1. Aristotle advocates, as well as uses, this approach in his own investigations in Met. A and Anim. I.

2. See Heliodorus, In Ethica Nicomachea Paraphrasis , in G. Heylbut (ed.), Heliodori in Ethica Nicomachea Commentaria (Berlin: Reimer, 1889); Aspasii , In Ethica Nicomachea Commentaria , in G. Heylbut (ed.), Aspasii in Ethica Nicomachea Ethica Commentaria (Berlin: Reimer, 1889); Eustratius, In Ethica Nicomachea I Commentaria , in G. Heylbut (ed.), Eustratii et Michaelis et Anonyma in Ethica Nicomaehea Commentaria

(Berlin: Reimer, 1892); J. Burnet, The Ethics of Aristotle (London: Methuen, 1900); L. H. G. Greenwood, Aristotle: Nicomachean Ethics, Book VI (Cambridge: Cambridge University Press, 1909).

3. See, for example, W. Jaeger, Aristotle: Fundamentals of the History of His Development (Oxford: Oxford University Press, 1948), especially chs. 9 and 10; W. F. R. Hardie, Aristotle's Ethical Theory (Oxford: Clarendon Press, 1968), especially ch. 3; G. E. R. Lloyd, Aristotle: The Growth and Structure of HIS Thought (Cambridge: Cambridge University Press, 1968), pp. 36-37; C. J. Rowe, The Eudemian and Nicomachean Ethics (Cambridge: Proceedings of the Cambridge Philological Society, 1971); T. Irwin, Nicomachean Ethics (Indianapolis: Hackett, 1985).

4. I follow tradition here and consider the following of Plato's dialogues to be among the Early or Socratic ones: Apology, Crito, Ion, Hippias Minor, Hippias Major, Charmides, Euthydemus, Euthyphro, Gorgias, Laches, Lysis, Protagoras, Meno . For a discussion of some of the problems about the dating and ordering of the Platonic Dialogues, see C. H. Kahn, "Did Plato Write Socratic Dialogues?" Classical Quarterly 31 (1981), pp. 305-320.

5. See, for example, the discussion in I. M. Crombie, Plato: The Midwife's Apprentice (London: Routledge & K. Paul, 1964). It is difficult to see how there could be any doubt about Socrates' interest in obtaining definitions when we consider the number of definitions that Socrates and his interlocutors put forth, examine, amend, and utilize in their discussions. The best account of these matters is to be found in G. X. Santas, Socrates (London: Routledge & K. Paul, 1979). Santas gives a list of all the definitions presented by Socrates' interlocutors and by Socrates himself, and shows that many are clarified and used in subsequent discussions (see especially ch. 4). Much of what I say here on Socrates follows Santas's line of argument.

6. Indeed, the refutations of definitions themselves may serve purposes that go beyond refutation. As Santas points out, op. cit. , p. 100, refutations may serve the purpose of showing that Socrates objected to some dominant ethical ideas, of showing that his contemporaries had unclear ideas about certain ethical ideals, of making clear the conditions that must be met by definitions, and so forth.

7. Santas comes to the same conclusion on this matter: "Socrates thought that the search for definitions is a viable and fruitful philosophical enterprise," op. cit. , p. 101.

8. The definitions that are presented or examined in the Socratic Dialogues are not all of the same type. For a discussion of the differences among them, see Santas, op. cit. , and R. E. Allen, Plato's "Euthyphro" and the Earlier Theory of Forms (New York: Humanities Press, 1970). That Socrates is not interested in ostensive definitions or definitions by example is made clear when in the Euthyphro he rejects as an answer to his request for a definition of piety Euthyphro's reply that piety is what he is doing now. None of the definitions that are given by others and that have the form Socrates approves of, and none of the definitions that Socrates himself gives, are ostensive or definitions by example. See on these matters the discussions by J. Beversluis, "Does Socrates Commit the Socratic Fallacy?" American Philosophical Quarterly 24 (1987), pp. 211-223, and A. Nehamas, "Confusing Universals and Particulars in Plato's Early Dialogues,'' Review of Metaphysics 29 (1975),

