¹ Bluck, R. S., Plato's Meno (Cambridge 1964) 23Google Scholar.

² See esp. Robinson, R., Plato's Earlier Dialectic (Oxford 1953) 114–22Google Scholar; Crombie, I. M., An Examination of Plato's Doctrines (London 1963) ii 529–48Google Scholar; Bluck (n. 1) 8–17; Brown, M. S., ‘Plato disapproves of the slave-boy's answer’, RMetaphys xxi (1967) 63–5Google Scholar; Rose, Lynn E., ‘Plato's Meno 86–89’, JHistPhilos viii (1970) 1–8Google Scholar; Allen, R. E., Plato's Euthyphro and the Earlier Theory of Forms (London 1970) 96Google Scholar; Zyskind, Harold and Sternfeld, R., ‘Plato's Meno 89c: “Virtue is Knowledge” a hypothesis?’, Phronesis xxi (1976) 130–4CrossRefGoogle Scholar.

³ Brown (n. 2) 57–93 rightly points out the precise parallelism between Socrates' dialogue with the slave and his dialogue with Meno, and says that the slave-boy experiment ‘is a model of the dialogue as a whole’ (65). However, as I shall argue, the slave-boy experiment is a model of Socrates' dialogue with Meno, but only up to the end of the argument ‘from a hypothesis’, i.e. 89c.

⁴ Ibid. 64.

⁵ Ibid. 63.

⁶ Denniston, J. D., The Greek Particles² (Oxford 1954) 12Google Scholar.

⁷ Bluck (n. 1) 322.

⁸ Cf. ibid. 92.

⁹ On the case of αὐτό, Bluck (n. 1) 322 rightly points out that by the regular Greek idiom the subject (virtue) of the indirect question (εἴτε διδακτόν ἐστι κτλ) is brought forward and associated with the introductory verb σκοπεῖσθαι. Bluck, however, does not seem to suspect that this fact may have influenced Plato's thinking in the argument ‘from a hypothesis’.

¹⁰ Ibid. 325.

¹¹ Zyskind–Sternfeld (n. 2) 131–2.

¹² Bluck (n. 1) 325.

¹³ ‘The role of the hypothetical method in the Phaedo’, Phronesis xxiv (1979) 113–14Google Scholar.

¹⁴ Cornford, F. M., Plato and Parmenides (London 1939) 245Google Scholar. Admittedly, it is not definition per genus et differentiam (see Allen [n. 2] 94). However, since Socrates, having defined figure as ‘that which alone always follows upon colour’, says he would be satisfied if Meno would define virtue for him ‘even like this’—κἄν οὕτως (75b), it seems that he would accept ‘virtue is knowledge’ as a satisfactory definition of virtue; though, clearly, in the context of the discussion, ‘virtue is knowledge of what is good’ would be a more satisfactory definition. Indeed, if, as I shall argue, we are meant to see the deduction of the proposition ‘virtue is knowledge’ from the proposition ‘virtue is good’ as an exemplification of the ‘upward path’ of the hypothetical method as described in the Phaedo, then it seems likely that Plato is hinting at ‘virtue is knowledge of the Good’ as the definition of virtue required here. Significantly, the hypothesis ‘virtue is good’ is said to stand (μένει, 89d), which presumably means it cannot be refuted. Thus, since virtue and knowledge are not really Forms, but rather psychical endowments (87d), it would seem that Plato has in mind even here in the Meno the view implicit in the Republic, namely that virtue is the effect of knowledge of the Good on the soul. See n. 54.

¹⁵ Brown (n. 2) 64.

¹⁶ See Meno 98b ff.

¹⁷ Crombie (n. 2) 532. Cf. also Robinson (n. 2) 51–2.

¹⁸ Socrates describes this as a true opinion and not knowledge (85b); for as he has already explained, if one does not know what a thing is, one cannot know anything about it. We are meant to understand that the boy does not know that the square of the diagonal is twice the size of the given square, precisely because he does not know what the square is, i.e. the Form). Once we recognize this, we shall be much less inclined to suppose that when Plato makes use of acquaintance with objects to illustrate what he means by knowledge properly so called he is ignoring ‘knowledge that…’ or propositional knowledge. He means that propositional knowledge presupposes knowledge by acquaintance of objects designated by the terms of the proposition. Note that γιγνώσκειν is used of ‘knowing Meno’ whereas εἰδέναι is used of knowing facts about him (71b). But see Bluck (n. 1) 213.

