meno’, Philosophical Review,  (), – at ; Fine discusses it in relation to the Meno and Posterior Analytics in ‘Aporêma’.  Aristotle’s general view of learning—namely, that it proceeds from what is better known to us to what is better known by nature (e.g. Metaph. b–)—also lends support to the claim that one can learn x from prior knowledge of something other than x. For he gives no indication that the better known to us and by nature are the same. Indeed, he is explicit that they are different (Post. An. . , b–a).  Hence I disagree with Barnes’s interpretation (Post. An. , ), according to which learning x always proceeds from knowledge of something other than x. In the Post. An. .  example one has prior knowledge of x itself (as Barnes himself notes, Post. An. ). Arguably we find other such cases in Post. An. .  (see a–).

Created on 28 November 2009 at 22.10 hours page 120



David Bronstein b

An. . ,  –). But we must bear in mind, as the example in Post. An. .  urges us, that learning need not always proceed in this way. This is important because it may be one of the places where Aristotle departs from Plato’s theory of learning as recollection. If, as Plato seems to argue (Meno  –), learning x consists in recovering knowledge of x already in us, then learning x always depends on prior knowledge of x itself. It is well known that Aristotle attacks the antecedent; I am suggesting that in his application of the prior knowledge requirement he also attacks the consequent. In sum, the opening sentence of the Posterior Analytics announces a theme with which Aristotle will be concerned in various parts of the work, from its first chapter to its last, namely, the conditions under which learning is possible. One such condition is prior knowledge, and it will be important for him to show what type of knowledge is necessary in each case. Post. An. .  contains an extended discussion of this issue, within which falls the reference to Meno’s paradox.

. Simultaneous learning (a–) In the first part of the chapter (a–) Aristotle states that the prior knowledge requirement holds across a wide variety of intellectual disciplines. Then in the passage beginning at a he introduces an example of a peculiar sort of learning, which illustrates the requirement in an interesting way: [] [A] ἔστι δὲ γνωρίζειν τὰ µὲν πρότερον γνωρίσαντα, τῶν δὲ καὶ ἅµα λαµβάνοντα τὴν γνῶσιν, οἷον ὅσα τυγχάνει ὄντα ὑπὸ τὸ καθόλου οὗ ἔχει τὴν γνῶσιν. [B] ὅτι µὲν γὰρ πᾶν τρίγωνον ἔχει δυσὶν ὀρθαῖς ἴσας, προῄδει· ὅτι δὲ τόδε τὸ ἐν τῷ ἡµικυκλίῳ τρίγωνόν ἐστιν, ἅµα ἐπαγόµενος ἐγνώρισεν. (a–) [A] It is possible to come to know [γνωρίζειν] by knowing [γνωρίσαντα] some things beforehand and acquiring knowledge [γνῶσιν] of other things at the same time [as one another], for instance, whichever things happen to fall under a universal which one knows [γνῶσιν]. [B] For he knew beforehand [προῄδει] that every triangle has two right angles. But 

For arguments against this interpretation of Plato see Fine, ‘Aporêma’. See Post. An. . , especially b–.  My claim about the difference between Plato and Aristotle applies only to cases in which one learns some sort of universal and not to cases in which one learns a particular in the light of the relevant universal. For further discussion see below. 

Created on 28 November 2009 at 22.10 hours page 121

Meno’s Paradox in Posterior Analytics . 



he came to know [ἐγνώρισεν] that this thing in the semicircle is a triangle at the same time as he made the inference [ἐπαγόµενος] [that it has two right angles].

In [A] Aristotle states that it is possible to acquire simultaneously more than one item of knowledge starting from prior knowledge of other things. In the example in [B] he presents a syllogism whose major premiss is known beforehand and whose minor premiss and conclusion are learnt simultaneously: Every triangle has . This thing in the semicircle is a triangle. Therefore, this thing in the semicircle has . Aristotle seems to have in mind an expert geometer who possesses what he elsewhere calls ‘first actuality’ knowledge (i.e. acquired non-occurrent knowledge) of the universal truth that every triangle has . While working through some other geometrical problem involving a semicircle, the geometer realizes that the figure inscribed within it is a triangle; and at the very moment that he grasps this, he grasps the conclusion that it has . It is important to notice that the sort of learning Aristotle describes presupposes that one has acquired knowledge of a universal truth (every triangle has ). He does not explain in this passage how such knowledge is acquired in the first place. In addition, it  Some remarks on my translation of [B]: I take ἐγνώρισεν (‘he came to know’) at a to govern the second ὅτι clause—‘that this thing in the semicircle is a triangle’. This preserves the grammatical parallel with the first ὅτι clause at a–, which is governed by προῄδει (‘he knew beforehand’). This leaves ἐπαγόµενος (‘he made the inference’) at a to refer to the conclusion that ‘it has two right angles’, which we must supply from the context. There is a controversy about the meaning of ἐπαγόµενος in this passage (and in Pr. An. . , a, which I discuss below). My own view is that Aristotle uses it to denote the inference from a universal to a particular and not, as is sometimes the case, from particulars to a universal. For further discussion see Gifford, ‘Paradox’; LaBarge, ‘Simultaneous’; R. McKirahan, ‘Aristotelian Epagoge in Prior Analytics .  and Posterior Analytics . ’, Journal of the History of Philosophy,  (), –; and Ross, Analytics, . On ἐπαγωγή in general see Ross, Analytics, –; T. Engberg-Pedersen, ‘More on Aristotelian Epagoge’, Phronesis,  (), –; and D. W. Hamlyn, ‘Aristotelian Epagoge’, Phronesis,  (), –.   = interior angles equalling the sum of two right angles.  See DA .  and . .  Hence in my view the geometer’s learning is not preceded by a deliberate search aimed at discovering the sum of the figure’s angles. However, the example can be interpreted differently. I return to this issue below.  In Post. An. . – he suggests that having unqualified knowledge (ἐπιστήµη