pp. 287-306. Nchamas in fact argues that even those definitions offered by some of Socrates interlocutors that seem to be definitions by example are not really in terms of concrete particulars but in terms of narrow universals. I do not of course mean to imply that Socrates does not use examples at all—e.g., in illustrating or testing definitions. For Socrates' use of examples, see G. X. Santas, "The Socratic Fallacy," Journal of the History of Philosophy 10 (1972), pp. 127-141; M. F. Burnyeat, "Examples in Epistemology: Socrates, Theaetetus, and G. E. Moore," Philosophy 52 (1977), pp. 381-398; and J. Beversluis, op. cit.

9. Socrates uses at Charmides 160D, where he asks his interlocutor to take into account what has been said and derive, or arrive at, a definition of temperance. Although it is clear that Socrates has no theory of the syllogism, he is nonetheless using the term to signify something like the drawing of a conclusion from some other facts or propositions—and this is the ordinary meaning of the term.

10. Thus at Top . 100a25 Aristotle writes, "A syllogism is an argument in which, certain things having been laid down, something other than these things necessarily results through them." See also some comments on this issue by J. Barnes in his "Proof and the Syllogism," in E. Berti, Aristotle on Science (Padova: Editrice Antenore, 1981).

11. The problem of distinguishing between knowledge and belief is more complex than the way Socrates presents it in the Meno . But even in this discussion, Socrates hints that at least two issues can be distinguished: one concerns the state of mind or cognitive state of the person who knows in contrast to the state of the one who believes; the other concerns a possible difference in the contents of the two cognitive states. Sometimes Plato uses the latter distinction as a way of showing that there is a difference in cognitive states. Socrates, however, in the Meno is not saying that the objects of the two states are different, in the sense that what is believed cannot be known and vice versa. Yet he is pointing to some difference: the structure of the contents of the two cognitive states is different—in the case of knowledge the contents have the structure of causal explanations while in the case of belief they don't. Whether the distinction between knowledge and belief should be attributed to Socrates instead of Plato is still a matter of dispute among scholars of Plato's writings. The Meno is considered by some to be a transitional dialogue whose contents perhaps reflect the views of Plato rather than Socrates. But the fact that Socrates hints at the same distinction in the Euthyphro suggests that Socrates' views may not differ from those of Plato.

12. Vlastos makes this point in his "Reasons and Causes in the Phaedo ," in G. Vlastos (ed.), Plato , vol. I (Garden City, N.J.: Anchor Books, 1971).

13. See also Vlastos's comments on this matter in his " Anamnesis in the Meno ," Dialogue 4 (1965), pp. 143-167. Vlastos argues elsewhere that we find in the Platonic dialogues two different philosophers that can be identified as Socrates. The one is a moral philosopher who has hardly any interest in any branch of knowledge or in the nature of knowledge (epistemology). The other is someone with strong interests in certain branches of knowledge (e.g., mathematics) as well as the nature of knowledge itself; see his "Socrates," Proceedings of the British Academy 74 (1988). P. Woodruff has argued that Socrates is represented by Plato

as "making a distinction in use between two conceptions of knowledge with different epistemic standards." The one is common or nonexpert knowledge. The other is expert knowledge, the kind that has to meet quite high epistemic standards; see his "Plato's Early Theory of Knowledge," in S. Everson (ed.), Epistemology (Cambridge: Cambridge University Press, 1990).

14. The argument using the first hypothesis can be represented as an instance of the Aristotelian syllogistic form AaB, BaC AaC ( Barbara ) and the one using the second hypothesis as an instance of AeB, AaC CeB.