¹⁹ This should mean that when Socrates says that if one does not know X, one cannot know what sort of thing X is, he is conscious of the fact that he is enunciating a paradox which requires for its solution a clear distinction between knowledge and true opinion. It is, however, not to be supposed that at the time of writing the Meno, Plato considered ‘knowing Meno’ and ‘knowledge of the road to Larisa’ as instances of knowledge properly so called. Plato is only making use of acquaintance with sensible particulars to illustrate what he means by knowledge that is the result of recollection. I have argued in a forthcoming article, ‘Sense-experience and recollection in Plato's Meno’, that at the time of writing the Meno Plato had already formulated his metaphysical theory of Forms, and that he was consciously aware of the importance of sense-experience in the slave-boy experiment.

²⁰ The genuineness of this letter is disputed by some scholars; however, whoever wrote it must have considered that, according to Plato, situated as we are, we can only approach τὸ ὄν ἑκάστου or τὸ τί through the consideration of τὸ ποῖόν τι (περὶ ἕκαστον). The nearest Plato comes to stating explicitly that the approach to knowledge of Forms must be indirect, starting with sensible images through verbal images, is Socrates' account of his ‘second voyage’ (δεύτερος πλοῦς) in the Phaedo. See Bedu-Addo, , ‘On the alleged abandonment of the Good in the Phaedo’, Apeiron xiii (1979) 104–11Google Scholar; art. cit. (n. 13) 112 ff.; ‘Mathematics, dialectic and the Good in the Republic VI–VII’, Platon xxx (1978) 112 ff.Google Scholar, and ‘Διάνοια and the images of Forms in Plato's Republic VI–VII’, Platon xxxi (1979) 93–103Google Scholar.

²¹ Plato's point in using this geometrical example seems clear enough, but the example itself as well as the statement of the determinative criterion are matters of scholarly dispute. Many different interpretations of these have been offered; of these the most important are discussed by Bluck, (n. i) 441–61. See also Sternfeld, Robert and Zyskind, H., ‘Plato's Meno 86e–87a: The geometrical illustration of the argument by hypothesis’, Phronesis xxii (1977) 206–11CrossRefGoogle Scholar. They use W. H. D. Rouse's translation (Great Dialogues of Plato [Mentor 1965] 52) of the statement of the determinative criterion: ‘If the space is such that when you apply it to the given line of the circle, it is deficient by a space of the same size as that which has been applied, one thing follows, and if this is impossible, another’ (87a3–6).

²² On the ‘operationalism’ of our geometer, see Sternfeld–Zyskind (n. 21) 210. What is described here as ‘a sort of hypothesis’ or ‘a hypothesis, as it were’ (ὥσπερ τινα ὑπόθεσιν) is the hypothetical statement, i.e. the statement of the determinative criterion which is not an assumption, but rather something that the geometer knows for certain. See n. 21 above. It is sometimes suggested that Plato is using this example to introduce the reader to the notion of ὑπόθεσις, and that he is apologizing for the use, in a semi-technical sense, of an unfamiliar word. Cf. Bluck (n. 1) 92–3. This would be a rather misleading way of introducing an unfamiliar notion, precisely because when the geometer, having made this hypothetical statement, proceeds to say ὑποθέμενος οὖν ἐθέλω εἰπεῖν σοι τὸ συμβαῖνον, it seems clear that his hypothesis is going to be the minor premise (i.e. ‘this area is such and such’) of the hypothetical syllogism, from which, if proved, the conclusion may be drawn. Similarly, when at the beginning of the Line passage in the Republic Socrates says ὥσπερ … γραμμὴν … λαβὼν … (509d), he is not really introducing the reader to the notion of γραμμή; he means that the intelligible and the visible do not really form a straight line. See Bedu-Addo, , Platon xxxiGoogle Scholar (n. 20) esp. 90-2 and 106-8. I submit that Plato was not really writing for people unfamiliar with elementary geometry. Presumably the word ὑπόθεσις was currently used indifferently to refer to both types of proposition, and Plato means that a hypothesis in the strict sense of the word is a proposition that is not known for certain.

