1. I shall follow the practice of listing at the beginning of the appropriate chapters all the relevant remarks Aristotle makes on exactness in the ethical treatises, starting with those from the N.E . I will also append any relevant remarks from M.M ., although I shall not draw any conclusions that are based solely on them since the authenticity of this treatise remains in doubt. I shall number Aristotle's remarks by using a system that indicates by the first digit of the number assigned to a remark the chapter in which the remark occurs. This system will make it easier to refer to Aristotle's remarks throughout the various chapters of this study. At times, I will also number some other passages that I quote from Aristotle and Plato in order to facilitate subsequent reference to them.

Following standard practice, I shall refer to passages in Aristotle's works by identifying the appropriate Aristotelian treatise followed by a Bekker page (e.g., N.E . 1097a15). Occasionally, I refer to a portion of Aristotle's text by identifying the appropriate Aristotelian treatise followed by the book and chapter of that treatise which contains the text (e.g., N.E . 1.x). Where the identity of an Aristotelian treatise is obvious from the context, I omit identification of the treatise in referring to a passage. Again following standard practice, I refer to passages in Plato's works by identifying the appropriate Platonic work followed by a Stephanus page (e.g., Republic 602B).

2. Xenophon, Atheniensium Respublica , 1.5.3.

3. Euripides, Hippolytus , 460ff., 1115. For a discussion of the different aspects the ancients associated with exactness, see D. Kurz, AKRIBEIA (Goppingen: Verlag Alfred Kummerle, 1970).

4. A. Grant argues in his commentary on the N.E . that its method is demonstrative, that the investigation proceeds by giving deductions from a priori principles—see his The Ethics of Aristotle (New York: Arno Press, 1973), pp. 396-397. More recently, T. Upton in his "Aristotle's Moral Epistemology," The New Scholasticism 56 (1982), pp. 169-184, and A.M. Wiles in her "Method in The Nicoma- chean Ethics," The New Scholasticism 56 (1982), pp. 239-243, defend a view which

is quite similar to that of Grant. D. Keyt's reconstruction of Aristotle's derivation of the human good in the N.E. provides the best evidence for the use of the deductive method; see his "Intellectualism in Aristotle," in J. P. Anton and A. Preuss (eds.), Essays in Ancient Greek Philosophy , vol. 2 (Albany: State University of New York Press, 1983), pp. 364-387. H. D. P. Lee, in his "Geometrical Method and Aristotle's Account of First Principles," Classical Quarterly 29 (1935), pp. 113-124, argues that Aristotle's epistemological model is that of the axiomatic-deductive method we encounter in Euclid's works and that Aristotle's views influenced Euclid. That the inductive method is the method of Aristotle's own ethical investigation has been advocated by J. A. Stewart, Notes on the Nicomachean Ethics of Aristotle (Oxford: Clarendon Press, 1892), vol. 1, p. 48, and more recently by R. A. Gauthier and J. Y. Jolif, Aristote: L'Ethique a Nicomaque (Louvain: Publicationes Universitaires, 1970), vol. 2, pp. 19-20, and N. O. Dahl, Practical Reason, Aristotle, and Weakness of the Will (Minneapolis: University of Minnesota Press, 1984), pp. 70ff. And that the method is dialectical has been advocated by J. Burnet in his text of and commentary on the N.E., The Ethics of Aristotle (London: Methuen, 1900), p. v, L. H. G. Greenwood, Aristotle: Nicomachean Ethics, Book VI (Cambridge: Cambridge University Press, 1909), pp. 131-133, and H. H. Joachim, Aristotle, The Nicomachean Ethics (Oxford: Clarendon Press, 1962), p. 3. More recently, some version of the dialectical method has been defended by T. Irwin in his "Aristotle's Methods in Ethics," in D. J. O'Meara (ed.), Studies in Aristotle (Washington: Catholic University of America Press, 1981), his ''First Principles in Aristotle's Ethics," Midwest Studies in Philosophy , vol. 3 (1978), his translation and commentary of the N.E. (Indianapolis: Hackett, 1985), and his Aristotle's First Principles (Oxford: Oxford University Press, 1988), as well as by J. Barnes, "Aristotle and the Methods of Ethics," Revue Internationale de Philosophie 34 (1980), pp. 490-511. For some critical comments on the view that the method of ethics is dialectical, see W. F. R. Hardie, Aristotle's Ethical Theory (Oxford: Clarendon Press, 1968), pp. 32-45.