15. Some of these conditions for having a proof or demonstration are, of course, the conditions that Aristotle himself discusses in the opening sections of the Post. Anal . That Socrates sees the limitations of the method of hypothesis is made clear at Meno 89, where he recognizes that a hypothesis used in a proof must be true and we must know it to be so in order to accept the conclusion. The importance of knowing the truth of the premises of a demonstrative argument along the lines Socrates suggests is also discussed extensively by Aristotle. In Post. Anal . (84a5) he says that, when we do not know the premises of a demonstrative argument better than we know the conclusion, we will not have knowledge absolutely, "but only by hypothesis [ ]." Of course, the term "hypothesis" has many other uses in both Plato and Aristotle that may be different from the one we are discussing here.

16. Aristotle, in whose philosophical thought demonstrative knowledge figures more prominently than any other kind of knowledge, argues that there are other kinds, and indeed that there must be, if there is to be demonstrative knowledge. The basic principles of the various disciplines cannot, according to Aristotle, be known by demonstration; they are instead known by intuitive induction or rational intuition. His arguments for the impossibility of knowing demonstratively the basic principles of the various disciplines are to be found in the opening chapters of Post. Anal. I and his account of the nature of nondemonstrative knowledge in the last chapter of Post. Anal. II. If P. Woodruff is correct ( op. cit. ), Socratic common or nonexpert knowledge is not knowledge by demonstration.

17. When speaking of kinds in the present context I am using the term "kind" to mean what it ordinarily means, i.e., a kind or type of thing, and do not mean to imply that matters of conduct constitute natural kinds.

18. Santas, op. cit. , designates this use of definitions as "epistemic use" and differentiates it from what he calls the "diagnostic use" (see below for a discussion of this use). In its diagnostic use a definition of F is to be used for determining whether some x is F whereas in its epistemic use it is a means for determining whether whatever is F is also G or whether F-ness itself is also G. Thus both these uses are epistemic in character and therefore designating one as epistemic does not really differentiate it from the other. Designating the use under discussion in the present context as demonstrative seems to me to better capture this role of definitions that Aristotle identifies in the Socratic theory/practice—namely, that they function as elements of demonstration.

19. Santas, op. cit. , pp. 125-126.

20. Socrates says, "If virtue is a kind of knowledge. . ." (86C), thus making a hypothesis about the nature of virtue. The form of the assumed definition of virtue

is that used elsewhere by Socrates, e.g., "Courage is a kind of endurance of the soul" ( Lathes 192B) or "Temperance is a kind of quietness" ( Charmides 159B).

21. Even at Protagoras 361, where Socrates gives the impression that the definition of virtue will be sufficient for knowing whether virtue is teachable, his strategy makes it clear that he presupposes additional premises that he considers to be self-evident—i.e., that all knowledge is teachable and whatever is not knowledge is not teachable: "If virtue were something other than knowledge, as Protagoras tried to prove, obviously it could not be taught. But if it turns out to be, as a single whole, knowledge . . . then it will be most surprising if it cannot be taught" (361C).

22. Santas, op. cit. , p. 123.

22. Santas, op. cit. , p. 123.

23. Ibid. , p. 126. J. Beversluis, op. cit. , argues that Socrates does not take the definition of F to be a necessary condition for knowing other things about F.

24. See, for example, R. Robinson, Plato's Earlier Dialectic (Oxford: Clarendon Press, 1953); W. D. Ross, Plato's Theory of Ideas (Oxford: Clarendon Press, 1951); N. Gulley, The Philosophy of Socrates (London: St. Martin's Press, 1968).

25. Socrates, for example, claims at Apology 29B that acting unjustly is bad and shameful although he does not give nor is there evidence that he has a definition of justice or injustice. This may very well be the kind of knowledge P. Woodruff designates as nonexpert, ordinry, or common knowledge.

26. J. Beversluis, op. cit. , recognizes this, but contends that Socrates does not hold the general thesis that the definition is necessary for diagnostic purposes. It is quite possible, however, that Socrates generalizes from the contexts of disagreement and dispute to the general diagnostic thesis that makes the definition necessary for knowing that some particular is of a certain kind.