²³ The geometrical example given is of a διορισμός—limiting condition or conditions for the solubility of a geometrical problem. Cf. Euclid i 22, vi 28. These διορισμόοί, it is important to note, always depended on some theorem already known. For good discussions of Greek geometrical analysis to which Plato seems to be indebted for his own practice and development of a ‘hypothetical method’, see Gulley, N., ‘Greek geometrical analysis’, Phronesis iii (1958) 1–14CrossRefGoogle Scholar; and Bluck (n. 1) 76–85.

²⁴ Zyskind and Sternfeld (n. 2) say that the basic hypothesis is ‘knowledge alone is teachable’ (87c), and that ‘textually it is this statement or the statement validly derivable from it which functions as the major premiss of the hypothetical syllogism: “if virtue is knowledge, clearly it could be taught”’ (p. 132). Similarly at Sternfeld–Zyskind (n. 21) 206, they argue as follows: ‘The objective is to state an hypothesis which will determine whether or not a given property is ascribable to a given object; that is whether the property inscribable triangularly, is ascribable to the joint object, a given area and a given circle, or whether the property teachable, is ascribable to the object virtue.’ It seems to me that they are mistaking the geometer's theorem or theorems, and Socrates’ self-evident truth (knowledge alone is teachable), on the basis of which they make their respective hypotheses, for the hypotheses themselves.

²⁵ Cf. Robinson (n. 2) 116; Stahl, H. P., ‘Beginnings of propositional logic in Plato’, trans, by Weiler, G. from Hermes, in Brown, M., Plato's Meno (Indianapolis 1971) 180–97Google Scholar; and Zyskind–Sternfeld (n. 2) 132.

²⁶ Bluck (n. 1) 87–8. See also nn. 23 and 40. It would seem that in Plato's ‘method of hypothesis’, even when we have an equivalence relation between two propositions, Plato is primarily interested not in the mutual deducibility or convertibility of the two propositions, but rather in the causal priority of the ‘limiting condition’. Thus we are here dealing with a causal relation—a relation that is asymmetrical: it is not because a given space is inscribable triangularly in a given circle that it has a certain characteristic; it is because it has that characteristic that it is inscribable triangularly in the circle. Similarly, it is not because virtue is teachable that it is knowledge; it is because it is knowledge that it is teachable. This, as we shall see, has an important bearing on the propriety of the arguments purporting to prove, on the ground that there are no successful teachers of virtue, that virtue is not knowledge. Again, since the ‘method of hypothesis’ is a means of establishing necessary and sufficient conditions for the truth of a hypothesis—in the present example, ‘virtue is knowledge’—we should expect the dialectician, at the end of the enquiry, to be able to formulate an ‘adequate proposition’ that will include the necessary and sufficient conditions for the truth of the hypothesis. As in the case of his description of the method in the Phaedo, Plato does not do this for his readers. But see n. 14 for my view that (i) the deduction of the proposition ‘virtue is knowledge’ from the proposition ‘virtue is good’ is to be seen as an instance of ‘reasoning out the cause’ (αἰτίας λογισμός), and that (ii) what Plato has in mind here as the ‘adequate proposition’ is ‘virtue is the effect of knowledge of goodness on the soul’. See also Bedu-Addo (n. 13) 122–4, and 130 n. 23.

²⁷ In effect, the difference is precisely that which exists between the dianoietic mathematician's treatment of his hypothesis and the dialectician's treatment of his hypothesis described at Repub. 510b ff. For the view that the hypothetical treatment of the propositions of dianoietic mathematics belongs to philosophical dialectic, see Bedu-Addo, , Platon xxx (n. 20), esp. 120 ff.Google Scholar

²⁸ Cf. Sayre, K. M., Plato's Analytic Method (Chicago/London 1969) 29–30Google Scholar n. 40, and 57–8 n. 1.