5. G. E. L. Owen, " Tithenai ta Phainomena ," in Aristote et les Problemes de Methode (Louvain: Publicationes Universitaires, 1961), pp. 83-103. For further discussion on the issues Owen raises, see M. Nussbaum, The Fragility of Goodness (Cambridge: Cambridge University Press, 1986), ch. 8, and T. Irwin, Aristotle's First Principles (Oxford: Oxford University Press, 1988). Irwin in the latter work distinguishes between strong and weak dialectic.

6. Of course, as Hardie, op. cit. , p. 36, has suggested, it is not obvious that we should be speaking of the method in ethics.

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

1. For the differences among practical, productive, and theoretical disciplines, see below.

2. See Eustratius, In Ethica Nicomachea I Commentaria , in G. Heylbut (ed.), Eustratii et Michaelis et Anonyma in Ethica Nicomachea Commentaria (Berlin: Reimer, 1892), p. 19; Aspasius, In Ethica Nicomachea Commentaria , in G. Heylbut (ed.), Aspasii in Ethica Nicomachea Commentaria (Berlin: Reimer, 1889), p. 7; and Heliodorus, In Ethica Nicornachea Paraphrasis , in G. Heylbut (ed.), Heliodori in Ethica Nicomachea Paraphrasis (Berlin: Reimer, 1889), pp. 4-5. See also the comments on these matters by J. A. Stewart, Notes on the Nicomachean Ethics of Aristotle (Oxford: Clarendon Press, 1892), vol. 1, pp. 26-27; J. Burner, The Ethics of Aristotle (London: Methuen, 1900), p. 11; A. Grant, The Ethics of Aristotle (New York: Arno Press, 1973), p. 427.

3. D.J. Allan, "Aristotle's Account of the Origin of Moral Principles," Actes du Xle Congress Internationale de Philosophie XII (1953), p. 124. By "practical reason" Allan understands ethics and, although he goes on to argue that practical reason is a type of knowledge, when he attempts to explain the difference between theoretical and nontheoretical disciplines he seems to disregard altogether the cognitive goals of ethics, which, Aristotle claims, are not any different from the cognitive goals of any other discipline—i.e., the attainment of truth (see below).

4. That Plato understands the transitivity principle in this way is also made evident in his discussion of friendship and love in the Lysis and the Symposium , where he again argues that we desire or love only the final object and that the only desire we have is that for the final object.

5. See N.E. 1094a where Aristotle states that the end of medicine is health, of shipbuilding a vessel, of economic management wealth, of strategy victory, and so forth (see also 1097a15 for similar claims). All of these arts are, according to Aristotle, subordinate to the political art or science—"Strategy, economic management, oratory, are subordinate to political science" (1094b3).

6. See Met. (1027a) where Aristotle argues that, although someone can produce health accidentally, there is a faculty or art (medicine) that is productive of health. Aristotle's views on this matter echo those of Plato in the Gorgias (464E-465E) and the Republic (438C-439). The view that medicine is to be differentiated from all other ways of producing or restoring health is defended in the treatise "The Science of Medicine" that is part of the Hippocratic writings. And as G. E. R. Lloyd observes, this view of medicine as a specific art or discipline evolved rather slowly in the Greek tradition. See his introduction to his edition of the Hippocratic Writings (London: Penguin Books, 1978), pp. 13-14.

7. I shall use the term "discipline" in the present context in order to avoid any commitment to a particular view of the epistemological character of medicine. I do not, for example, wish to assume that medicine is a demonstrative science like geometry.

8. See also Top. (141a10) where the definition of medicine as "science [ ] of matters of health for animals and humans" is criticized only on the grounds that the inclusion of humans in the definition is redundant since what the term "human" designates falls under or is included in what "animal" designates. That medicine is a science was the prevalent view in antiquity has been recently defended by M. Frede; see his ''Philosophy and Medicine in Antiquity," in A. Donagan, A. Perovich, Jr., and M. V. Wedin (eds.), Human Nature and Natural Knowledge (Dordrecht: D. Reidel, 1986), pp. 211-232.