Created on 28 November 2009 at 22.10 hours page 122



David Bronstein

is significant that in [A], where he gives a general description of the phenomenon of simultaneous learning, he uses gnōsis and one of its verbal cognates (gnōrizein) for the learner’s prior knowledge, terms that leave open whether the relevant knowledge is lower- or higher-level; however, in [B], where he gives a specific description of the case of learning he wishes to examine, he uses προῄδει (a form of eidenai), a term that is more likely than gnōsis or gnōrizein to indicate higher-level knowledge. This is confirmed in the next passage we shall examine (a–, passage [] below), where he uses ᾔδει (again a form of eidenai) interchangeably with forms of epistasthai (verbal cognate of epistēmē), a verb that clearly indicates higher-level knowledge. For these reasons it seems fair to say that in [B] Aristotle is depicting the learning of the expert geometer rather than the learning of the student of geometry, for it is the expert who will have higher-level knowledge (epistēmē) of the universal (every triangle has ), not the student. If this is right, then we are in much different territory from that of the Meno. In the Meno the sort of learning that is at issue is not the learning of those who already know the relevant universal truths but the learning of those who wish to. Socrates and Meno want to know the nature of virtue; the slave-boy (after some prodding) wants to ἁπλῶς) that every triangle has  requires a demonstrative proof starting from the essence of triangle. One knows without qualification that every triangle has  when one knows that triangles have  qua triangles, i.e. in virtue of their very nature as triangles. ‘Having ’ is a per se accident of triangle, and a per se accident is a property that is explained by the essence. It seems likely that Aristotle would also allow that one can acquire by other means (e.g. induction) knowledge that every triangle has , but in that case one would fall short of having unqualified knowledge, as defined in Post. An. . .  Cf. Burnyeat, ‘Understanding’, –. Burnyeat argues that ἐπίστασθαι in the Posterior Analytics should be translated ‘to understand’, in contrast to γνωρίζειν and γιγνώσκειν (verbal cognates of γνῶσις), which should be translated ‘to know’. While I am in broad agreement with much of Burnyeat’s account, I have decided to use ‘to know’ for ἐπίστασθαι (and ‘knowledge’ for ἐπιστήµη). For it is clear that at least in Post. An. .  Aristotle treats ἐπιστήµη as a type of γνῶσις, and so it seems best to use a single English word for both. To see this, consider the prior knowledge requirement. Aristotle says that learning requires prior γνῶσις. In a– (passage [] below) he illustrates his requirement with an example of someone who learns on the basis of prior ἐπιστήµη. But then surely ἐπιστήµη is a type of γνῶσις, otherwise the requirement is violated. If there is a distinction in Post. An. .  between ἐπιστήµη and γνῶσις (ἐπίστασθαι and γιγνώσκειν/γνωρίζειν), then it seems to me that it is a distinction in degree, not in kind. My talk in this paragraph of ‘higher-’ and ‘lower-level knowledge’ is intended to capture this. (Cf. Fine’s talk of ‘higher’ and ‘lower cognition’ in ‘Aporêma’.)  For a different view see Fine, ‘Aporêma’, to whose account I am indebted.

Created on 28 November 2009 at 22.10 hours page 123

Meno’s Paradox in Posterior Analytics . 



know how to double the area of a square. The paradox Plato introduces and the solution he goes on to propose occur in this context. This is why, as we approach Aristotle’s only explicit reference to Meno’s paradox, we should not be on the lookout for his solution to the problem from the Meno as it applies to the sort of learning discussed there, nor for his alternative to Platonic recollection. To borrow a distinction from the Nicomachean Ethics (which Aristotle himself borrowed from Plato), the Meno deals with the sort of learning that occurs on the way to first principles, Post. An. .  deals with the sort of learning that occurs on the way from them (a–b). None the less, I shall try to show that what the two sorts of learning have in common is that they are both vulnerable to structurally similar arguments threatening their very possibility. But first a brief word on the ‘syllogism’ Aristotle discusses in passage []. This is a syllogism only in a loose sense, since the minor term (‘this thing in the semicircle’) refers to a particular and so the minor premiss and conclusion do not conform to any of the four types of assertion Aristotle allows in his formal syllogistic theory (i.e. every A is B, some A is B, not every A is B, no A is B). The syllogism is also a demonstration (apodeixis) in a loose sense. A demonstration in the proper sense is a special sort of syllogism whose premisses meet a strict set of criteria, which include being explanatory of the conclusion and being indemonstrable (Post. An. . , b–). There is a sense in which the premisses of the syllogism in passage [] are explanatory: the figure in the semicircle has  because it is a triangle. Therefore, there is a sense in which this is a demonstration. However, the geometer who possesses this syllogism will know in the proper sense the explanation of the conclusion only if he knows the explanation of the major premiss (i.e. only 

For that we must wait until Post. An. . . This is confirmed by the conception of science Aristotle articulates in Post. An. . Very roughly, a science is a chain of interconnected demonstrations in which the conclusions of higher demonstrations serve as premisses in lower ones. In Post. An. . – Aristotle argues at length that such demonstrative chains must be finite— a science has both a top and a bottom, so to speak. At the top are demonstrations in the strict sense, which proceed from indemonstrable first principles to theorems (e.g. every triangle has ), which can in turn be used as premisses in demonstrations further down the chain. At the bottom are demonstrations that proceed from demonstrable premisses to conclusions whose minor terms are ultimate subjects of predication, i.e. subjects that have predicates but are not themselves predicated of anything else, e.g. this figure has —the conclusion of the syllogism in passage [B] (see Post. An. . , a–b). 

Created on 28 November 2009 at 22.10 hours page 124



David Bronstein

if he knows why every triangle has ). Since the major premiss admits of explanation, it is not indemonstrable. Therefore, this is not a demonstration in the strict sense. However, the fact that it is a demonstration even in a loose sense may explain why Aristotle, in the passage we are about to examine, is comfortable using forms of epistasthai for the geometer’s knowledge, even though the geometer’s grasp of the syllogism does not satisfy the requirements for ἐπιστήµη in the strict sense laid out in the following chapter (Post. An. . ). For Aristotle, epistēmē is the mental state we are in when we grasp a demonstration. A demonstration in a loose sense yields epistēmē only in a loose sense—but epistēmē none the less.

. Knowing universally vs. knowing without qualification (a–) In the following passage Aristotle discusses the sort of knowledge that the geometer possesses prior to his simultaneous learning: [] [A] πρὶν δ᾿ ἐπαχθῆναι ἢ λαβεῖν συλλογισµὸν τρόπον µέν τινα ἴσως ϕατέον ἐπίστασθαι, τρόπον δ᾿ ἄλλον οὔ. [B] ὃ γὰρ µὴ ᾔδει εἰ ἔστιν ἁπλῶς, τοῦτο πῶς ᾔδει ὅτι δύο ὀρθὰς ἔχει ἁπλῶς; [C] ἀλλὰ δῆλον ὡς ὡδὶ µὲν ἐπίσταται, ὅτι καθόλου ἐπίσταται, ἁπλῶς δ ᾿ οὐκ ἐπίσταται. (a–) [A] Before making the inference or grasping the syllogism, perhaps we ought to say that in one way he knows [ἐπίστασθαι], but in another way he does not. [B] For, if he did not know without qualification [ᾔδει . . . ἁπλῶς] whether [the triangle in the semicircle] exists, how did he know without qualification [ᾔδει . . . ἁπλῶς] that it has two right angles? [C] But it’s clear that [before grasping the syllogism] he knows [ἐπίσταται] [that it has two right angles] in this way: he knows [ἐπίσταται] [this] universally [καθόλου], but not without qualification [ἁπλῶς].