27. If forming a belief that some x is F by using the definition of F is to be of use in settling disputes about x being F, we must assume that those disputing about x at least agree on the definition of F. We must also assume that they agree on the relation the definition bears to the belief that x is F, that such relation justifies believing that x is F, and so forth. These assumptions may not be unreasonable to make, but it is not clear that, once they are made, what we have is only a belief and not knowledge, or whether anything less than knowledge will be sufficient.

28. This, of course, may not be so simple. For whatever is sufficient for knowing may be said to provide objective reasons that are sufficient for believing. Yet there could be subjective factors that might render these reasons insufficient for believing.

29. The strongest argument supporting the view that Socrates commits the Socratic Fallacy is made by P. Geach, "Plato's Euthyphro : Analysis and Commentary," The Monist 50 (1966), pp. 369-382. Santas had argued earlier ("The Socratic Fallacy," Journal of the History of Philosophy 10 (1972), pp. 127-141) that Socrates does not commit the Socratic Fallacy, but in his Socrates he claims that most likely Socrates did commit the Fallacy. But Santas argues that Socrates does not hold that the definition of F is necessary for forming a belief or judging that some x is F. Hence, he argues, Socrates does not make it impossible to proceed with the search for definitions by requiring knowledge of the definition of F in order to have a belief or judgment that some x is F. He does not require knowledge of the definition of F in order to believe or judge that something is a sample of F that can in turn be used as a basis for formulating a definition of F (see pp. 120-122

and 311-312). For criticisms of the views of Geach and Santas, see J. Beversluis, op. cit.

30. Socrates and Plato at times refer to the entities they are trying to define by using the abstract noun, e.g., Justice ( ), or the neuter of the adjectival form, e.g., the just ( ).

31. Thus, Aristotle writes, "But Socrates did not make the universals or the definitions exist apart; they [the Platonists], however, gave them separate existence, and this was the kind of thing they called Forms" ( Met. 1078b30).

32. N.E. I.vi and E.E. I.viii.

33. Meno 74D.

34. I mean that there could be factors other than the nature of the objects of definition that make it difficult or impossible to define such objects. Such reasons may, for example, include our inability to express or formulate certain things, our ignorance, and so forth.

35. Whether what we demonstrate does not only follow necessarily from some other things but is also necessary is, of course, another matter (see below).

36. As I said earlier, most often Socratic definitions are indefinite but are meant to be universal in form. See the list of Socratic definitions in Santas, Socrates , ch. 4.

37. See on this matter J. Hintikka, "Time, Truth and Knowledge in Ancient Greek Philosophy," American Philosophical Quarterly 4 (1967), pp. 1-14, and A. Wedberg, "The Theory of Ideas," in G. Vlastos (ed.), Plato , vol. 1 (Garden City, N.J.: Anchor Books, 1971).

38. It is true that Socrates speaks at times precisely about this feature of some matters of conduct, that some properties of matters of conduct do not belong to them in all cases. Thus Socrates at Lathes 192C argues that endurance is not in all cases something noble, at Meno 87E that wealth is not always beneficial (see also the Euthydemus ). But in spite of this, it cannot be said that Socrates recognizes some feature of matters of conduct that other domains of inquiry do not presumably possess in the way Aristotle does. Socrates does not argne, in the way Aristotle does, that there is something problematic with the subject matter of ethics. Perhaps he did not see the implications of some of his observations or he did not generalize his isolated findings.

39. I have in mind here Socrates' remarks about the various arts or disciplines in the Charmides and Gorgias that focus on their subject matter and their goals.

40. Thus Socrates remarks at Meno 81A-B: "Thus the soul, since it is immortal and has been born many times, and has seen all things both here and in the other world, has learned everything that is. So we need not be surprised if it can recall the knowledge of virtue or anything else which, as we see, it once possessed. All nature is akin, and the soul has learned everything, so that when a man has recalled a single piece of knowledge . . . there is no reason why he should not find out all the rest." Considerable controversy, as is well known, surrounds the view presented by Socrates in the above words, and there is even doubt as to whether Socrates accepts the view expressed by them or only Plato does, or whether either of them does.