²⁹ Cf. Crombie (n. 2) 528 where, commenting on hypotheses in Meno, Phaedo and the Republic, he says: ‘It seems that there is some technical doctrine connected with this word that Plato is anxious to communicate to us… and that he failed to notice that he had not given us enough clues to enable us to follow him with confidence. …’ However, on Plato's conception of the nature of philosophical writing, see Phdr. 276c–d, and Epist. 7 343 ff.

³⁰ See Bedu-Addo (n. 13) 117–18, where I have argued that far from being a digression, Phaedo 100c–101c is an illustration of this part of the hypothetical method. Here in the Meno Socrates obviously has in mind the hypothesis that virtue is knowledge in his examination of Meno's definitions, since he makes him admit at each stage that all acts or cases of virtue involve knowledge of what is good and what is bad.

³¹ See n. 30. It is not to be supposed that in the first part of the dialogue with Meno, Socrates and Meno dispense with what each of them supposes to be instances or cases of what virtue is like, for if as I believe (see n. 3) the slave-boy experiment is a model of Socrates' dialogue with Meno, then we are meant to understand that Meno, in his attempts at defining virtue, and Socrates, in his examination of Meno's definitions, are drawing upon their previous experience of what each of them supposes to be instances or cases of what virtue is like.

³² Crombie (n. 2) 536.

³³ I think Zyskind and Sternfeld (n. 2) 131–2 are right in maintaining that Lamb's translation, ‘and plainly, Socrates, on our hypothesis that virtue is knowledge, it must be taught’, is mistaken, and that the hypothesis referred to here is ‘if virtue is knowledge, it is teachable’.

³⁴ Crombie (n. 2) 536.

³⁵ See Bedu–Addo (n. 13) 117 ff.

³⁶ See Analytica Priora 50a16–28.

³⁷ Cf. Crombie (n. 2) 544–5.

³⁸ Zyskind and Sternfeld (n. 2) do not explain why, in spite of the fact that the minor premiss of the hypothetical syllogism ‘has been proved’, thus justifying the conclusion ‘virtue is teachable’ ‘in a simple modus ponens inference’ (132–3), Socrates finds it necessary to proceed to argue that since there are no teachers of virtue, it is not teachable, and hence that it is not knowledge. Nor indeed do they explain why, if ‘virtue is knowledge’ is not a hypothesis in the argument, the proposition ‘virtue is good’ which is not hypothetical is described as a hypothesis at 87d.

³⁹ Cherniss, H., ‘Some war-time publications concerning Plato’, AJP lxviii (1947) 140Google Scholar.

⁴⁰ As Gulley, N., Plato's Theory of Knowledge (London 1962) 14Google Scholar, rightly says: ‘We may give greater precision to Plato's phrase “a chain of causal reasoning” by associating it with a particular method of analysis the aim of which is to find the antecedent conditions for the solution of a problem or for the truth of a proposition’, i.e. Greek geometrical analysis. See n. 23 above.

⁴¹ Similarly, at the end of the ‘upward path’ of the hypothetical method in the Phaedo, Cebes and Simmias only attain true opinion, whereas Socrates attains knowledge of the cause of generation, existence and destruction. See Bedu-Addo (n. 13) 126–7. Cf. also my ‘A theory of mental development: Plato's Republic V–VII’, pt 1, Platon xxviii (1976) 296 ff.Google Scholar, and pt 2, Platon xxix (1977) 222–4Google Scholar.

⁴² Bluck (n. 1) 19–30.

⁴³ See Cornford (n. 14) 245, and his Principium Sapientiae (Cambridge 1952) 60Google Scholar n. 1; Koyré, A., Discovering Plato, trans. Rosenfield, L. C. (New York 1945) 17Google Scholar; Goldschmidt, V., Les dialogues de Platon (Paris 1947) 117 ff.Google Scholar

⁴⁴ Bluck (n. 1) 22.

⁴⁵ Ibid. 22–3.

⁴⁶ Ibid. 29.

⁴⁷ Devereux, D. T., ‘Nature and teaching in Plato's Meno’, Phronesis xxiii (1978) 122–3Google Scholar.

⁴⁸ Ibid. 122.