Aristotle’s question in this passage is this: what sort of prior knowledge of the syllogism’s conclusion (‘this thing in the semicircle has ’) must we attribute to the geometer in order to explain the fact that he learns the minor premiss (‘this thing in the semicircle is a triangle’) and conclusion simultaneously? Aristotle’s answer is succinctly stated in [C]: before the deduction the geometer knows 

For Aristotle’s account of how such knowledge is obtained, see n.  above. This is a partial answer to Gifford’s worries about uses of ἐπίστασθαι in Post. An. .  (see ‘Anomalies’). For further discussion see LaBarge, ‘Simultaneous’. 

Created on 28 November 2009 at 22.10 hours page 125

Meno’s Paradox in Posterior Analytics . 



‘universally’ (καθόλου), and not ‘without qualification’ (ἁπλῶς), that the figure in the semicircle has . [B] makes it clear that the syllogism’s conclusion is the object of the two ways of knowing distinguished in [C]. So as a preliminary interpretation of [] we can say this: knowing universally and knowing without qualification are two different ways of knowing that the figure in the semicircle has  (the conclusion). Let us examine these points in more detail. In what follows I am going to discuss the relationship between three different types of knowledge: (i) knowing without qualification a particular; (ii) knowing universally a particular; (iii) knowing a universal. Let us begin with the distinction between (i) and (ii). These are different ways of knowing a particular, e.g. that this triangle has . What they have in common is that in both cases one knows the relevant universal ‘every triangle has ’. When the geometer knows without qualification that the triangle in the semicircle has , he knows that the particular triangle exists and he brings this under the universal. When he knows universally that the triangle in the semicircle has , he does not know that the particular triangle exists (and so of course he does not bring it under the universal). Therefore, at least part of what distinguishes knowing without qualification and universally a particular is knowing that the particular exists. What about knowing a universal—for example, knowing that every triangle has ? We need to see how this is connected to the other two ways of knowing. The short answer, which is suggested by text [] and Prior Analytics .  (a–), is this: knowing a universal entails the other two. So if you know that every triangle has , then this entails (i) that you know without qualification that the triangles whose existence you are aware of have  (provided 

See also Post. An. . , b–, and Pr. An. . , a–. Some commentators (e.g. Ferejohn, ‘De Re’) miss this and assume that by ‘knowing universally’ Aristotle means ‘knowing that every triangle has ’ and that by ‘knowing without qualification’ he means ‘knowing that the figure in the semicircle has ’. In other words, these commentators see the distinction between knowing universally and without qualification as the distinction between knowing the major premiss and knowing the conclusion, and not, as I am urging, as a distinction between two ways of knowing the conclusion. 

Created on 28 November 2009 at 22.10 hours page 126



David Bronstein

you have brought them under the universal) and (ii) that you know universally that the triangles whose existence you are not aware of have . In fact, Aristotle suggests elsewhere that in the cases where you do not know that the particular triangle exists, you know potentially that it has . So knowing universally a particular means knowing it potentially. And in the case we have been examining the geometer’s potential knowledge of the conclusion is immediately actualized when he sees that the figure in front of him is a triangle. It is clear, then, why in passages []–[] the geometer’s prior knowledge of the conclusion falls short of unqualified knowledge: he does not know that the triangle in the semicircle exists and so he cannot know without qualification that it has . But this is not the whole story. For it is also obvious that the geometer’s knowledge exceeds what we might call ‘unqualified ignorance’. Consider a beginning student in geometry, such as the slave-boy in the Meno, who is barely familiar with triangles and who does not know the universal truth ‘every triangle has ’. Like the geometer, the slave-boy does not know that the figure in the semicircle has —that is, like the geometer, the slave-boy is ignorant of the syllogism’s conclusion. None the less, the geometer and the slave-boy’s cognitive state with respect to the conclusion are crucially different. The slave-boy’s ignorance is more pronounced; or, put differently, the geometer is closer to knowing the conclusion than the slave-boy is. The phenomenon of simultaneous learning makes this clear. Both the geometer and the slave-boy can learn that the figure in the semicircle has , but their learning will be significantly different. Since the slaveboy lacks knowledge of the universal ‘every triangle has ’, learning that this particular triangle has  will require a long process of discursive reasoning, probably under the guidance of an instructor 

See Gifford, ‘Paradox’, –, and Mansion, ‘Universel’, –. See Post. An. . , a–: οἷον εἴ τις οἶδεν ὅτι πᾶν τρίγωνον δυσὶν ὀρθαῖς, οἶδέ πως καὶ τὸ ἰσοσκελὲς ὅτι δύο ὀρθαῖς, δυνάµει, καὶ εἰ µὴ οἶδε τὸ ἰσοσκελὲς ὅτι τρίγωνον (‘if someone knows that every triangle has two right angles, he also knows in a way that the isosceles has two right angles—potentially—even if he does not know that the isosceles is a triangle’). Here Aristotle says that knowing the universal ‘every triangle has ’ entails potential knowledge of specific types (e.g. isosceles) that fall within the general type (triangle). This is not the same thing as claiming that knowing the universal entails potential knowledge of its particular instances. But the two claims are closely connected. Aristotle’s general idea seems to be that if you know that every triangle has , you know that every triangle has —every type and every token, even those types and tokens whose existence you are not aware of. 

Created on 28 November 2009 at 22.10 hours page 127

Meno’s Paradox in Posterior Analytics . 



(Socrates?). Given the slave-boy’s lack of geometrical knowledge, we can expect that there will be a significant temporal gap between his learning that the figure in the semicircle is a triangle and that it has . This is what distinguishes the slave-boy’s learning from the geometer’s, for the two occurrences of ‘simultaneously’ (ἅµα) in passage [] make it very clear that there is no temporal gap (or at most a very small one) between the geometer’s grasp of the two propositions. The difference between the geometer’s and the slave-boy’s learning is important, for it allows us to determine more precisely the geometer’s epistemic state prior to his learning. The geometer’s prior knowledge of the conclusion falls between (i) his own unqualified knowledge that particular triangles whose existence he is aware of have  and (ii) the slave-boy’s unqualified ignorance that the figure in the semicircle has . The geometer does not know the minor premiss, and so (like the slave-boy) he does not have unqualified knowledge of the conclusion; but he knows the major premiss, and so (unlike the slave-boy) he far exceeds unqualified ignorance. This is the upshot of [C]: knowing universally (or potentially) is an intermediate cognitive state that falls between unqualified knowledge and ignorance (though it lies much closer to unqualified knowledge). And as we are about to see, Aristotle thinks that if you deny this, you will be left with a version of Meno’s paradox.