41. Plato, however, does not explicitly connect his claims that justification or proof may vary across disciplines to exactness, whereas Aristotle does.

42. I shall discuss Plato's remarks in the Philebus concerning the variation of exactness across disciplines in later chapters.

43. H. Cherniss, "The Philosophical Economy of the Theory of Ideas," in G. Vlastos (ed.), Plato , vol. I (Garden City, N.J.: Anchor Books, 1971).

44. See in this connection the discussion by J. Hintikka, "Time, Truth and Knowledge in Ancient Greek Philosophy," American Philosophical Quarterly 4 (1967), pp. 1-14; and his "Knowledge and Its Objects in Plato," and the comments of G. Santas, "Hintikka on Knowledge and Its Objects in Plato," both in J. M. E. Moravcsik (ed.), Patterns in Plato's Thought (Dordrecht: D. Reidel, 1973); also, N. P. White, Plato on Knowledge and Reality (Indianapolis: Hackett, 1976).

45. See the discussion by G. Vlastos, "Reasons and Causes in the Phaedo " in G. Vlastos (ed.), Plato , vol. 1 (Garden City, N.J.: Anchor Books, 1971).

46. My discussion on the Republic draws from recent commentaries on that work by N. P. White, A Companion to Plato's "Republic" (Oxford: Blackwell, 1979), and J. Annas, An Introduction to Plato's "Republic" (Oxford: Clarendon Press, 1981).

47. The term (or , often means more clear, but sometimes it means more exact or precise. Practically all translations take it to mean the latter in this passage. For more discussion on this term and its relation to other terms that signify exactness, see chapters 4 and 5.

48. At 548C, however, Plato writes: "Such, then, would be the origin and nature of this polity if we may merely outline [ ] the shape of a constitution in words and not elaborate it precisely [ ], since even the sketch will suffice to show us the most just and the most unjust type of man, and it would be an impracticable [ ] task to set forth all forms of government without omitting any, and all customs and qualities of men." Here Plato appears to be saying that the most exact (detailed) description is not needed, and that the difficulties with attaining the most exact ones are practical rather than logical. But even this passage should not be taken as clear evidence that Plato was concerned with the problems of the level of exactness required in disciplines whose goals are practical or the attainability of such levels. For in this passage he is more concerned with describing the degenerate forms of government than with providing a guide to action.

49. It is often said about Plato that the Forms are treated as if they are individuals. But this does not solve the difficulty at issue. It rather merely acknowledges that there is a difficulty in Plato's conception of the Forms, a conception that seems at times to treat Forms as being both universals and individuals.

50. Aristotle raises a number of objections against Plato's views of the Good in N.E. I.vi. The objections I am speaking of in relation to exactness/inexactness are those concerning the efficacy of knowledge of the Platonic Good for action, which we need to distinguish from the many other criticisms Aristotle raises against Plato's views. In particular, we need to distinguish Aristotle's question about the efficacy of our knowledge of the Platonic Good from the other question Aristotle often raises as to whether Plato's Good is the goal of anyone's practice.

51. Statesman 294Bff.

52. Statesman 295B, 297Aff.

53. It might be said in this connection that the problems Aristotle raises stem from the fact that he denies the existence of Platonic Forms. This is not, however, the problem For Aristotle denies Platonic Forms of everything, including those

of mathematical objects, and yet some disciplines deal, according to him, with subject matter that does exhibit essential structures.

54. Actually, much in Aristotle's account of demonstrative knowledge can, as J. Barnes has argued, be formulated independently of Aristotle's own logical theory; see his translation and commentary of the Post. Anal., Aristotle's Posterior Analytics (Oxford: Clarendon Press, 1975), pp. xiv-xv.