⁴⁹ It may be suggested that this argument is valid and that the conclusion does not really contradict the premiss that the only guides to right conduct are true opinion and knowledge. On this view, Socrates is saying that knowledge is not a useful guide in political conduct (i.e. in social and moral life), but that it may well be a good and useful guide in other areas, e.g. in the application of technical skills. This view, however, is so patently opposed to the political views both of the historical Socrates and Plato that it is difficult to imagine that the irony in the conclusion of this argument was lost on contemporary readers of the Meno. I suggest that Plato expects his readers to see that the fault in this argument can be traced to the premiss ‘virtue is not knowledge’, the arguments in favour of which, I have argued, are deliberately fallacious. For Plato's deliberate use of sophistical arguments as an indirect recommendation of his own position, see Sprague, Rosamond K., Plato's Use of Fallacy (London 1962) esp. 1–33Google Scholar.

⁵⁰ Indeed, the view that virtue is true opinion imparted by divine dispensation (θείᾳ μοίρᾳ) without understanding or intelligence (ἄνευ νοῦ) is particularly absurd in the context of this dialogue, since we are explicitly told (i) that the nature of virtue can be recollected (81c), and (ii) that true opinion is only a stage in this process of recollection (85c). Bluck recognizes that Plato is here ‘being very ironical’ (n. 1) 434. However, he maintains that ‘we need not suppose … that the whole of what is said about virtue based on true belief is not seriously meant’ (435). The argument, however, purports to establish, not that virtue or some sort of virtue can be based on true opinion, but rather that true opinion is just what virtue is. See n. 53.

⁵¹ It seems clear from what Plato says in this dialogue about knowing what a thing is (τί ἐστι) and knowing what it is like (ποῖόν τι), that there can be only one true opinion about what virtue is, namely that it is knowledge (of what is good and what is bad), whereas there may be many true opinions about what virtue is like, i.e. about particular instances of virtue. Again, the view that true opinion is not teachable reckons without the demonstration of recollection in this dialogue. Perhaps this misunderstanding is due to the fact that at Tim. 51e2–3 Plato suggests that true opinion is not teachable; but it is important to note that there Plato is adverting not to true opinions about what things are, but rather true opinions about what things are like, i.e. particulars. On levels or grades of opinion, see my article cited in n. 41, pt 2, 223–4.

⁵² As I have suggested, in this argument Socrates is talking as if the theory of recollection has not been mentioned at all in the dialogue, and he deliberately talks as if knowledge can be handed over from one person to another. Thus it is clear that he has in mind not only virtue as popularly conceived, but also teaching as popularly conceived. Nevertheless, he concludes that virtue (as properly conceived) is not knowledge, but rather true opinion! See n. 26.

⁵³ Immediately after rejecting knowledge as a good and useful guide in political conduct, Socrates says (99b): ‘So it is not by the possession of any wisdom that such men as Themistocles, and others whom Anytus mentioned just now, became leaders in their cities. This fact.. will explain why they are unable to make others like themselves.’ Note that it is not really Anytus who mentions the names of these highly respected and renowned statesmen; it is Socrates himself! Indeed, as far as Anytus himself is concerned, it is quite unnccessary to mention the name of any individual—any Athenian gentleman (καλὸς κἀγαθός) is quite capable of making Meno a good man (92c). The whole of this section (i.e. 99b ff.) up to the end of the dialogue is shot through and through with subtle sarcasm. See also n. 50.

⁵⁴ As Bluck (n. 1) 31 rightly says, ‘in view of the suggestion that αἰτίας λογισμός is recollection “as we agreed before”, we may assume that although the expression αἰτίας λογισμός was not used earlier on, we may gloss with these words what was said at 85c about the possibility of converting true opinions into knowledge by further questioning’.

⁵⁵ It would seem then, that ἐκ τούτου τοῦ λογισμοῦ (100b) refers to ‘our present’ discussion of the question whether there are successful teachers of virtue, rather than to the entire discussion right from the introduction of the argument ‘from a hypothesis’.

⁵⁶ Cf. Erbse, H., ‘Über Platons Methode in den sogenannten Jugenddialogen’, Hermes xcvi (1968) 21–40Google Scholar, where he argues convincingly that Plato was not merely experimenting in the aporetic dialogues, but was rather producing artistically framed teaching works designed to prepare his readers step by step towards his main philosophical doctrines which he had already developed to a considerable degree.