. Meno’s paradox (a–) In the lines immediately following passage [], Aristotle rather abruptly introduces Meno’s paradox: [] εἰ δὲ µή, τὸ ἐν τῷ Μένωνι ἀπόρηµα συµβήσεται· ἢ γὰρ οὐδὲν µαθήσεται ἢ ἃ οἶδεν. (a–) But if not, the problem in the Meno will come about; for one will learn either [ἢ] nothing or [ἢ] what one [already] knows [οἶδεν].

At this point it will be helpful to recall the passage from Plato’s Meno to which Aristotle refers: [] [A] καὶ τίνα τρόπον ζητήσεις, ὦ Σώκρατες, τοῦτο ὃ µὴ οἶσθα τὸ παράπαν ὅτι ἐστίν; ποῖον γὰρ ὧν οὐκ οἶσθα προθέµενος ζητήσεις; ἢ εἰ καὶ ὅτι µάλιστα ἐντύχοις αὐτῷ, πῶς εἴσῃ ὅτι τοῦτό ἐστιν ὃ σὺ οὐκ ᾔδησθα;

Created on 28 November 2009 at 22.10 hours page 128



David Bronstein

[B] µανθάνω οἷον βούλει λέγειν, ὦ Μένων. ὁρᾷς τοῦτον ὡς ἐριστικὸν λόγον κατάγεις, ὡς οὐκ ἄρα ἔστιν ζητεῖν ἀνθρώπῳ οὔτε ὃ οἶδε οὔτε ὃ µὴ οἶδε; οὔτε γὰρ ἂν ὅ γε οἶδεν ζητοῖ—οἶδεν γάρ, καὶ οὐδὲν δεῖ τῷ γε τοιούτῳ ζητήσεως— οὔτε ὃ µὴ οἶδεν—οὐδὲ γὰρ οἶδεν ὅτι ζητήσει. (Meno   – ) [A]    . How are you going to search for this, Socrates, when you do not at all know what it is? Which of the things you do not know will you set up as the target for your search? And even if you do actually come across it, how will you know that it is that thing which you do not know? [B]  . I understand what you mean, Meno. Do you see what an eristic argument you are bringing down on us—how it is impossible for a person to search either for what he knows or for what he does not know? He could not search for what he knows, for he knows it and no one in that condition needs to search; on the other hand he could not search for what he does not know, for he will not even know what to search for.

These famous and much-disputed lines raise a host of questions, some of which I shall return to below. For now we can note that there are good prima facie grounds for connecting passages [] and []. Aristotle makes explicit reference to Plato’s dialogue and to a puzzle in it (‘the ἀπόρηµα in the Meno’), and the phrase ‘one will learn either nothing or what one [already] knows [ἢ . . . οὐδὲν . . . ἢ ἃ οἶδεν]’ is close to Socrates’ statement that ‘it is impossible for a person to search either for what he knows or for what he does not know [οὔτε ὃ οἶδε οὔτε ὃ µὴ οἶδε]’. The occurrence of ‘either . . . or’ constructions in both statements suggests that Aristotle saw himself as introducing a dilemma of the sort he found articulated in Socrates’ formulation of the puzzle Meno raises in [A]. There are important differences between what Aristotle and Socrates say—Aristotle worries about learning, Socrates about enquiry (see below); Aristotle worries about reasoning from universals, Socrates about reasoning to them (see above)—but the similarities seem sufficient to warrant Aristotle’s reference. In examining passage [], therefore, we should be on the lookout for a dilemma corresponding to the following argument, which summarizes Socrates’ statement of the puzzle: (i) Either one knows x or one does not know x. 

Day’s translation (Focus, ), altered slightly. For additional discussion see A. Nehemas, ‘Meno’s Paradox and Socrates as a Teacher’, in Day (ed.), Focus, –; Fine, ‘IM’; Scott, PM; and White, ‘Inquiry’. 

Created on 28 November 2009 at 22.10 hours page 129

Meno’s Paradox in Posterior Analytics . 



(ii) If one knows x, one cannot search for x. (iii) If one does not know x, one cannot search for x. (iv) Therefore, one cannot search for x. Let us turn to passage []. It presents several difficulties. For one thing, it is hard to see what chain of reasoning moves us from the distinction in [] between knowing universally and without qualification to the reference to Meno’s paradox in []. Aristotle indicates that denying the distinction leads to a version of the puzzle. But how? Another difficulty is this. Evidently Aristotle wants to connect his puzzle to Plato’s, and some of the affinities between them are, I have suggested, relatively clear. However, it is not obvious exactly how the two puzzles are supposed to correspond. There are two separate issues here. First, as I noted just above, the Meno puzzle is concerned primarily with enquiry (zētēsis), with how one begins searching for something, whereas Aristotle’s puzzle is concerned with learning (mathēsis), with how one finishes acquiring knowledge of it. The gap seems especially wide given that in Aristotle’s example, as I have interpreted it, the geometer’s learning is not preceded by a deliberate search for the thing he learns (‘the figure has ’) but occurs spontaneously in the course of his investigation of a different geometrical problem. What should we make of this apparent discrepancy? Second, it is difficult to tease out of Aristotle’s very compressed sentence a genuine, two-horned dilemma such as we find in [B]. In fact one recent commentator, Scott LaBarge, has argued that the puzzle Aristotle has in mind in passage [] is ‘only an apparent dilemma’ with only a ‘vague resemblance’ to the puzzle in the Meno. According to LaBarge, Aristotle’s puzzle is only concerned with the possibility of learning x when one already knows it. If LaBarge is right, then Aristotle has left out the second horn: the difficulty of learning x when one does not know it. So in the second part of passage [] Aristotle does not present two genuine possibilities (‘one will learn either nothing or  Even if this aspect of my interpretation is mistaken and the geometer does learn as the result of a deliberate search, it would still be the case that Aristotle’s puzzle focuses on the last stage of enquiry whereas Plato’s puzzle focuses primarily on the first.  My thanks to an anonymous reader for comments on this issue.  ‘Simultaneous’, .  LaBarge goes so far as to say that ‘[t]here really is no way to find two distinct problems in Aristotle’s treatment of the paradox to correspond to the two problems that Plato’s version of the dilemma produced’ (‘Simultaneous’, ).