55. I am following tradition here and translate as knowledge. J. Barnes in his recent translation has, for good reasons, translated the term as understanding. This has allowed Barnes to differentiate easily between what is produced by demonstration, i.e., understanding, and what is produced by other modes of cognition, e.g., intuition. At times, however, Aristotle uses to refer to the various disciplines in general or to the various demonstrative disciplines, e.g., at 99a23.

56. I will return to some of these issues later.

57. See Post. Anal. 75a and J. Barnes's comments on this passage in his translation and commentary of this work.

58. For the role of definitions in Aristotle's conception of demonstrative science see the discussion of J. Barnes, op. cit. , pp. xi, 103, 109; M. Fetejohn, "Definition and the Two Stages of Aristotelian Demonstration," Review of Metaphysics 35 (1982-1983), pp. 375-395; and R. Bolton, "Definition and Scientific Method in Aristotle's Posterior Analytics and Generation of Animals ," in A. Gotthef and J. Lennox (eds.), Philosophical Issues in Aristotle's Biology (Cambridge: Cambridge University Press, 1987), pp. 120-166.

59. See on this matter the perceptive discussion of R. Bolton in his "Essentialism and Semantic Theory in Aristotle," The Philosophical Review 75 (1976), pp. 514-544.

60. See in this connection the commentary of J. Barnes on the Post. Anal. as well as his introduction, p. xi. The same view is put forth by M. F. Burnyeat in his "Aristotle on Understanding and Knowledge," in E. Berti, op. cit. , pp. 97-140.

61. Questions about the scope of Aristotelian essentialism have recendy been raised by W. Leszl, "Knowledge of the Universal and Knowledge of the Particular in Aristotle," Review of Metaphysics 26 (1972-1973), pp. 278-313, and N. P. White, "Origins of Aristotle's Essentialism," Review of Metaphysics 26 (1972-1973), pp. 57-85. D. M. Balme, "Aristotle's Biology Was Not Essentialist," in A. Gotthell and J. Lennox (eds.), Philosophical Issues in Aristotle's Biology (Cambridge: Cambridge University Press, 1987), pp. 291-312, has also argued that Aristotelian explanations in biology, especially those concerning the development of an animal, do not depend on essentialist views. The evidence I give from the treatises on conduct provides additional support for the view that Aristotle at some point began to question the scope of the kind of essentialism that Socrates, Plato, and at times he himself advocated.

62. See W. Jaeger, Aristotle (Oxford: Oxford University Press, 1948), pp. 228-258. The Protrept. , of which only fragments remain, is considered to be an early Aristotelian dialogue modeled after Plato's own dialogues.

63. C.J. Rowe, op. cit. , especially pp. 63-76.

64. D.J. Allan, "Quasi-mathematical Method in the Eudemian Ethics," in Aristote

et les Problemes de Metbode (Louvain: Publications Universitaires, 1961), pp. 303-318.

65. See H. D. P. Lee, "Place-names and the Date of Aristotle's Biological Works," Classical Quarterly 13 (1948), pp. 61-67, and "The Fishes of Lesbos," in A. Gotthelf (ed.), Aristotle on Nature and Living Things (Pittsburgh: Mathesis Publications, 1985), pp. 3-8; M. Greene, A Portrait of Aristotle (Chicago: University of Chicago Press, 1963); G. E. R. Lloyd, Aristotle: The Growth and Structure of His Thought (Cambridge: Cambridge University Press, 1968), pp. 19-41; G. E. L. Owen, "The Platonism of Aristotle," in P. E Strawson (ed.), Studies in the Philosophy of Thought and Action (Oxford: Oxford University Press, 1968).

66. I assume here that, contrary to Burnet's claims, the E.E. is a work of Aristotle. The chronological order of the Aristotelian ethical treatises has not, however, been settled to everyone's satisfaction. Among those who take the E.E. to precede the N.E. are Case, Jaeger, Dirlmeier, Gauthier, and more recently J. Cooper. But others, among them Schacher, Verbeke, and more recently A. Kenny, have argued that the N.E. precedes the E.E