Created on 28 November 2009 at 22.10 hours page 130



David Bronstein

what one [already] knows’, in my translation) but a single possibility expressed in two ways (‘“[he] learns nothing, since he learns nothing he does not already know”’ in LaBarge’s paraphrase). The problem for LaBarge’s interpretation is that we have in our text an ‘either . . . or’ (ἤ . . . ἤ) construction, which clearly suggests two possibilities, not one. In other words, the sentence points strongly in the direction of a dilemma of the sort set out above. The difficulty is, how do we get the second horn? I shall now argue for an interpretation of passage [] that solves these difficulties. I shall begin by showing how both horns of Aristotle’s dilemma arise and how there is a coherent train of thought from passages [] to []. I shall then turn to the differences between the Posterior Analytics and Meno puzzles. The dilemma’s first horn is easy enough to understand. Passage [] begins with a conditional statement whose antecedent denies what Aristotle has said in the previous passage, []—namely, that there is a difference between knowing universally and without qualification. If there is no such difference, then one possibility is that before learning the geometer already knows without qualification the conclusion. But in that case he learns what he knows without qualification, and so he does not learn at all. It is absurd, Aristotle goes on to say, to hold that prior to learning one must know something in the very way one is meant to learn it (b–). In effect, the first horn is generated by denying that there is such a thing as knowing universally as distinct from knowing without qualification—by denying, in other words, that there are different ways of knowing something, that knowledge, as we might say, comes in degrees. The second horn is harder to work out, but I think it can become clear once we remind ourselves of the context of the passage and introduce two implicit assumptions. Aristotle is discussing, by way of illustration, his principle that all learning requires prior knowledge (gnōsis). Let us say (as the antecedent of the conditional in [] says) that there is no distinction between knowing universally and without qualification, and let us say (as passage [] says) that the geometer lacks unqualified knowledge of the conclusion. In that case, learning will be possible only if the geometer has some other 

‘Simultaneous’, . A single ἤ in Greek could be read as a correction or explanation of what immediately precedes, in which case LaBarge’s interpretation would be plausible. However, I do not see how this reading is possible with ἤ . . . ἤ. 

Created on 28 November 2009 at 22.10 hours page 131

Meno’s Paradox in Posterior Analytics . 



type of knowledge, one that allows him to make the inference. Here we encounter the argument’s first implicit assumption: the geometer’s prior knowledge must consist in (some sort of) knowledge of the conclusion—i.e. of the very thing he is about to learn. At first glance this assumption is puzzling. We might think that the geometer could be completely ignorant of the conclusion and still learn it. For he might know something else on the basis of which he could learn the conclusion, provided the two are connected in some appropriate way. After all, we know from the example in Post. An. .  discussed above that Aristotle thinks we sometimes learn in this way. However, in the context of Post. An. .  the assumption is a reasonable one. Recall that the explanandum for which Aristotle’s concept of knowing universally is the explanans is not merely the fact that the geometer learns that the figure has  (even the slaveboy is capable of this); rather, the explanandum is the fact that he learns this immediately after recognizing that the figure is a triangle (an ability characteristic of an expert). Seen in this light, Aristotle’s view that learning the syllogism’s conclusion requires (some sort of) prior knowledge of it (and not of something else) makes good sense. So far three facts about the geometer’s pre-learning epistemic state are in play: (a) there is no distinction between knowing universally and without qualification (passage []), and (b) the geometer lacks unqualified knowledge of the conclusion (passage []), but (c) he requires (some sort of) prior knowledge of it (first assumption). Now consider a second assumption: suppose that there is no other knowledge of the conclusion apart from unqualified knowledge—that there is no other gnōsis apart from unqualified epistēmē. This is what denying the distinction between knowing universally and without qualification might be thought to amount to. If there is no such distinction, then either one has unqualified knowledge or (we now assume) one has no knowledge at all. Here we find the dilemma’s missing second horn: learning will now be impossible. Prior to learning the geometer will not have any gnōsis at all of the conclusion—he will be in a cognitive blank with respect to it. For he lacks unqualified knowledge of the conclusion, and there is no other knowledge available to him. Since learning (in our  It is legitimate to infer ‘cognitive blank’ from ‘no γνῶσις at all’ because γνῶσις, as I discussed above, covers such a broad range of cognitive states, from the very lowest (perception) to the very highest (νοῦς).

Created on 28 November 2009 at 22.10 hours page 132



David Bronstein

example) requires prior gnōsis of the conclusion, and since ex hypothesi the geometer has none, he learns nothing. I suggest that this second assumption—that unqualified ignorance is the only alternative to unqualified knowledge, that knowledge is all-or-nothing in this extreme sense—is the key to understanding Aristotle’s puzzle. Both horns of the dilemma are generated by denying not only the distinction between knowing universally and without qualification but the general claim that knowledge (epistēmē in particular and gnōsis in general) comes in degrees, that there are intermediate cognitive states between unqualified knowledge and unqualified ignorance. For in Aristotle’s view such states are necessary for explaining different types of learning. The reference to Meno’s paradox is intended to call attention to—and warn against—the extreme all-or-nothing view of knowledge. Here, then, is the puzzle: () Either the geometer knows without qualification the conclusion or he does not at all know it. () If the geometer knows without qualification the conclusion, he cannot learn it (he learns what he already knows). () If the geometer does not at all know the conclusion, he cannot learn it (he learns nothing). () Therefore, the geometer cannot learn the conclusion—he learns either nothing or what he already knows. Aristotle’s solution is that prior to learning the geometer knows universally the conclusion and not without qualification. This means that he accepts premisses () and () but denies premiss (): there is an intermediate cognitive state that satisfies the prior knowledge requirement and makes learning possible. In other words, his assertion that there are different ways of knowing the conclusion prior to learning it is best understood, in my view, as an attempt to delineate cognitive space between unqualified knowledge and ignorance. Aristotle’s immediate aim in introducing Meno’s paradox is to highlight the importance of distinguishing between different types of epistēmē. But if my interpretation is right, the puzzle also serves a broader philosophical purpose. Aristotle says that all learning requires prior gnōsis. The key assumption implicit in the puzzle is that all gnōsis is unqualified epistēmē. This assumption, if true, would have disastrous consequences for Aristotle’s requirement. It would

Created on 28 November 2009 at 22.10 hours page 133

Meno’s Paradox in Posterior Analytics . 



mean that in all cases where learning x requires (some sort of) prior knowledge of x, learning x would be impossible. For if the assumption were true, the all-or-nothing conception of knowledge—i.e. premiss ()—would immediately follow. And once premiss () is in place we have all the ingredients for Meno’s paradox: either one knows without qualification x or one does not at all know it, and either way learning x is impossible. Seen in the context of his prior knowledge requirement, we can understand Aristotle’s reference to Meno’s paradox as intended to convey important philosophical lessons about the relationship between gnōsis and epistēmē and the nature of knowledge in general. The principal lesson is that while unqualified epistēmē may be (one of) the highest forms of gnōsis, it is not the only form. My interpretation of Aristotle’s reference to Meno’s paradox solves two of the problems I raised above. First, we have a genuine dilemma, which has a clear resemblance to the puzzle in Plato’s Meno (although I shall have more to say about this below). Second, there is a coherent train of thought from passage [] to passage []. Aristotle begins with the interesting phenomenon of simultaneous learning, and he wonders: how is it that the geometer can reach the conclusion so quickly? The answer is: in a way, the geometer already knew it. He did not know it in the very same way in which he learns it—that would be absurd (b–); but he did know it in a different way: he knew it universally (or potentially). And all it takes for the geometer’s potential knowledge to be actualized is his seeing that there is a triangle in front of him. Hence, prior to learning, in one way the geometer does not already know the conclusion, which makes genuine learning possible; but in another way he does already know it, which makes simultaneous learning possible. Aristotle takes this to be a good explanation of the phenomenon. When he refers to Meno’s paradox he suggests that if you deny this explanation, you will have a harder time making sense of it.

. Meno and Post. An. . : similarities and differences Let us return to a difficulty I raised above—namely, that while Aristotle’s puzzle concerns learning, the puzzle in the Meno concerns  νοῦς is also a form of γνῶσις, and it is higher than unqualified ἐπιστήµη (Post. An. . , b–).

Created on 28 November 2009 at 22.10 hours page 134



David Bronstein

enquiry. One way to approach this issue is to see what Aristotle takes from the relevant part of Plato’s text, passage []. I contend that a close look at the passage reveals that the discrepancy is not as wide as it might at first seem. We have already seen that Aristotle adopts the dilemmatic structure from Socrates’ formulation. Here are four additional points of connection: (a) Meno asks three questions, the first two of which correspond closely to the second horn of the Post. An. .  dilemma, as I have interpreted it (namely, that it is impossible to learn the conclusion when one is totally ignorant of it). Meno first asks how he will search for what he does not at all know (  –). The qualifier ‘at all’ (τὸ παράπαν) is important, for it indicates a lack of knowledge in a very strong sense—indeed, a state of total ignorance. This becomes clear in Meno’s second question, when he asks: ‘Which of the things you do not know will you set up as the target for your search?’ (  – ). The implication of the question is that it is impossible to set up as the target of a search an object of which one is totally ignorant, an implication that requires us to supply the now omitted qualifier ‘at all’. Hence Meno’s puzzle rests on an assumption of total ignorance, as does Aristotle’s (in part). (b) Meno’s first two questions worry about the possibility of searching for something when one is totally ignorant of it, suggesting that the ability to search for x requires (some sort of) prior knowledge of x itself. I argued above that Aristotle’s dilemma rests on a very similar assumption: the geometer can learn the conclusion only if he has (some sort of) prior knowledge of it. (c) When Socrates recasts Meno’s puzzle in the form of a dilemma (by introducing the problem of searching for what one already knows), he too relies on an assumption key to Aristotle’s argument. Although Socrates does not spell this out explicitly, and although he omits the qualifier ‘at all’ (as does Meno in his second question), it seems that his dilemma rests on the same all-or-nothing conception of knowledge that we find in Post. An. . . Either one completely knows x or one does not at all know it. In the first case enquiry is unnecessary; in the second, impossible. (d) Finally, returning to Meno, it is important to notice that his 

For a similar interpretation of Meno’s first two questions see Scott, PM . I also suggested that Plato and Aristotle may differ in this regard, for it may be that Plato makes this a requirement for all learning (of universals), whereas it is clear that Aristotle restricts it to select cases. 

Created on 28 November 2009 at 22.10 hours page 135

Meno’s Paradox in Posterior Analytics . 



third question raises a worry, not about how enquiry begins, but about how it ends, about how we learn or discover something: ‘even if you do actually come across it, how will you know that it is that thing which you do not know?’ (  –). Meno objects that even if, per impossibile, we could begin to search for what we do not at all know, we will have no way of knowing that anything we find is the thing we were looking for in the first place. In other words, we will have no way of discovering anything. Socrates does not address this worry in his formulation, but we should not neglect it, because it suggests that Meno’s concern is with the whole trajectory of enquiry, from beginning to end. His objection to Socrates is not just that he cannot enquire (i.e. that he cannot begin to enquire), but that he cannot enquire successfully, that he cannot learn. This concern with learning helps close the gap between the Meno and Post. An. .  puzzles. By combining Meno’s worry about learning with Socrates’ dilemmatic argument, we can see how Aristotle would have found in passage [] sufficient resources for his own specific puzzle, adapted to his own specific case of learning. There is good reason to think that Plato too was attuned to the full range of worries raised in Meno’s three questions. For instance, Socrates introduces the theory of recollection immediately after passage [] with the explicit intention of explaining both how we enquire (how we launch a search) and how we learn (how we conclude it). As Socrates says, ‘enquiring and learning are as a whole recollection’ (τὸ γὰρ ζητεῖν ἄρα καὶ τὸ µανθάνειν ἀνάµνησις ὅλον ἐστίν:   –). In addition, notice how Socrates sums up the stretch of dialogue that responds to Meno’s worries: [] καὶ τὰ µέν γε ἄλλα οὐκ ἂν πάνυ ὑπὲρ τοῦ λόγου διισχυρισαίµην· ὅτι δ᾿ οἰόµενοι δεῖν ζητεῖν ἃ µή τις οἶδεν βελτίους ἂν εἶµεν καὶ ἀνδρικώτεροι καὶ ἧττον ἀργοὶ ἢ εἰ οἰοίµεθα ἃ µὴ ἐπιστάµεθα µηδὲ δυνατὸν εἶναι εὑρεῖν µηδὲ δεῖν ζητεῖν, περὶ τούτου πάνυ ἂν διαµαχοίµην, εἰ οἷός τε εἴην, καὶ λόγῳ καὶ ἔργῳ. (  – ) I do not insist that my argument is right in all other respects, but I would contend at all costs both in word and deed as far as I could that we shall be better, braver, and less idle if we believe that we must search [δεῖν ζητεῖν] for the things we do not know, rather than if we believe that

Created on 28 November 2009 at 22.10 hours page 136



David Bronstein it is not possible to discover [µηδὲ δυνατὸν εἶναι εὑρεῖν] what we do not know and that we must not search for it [µηδὲ δεῖν ζητεῖν].

Socrates mentions both enquiry and discovery, emphasizing our duty to enquire and ability to discover. Both points make sense in the light of the nature of Meno’s and Socrates’ relationship at this stage of the dialogue. After the famous stingray speech (  –  ) in which Meno condemns Socrates’ method of questioning, Meno raises his puzzle, indicating that he is fed up with the whole enterprise of philosophical enquiry. Socrates, in turn, wants to convince Meno that he ought to enquire (δεῖν ζητεῖν,   ). But to do that he needs to convince him that he can enquire. And to do that in a compelling way he needs to convince him that he can enquire successfully, that he can learn and discover. Hence Socrates entices Meno with the appealing idea that he can discover within himself the knowledge he seeks (i.e. recollection), an idea that also purports to explain how he can begin searching in the first place, as   – makes clear. In other words, Socrates’ response addresses both the letter of Meno’s puzzle, which concerns both enquiry and discovery, and the spirit of his character—an obstinate and impressionable young man who is keen to have knowledge and is not content merely to search for it. If Plato has Socrates emphasize Meno’s ability to discover and learn, it is not because he ignores the worries about enquiry or does not take them seriously, but because he is sensitive to what would count, for Meno, as a satisfying solution to his puzzle. I have argued that passage [] provided Aristotle with all the ingredients necessary for his puzzle about learning in Post. An. . , and that Plato too used the passage as a springboard to de G. M. A. Grube’s translation, Plato: Meno, nd edn (Indianapolis and Cambridge, Mass., ), altered slightly.  For a different view see Scott, PM –, who takes [] as evidence for his view that Plato does not take the puzzle of enquiry seriously and that he does not introduce the theory of recollection in order to solve it. Scott argues that recollection solves a different puzzle—‘the problem of discovery’ (PM –)—and that the problem of enquiry is overcome by the distinction between knowledge and true belief. Contra Scott,   – (‘enquiring and learning are as a whole recollection’) strongly suggests that recollection explains how enquiry is possible. However, Plato’s view might be that it does so in conjunction with true belief, for he might think that our having latent innate knowledge entails that we have the capacity to form true beliefs, which then provide the basis for our enquiries. I hope to argue elsewhere that this is in fact Plato’s view. For further discussion of Scott’s interpretation see G. Fine, ‘Enquiry and Discovery: A Discussion of Dominic Scott, Plato’s Meno’, Oxford Studies in Ancient Philosophy,  (), –.

Created on 28 November 2009 at 22.10 hours page 137

Meno’s Paradox in Posterior Analytics . 



velop his own explanation of how learning, in addition to enquiry, takes place. However, these similarities should not distract us from a distinction I made above—namely, that the context of the Meno puzzle is the problem of searching for and learning universal truths, whereas the context of the Post. An. .  puzzle is the problem of learning particular truths (in the light of the relevant universals). The reason I urge this distinction is that without it we may be misled about the differences between Plato’s and Aristotle’s positions. Plato’s solution to Meno’s paradox is the theory of recollection, which Aristotle rejects, as is clear from Post. An. . , where he rejects the existence of latent innate knowledge. However, although Plato and Aristotle disagree about the origin of our knowledge of universal truths, it may very well be the case that they agree about how we make inferences from such known universals to unknown particulars—inferences of the sort Aristotle is concerned to explain in Post. An. . . In other words, while Plato and Aristotle may disagree about how to solve the Meno version of the puzzle, they may very well agree about how to solve the Post. An. .  version—namely, by distinguishing between different ways of knowing a particular in the light of the relevant universal. At the very least it is highly unlikely, I think, that Plato would appeal to his theory of recollection to explain how a geometer who already knows that every triangle has  learns that some particular triangle in his perceptual environment has , even though Plato would appeal to this theory in order to explain how the geometer learns the relevant universal in the first place. This is why we should be sensitive to the differences between the puzzles that Plato and Aristotle attempt to solve. Since they are concerned with different sorts of learning, it is possible that in the one case (the Post. An. .  puzzle) their solutions will be the same, even though in the other (the Meno puzzle) they are different.  This raises several important questions which I cannot address here. For example, does Plato in the Meno allow knowledge of particulars in the light of relevant universals? What about other dialogues, such as the Republic? What is the connection to the puzzle we find in the Euthydemus ( ), which is reminiscent of Meno’s paradox and seems to bear on this issue?  Ross, Analytics,  (cf. ), is misleading in this regard, for he compares Aristotle’s solution in Post. An. .  to Plato’s in the Meno as though these solutions are directed at the same puzzle threatening the same sort of learning.  I do not wish to claim with any certainty that Plato would solve the Post. An. .  puzzle in the same way Aristotle does. I only wish to claim that from Plato’s theory of recollection alone we cannot infer that he would not.

Created on 28 November 2009 at 22.10 hours page 138



David Bronstein

With these considerations in mind, consider the following passage from Pr. An. . . Aristotle is discussing the now familiar case of a geometer who knows universally that a particular triangle C, whose existence he is not aware of, has , in virtue of the fact that he knows that all triangles have . Aristotle explains how the geometer then learns that C has : [] [A] ὁµοίως δὲ καὶ ὁ ἐν τῷ Μένωνι λόγος, ὅτι ἡ µάθησις ἀνάµνησις. [B] οὐδαµοῦ γὰρ συµβαίνει προεπίστασθαι τὸ καθ᾿ ἕκαστον, ἀλλ᾿ ἅµα τῇ ἐπαγωγῇ λαµβάνειν τὴν τῶν κατὰ µέρος ἐπιστήµην ὥσπερ ἀναγνωρίζοντας. ἔνια γὰρ εὐθὺς ἴσµεν, οἷον ὅτι δύο ὀρθαῖς, ἐὰν ἴδωµεν ὅτι τρίγωνον. ὁµοίως δὲ καὶ ἐπὶ τῶν ἄλλων. (a–) [A] [This] is similar to the argument in the Meno that learning is recollection [ἀνάµνησις]. [B] For it never happens that one has prior knowledge of the particular, but at the same time as he makes the induction he acquires knowledge of the particulars, as though he is recognizing [ἀναγνωρίζοντας] them. For we know some things immediately, e.g. that [the angles] are equal to two right angles, if we see that [the figure] is a triangle.

Aristotle depicts the same case of simultaneous learning described in Post. An. . : upon grasping that the figure before him is a triangle, the geometer learns immediately that it has . What is new and interesting is the reference to the Meno and recollection (ἀνάµνησις) in [A] and to recognition (ἀναγνωρίζοντας) in [B]. Commentators often take Aristotle’s point to be hostile to Plato. On this reading he is criticizing Plato’s view that learning x consists in recollecting prior innate knowledge of x by providing a counterexample in which one learns that C has  without prior (unqualified) knowledge of this same fact. The problem with this interpretation is that it attributes to Aristotle a surprisingly bad argument based on an excessively uncharitable interpretation of Platonic recollection. For the argument works only if our inferences from known universals to unknown particulars count, for Plato, as cases of recollection. However, as I suggested above, it is implausible to suppose that Plato would have agreed to this uncharitable charac See e.g. Ross, Analytics, ; A. J. Jenkinson’s translation (in J. Barnes (ed.), The Complete Works of Aristotle: The Revised Oxford Translation,  vols. (Princeton, )) of [A] (a): ‘The argument in the Meno that learning is recollection may be criticized in a similar way’; and H. Tredennick’s marginal note to his Loeb translation (in Aristotle: The Organon. The Categories, On Interpretation, Prior Analytics (London and Cambridge, Mass., ), ): ‘The Platonic doctrine of ἀνάµνησις criticized’.

Created on 28 November 2009 at 22.10 hours page 139

Meno’s Paradox in Posterior Analytics . 



terization of his view, and strange to think that Aristotle would have read him this way. For one thing it ignores the context in which recollection is introduced, namely, as a response to a puzzle about enquiring into and learning universal truths, not particular ones. A better reading of passage [] finds Aristotle making a subtler point. Learning that C has  on the basis of prior knowledge of the universal is similar to (ὥσπερ) what Plato in the Meno calls recollection. For the geometer feels less as if he is acquiring a new piece of knowledge and more as if he is reactualizing or recognizing knowledge he has previously acquired. After all, there is a way in which prior to learning that C has  the geometer already knows it—he knows it universally or potentially—and his learning consists in actualizing his potential knowledge. So Plato’s account captures metaphorically the experience or ‘feel’ of a certain kind of learning. However, Aristotle pays homage to Plato even as he implicitly distances himself from him. For in Aristotle’s view Plato misapplied the recollection metaphor to learning universals and took it too literally. His point in passage [] is that learning a particular in the light of a universal is similar, but not identical, to recollection, and Post. An. .  suggests that learning universals is neither. Plato and Aristotle agree that we can have knowledge of universals, and they may even agree about how we make inferences from them. They disagree, however, about how knowledge of universals is acquired in the first place.

. Conclusion I have sought to interpret Aristotle’s reference to Meno’s paradox in Post. An. .  in a way that preserves the connection to the puzzle we find in Plato’s Meno and acknowledges the differences between them. The Meno puzzle concerns the sort of enquiry and learning one must undertake in order to acquire scientific knowledge,  Gifford, ‘Paradox’, –, also argues that in [A] Aristotle favourably compares his own view to Platonic recollection. However, Gifford provides a much different interpretation of [B], according to which Aristotle is describing how one acquires knowledge of a universal from prior knowledge of particulars, and not the other way round. I am not convinced by Gifford’s unorthodox reading. For one thing, the parallel with the Post. An. .  passage supports the more traditional view. My interpretation comes closest to LaBarge, ‘Simultaneous’, –, who also discusses  Gifford’s account. Cf. Gifford, ‘Paradox’, –.

Created on 28 November 2009 at 22.10 hours page 140



David Bronstein

whereas the Post. An. .  puzzle concerns the sort of learning one can undertake in virtue of having it. For this reason Aristotle’s puzzle finds a happy home at the beginning of the Posterior Analytics, a work largely devoted to explaining what scientific knowledge is. University of Oxford

BI BL I OG R APH Y Barnes, J., Aristotle: Posterior Analytics [Post. An.], nd edn. (Oxford, ). Berti, E. (ed.), Aristotle on Science: The Posterior Analytics [Science] (Padua, ). Brown, L., ‘Review of Dominic Scott’s Plato’s Meno’, Philosophical Review,  (), –. Burnyeat, M. F., ‘Aristotle on Understanding Knowledge’ [‘Understanding’], in Berti (ed.), Science, –. Day, J. (ed.), Plato’s Meno in Focus [Focus] (London, ). Engberg-Pedersen, T., ‘More on Aristotelian Epagoge’, Phronesis,  (), –. Ferejohn, M., ‘Meno’s Paradox and De Re Knowledge in Aristotle’s Theory of Demonstration’ [‘De Re’], History of Philosophy Quarterly,  (), –. Fine, G., ‘Aristotle and the Aporêma of the Meno’ [‘Aporêma’], in V. Harte, M. M. McCabe, R. W. Sharples, and A. Sheppard (eds.), Aristotle and the Stoics Reading Plato (London, ). ‘Enquiry and Discovery: A Discussion of Dominic Scott, Plato’s Meno’, Oxford Studies in Ancient Philosophy,  (), –. ‘Inquiry in the Meno’ [‘IM’], in R. Kraut (ed.), The Cambridge Companion to Plato (Cambridge, ), –. Gifford, M., ‘Aristotle on Platonic Recollection and the Paradox of Knowing Universals: Prior Analytics B.  a–’ [‘Paradox’], Phronesis,  (), –. ‘Lexical Anomalies in the Introduction to the Posterior Analytics, Part ’ [‘Anomalies’], Oxford Studies in Ancient Philosophy,  (), –. Grube, G. M. A. (trans.), Plato: Meno, nd edn (Indianapolis and Cambridge, Mass., ). Hamlyn, D. W., ‘Aristotelian Epagoge’, Phronesis,  (), –. Jenkinson, A. J. (trans.), Aristotle: Prior Analytics, in J. Barnes (ed.), The

Created on 28 November 2009 at 22.10 hours page 141

Meno’s Paradox in Posterior Analytics . 



Complete Works of Aristotle: The Revised Oxford Translation,  vols. (Princeton, ). Kraut, R. (ed.), The Cambridge Companion to Plato (Cambridge, ). LaBarge, S., ‘Aristotle on “Simultaneous Learning” in Posterior Analytics .  and Prior Analytics . ’ [‘Simultaneous’], Oxford Studies in Ancient Philosophy,  (), –. McKirahan, R., ‘Aristotelian Epagoge in Prior Analytics .  and Posterior Analytics . ’, Journal of the History of Philosophy,  (), –. Mansion, S., ‘La signification de l’universel d’après An. Post. I ’ [‘Universel’], in Berti (ed.), Science, –. Nehemas, A., ‘Meno’s Paradox and Socrates as a Teacher’, in Day (ed.), Focus, –. Pellegrin, P., Aristote: Seconds Analytiques (Paris, ). Ross, W. D., Aristotle: Prior and Posterior Analytics [Analytics] (Oxford, ). Scott, D., Plato’s Meno [PM] (Cambridge, ). Tredennick, H., Aristotle: The Organon. The Categories, On Interpretation, Prior Analytics (London and Cambridge, Mass., ). White, N. P., ‘Inquiry’ [‘Inquiry’], in Day (ed.), Focus, –.

Lihat lebih banyak...

Comentários

Copyright © 2017 DADOSPDF Inc.