9. W. F. R. Hardie, Aristotle's Ethical Theory (Oxford: Clarendon Press, 1968), p. 30.

10. D.J. Allan, op. cit. , p. 76. Allan in this discussion is quite critical of Jaeger's views on practical wisdom. Jaeger took Aristotle to be advocating the view that practical wisdom is solely concerned with the means and the particulars; see Jaeger, op. cit. , pp. 83, 84, 88, 242.

11. See also 1141b8: "Practical wisdom, on the other hand, is concerned with things human and things about which it is possible to deliberate; we say this is above all the work of the man of practical wisdom, to deliberate well."

12. See J. D. Monan, Moral Knowledge and Its Methodology in Aristotle (Oxford: Clarendon Press, 1968). Monan argues that the view of moral knowledge as theoretic in character is to be found in the Protrept. and that, with the exception of a few isolated passages in N.E. I and X, it is not to be found in the later treatises on conduct. Monan's discussion of the problems about practical wisdom and the views of Jaeger and Allan on its nature is most informative.

13. See his introduction to his commentary on the N.E., op. cit.

14. See D.J. Allan, op. cit. , pp. 73-75; also, W. F. R. Hardie, op. cit. , p. 30, and T. Ando, Aristotle's Theory of Practical Cognition (The Hague: Martinus Nijhof, 1971), especially pp. 21 Off., and J. D. Monan, op. cit. , pp. 48-59.

15. Julius Walter argues for the position outlined here in his Die Lehre yon der praktischen Vernunft in der Griechischen Philosophie (Jena, 1874), especially pp. 189-190, 537-555.

16. See R. A. Gauthier and J. Y. Jolif, Aristote: L'Ethique a Nicomaque (Louvain: Publicationes Universitaires, 1970), vol. 1, pp. 267-283.

17. D. Wiggins, "Deliberation and Practical Reason," Proceedings of the Aristo-

telian Society 76 (1975-1976), pp. 29-51; also R. Sorabji, "Aristotle on the Role of Intellect in Virtue," Proceedings of the Aristotelian Society 74 (1973-1974), pp. 107-129; M. Nussbaum, Aristotle's "De Motu Animalium" (Princeton: Princeton University Press, 1978), pp. 170ff.; and N. O. Dahl, Practical Reason, Aristotle, and Weakness of the Will (Minneapolis: University of Minnesota Press, 1984), pp. 73-83.

18. J. Cooper, Reason and the Human Good in Aristotle (Cambridge: Harvard University Press, 1975), pp. 19-22, 58-72.

19. T. Irwin, "First Principles in Aristotle's Ethics," Midwest Studies in Philosophy 3 (1978), pp. 252-272, especially 262-263. See also his comments in his translation of the N.E. Irwin, in fact, translates as "intelligence" instead of as "practical wisdom,'' "practical thought," "practical reason," or "prudence," and thus makes the connection to theoretical thought even closer.

20. N.E. X.vi-ix.

21. W. F. R. Hardie, op. cit. , p. 30, uses the passage just quoted (3.10) to support the view that Aristotle takes ethics and politics to be "an exercise of practical intellect." This, however, does not explain either what the nature of ethical inquiry is or how we are supposed to distinguish between the two kinds of practical wisdom Aristotle himself identifies in this passage.

22. For a discussion of this, see C.J. Rowe, The Eudemian and Nicomachean Ethics: A Study in the Development of Aristotle's Thought (Cambridge: Proceedings of the Cambridge Philological Society, 1971), especially pp. 63-73.

23. Or we make all deliberation similar to theoretical inquiry. This is done to some extent by T. Irwin who moves in this direction by making what he takes to be the type of reasoning ethical inquiry uses (i.e., dialectical) a part of deliberation (see T. Irwin, op. cit. , p. 262). But doing so, I think, obscures the contrast Aristotle wishes to draw between the two kinds of practical wisdom.

24. That practical wisdom is concerned with the universal is one of the reasons Teichmüller gives for equating it with ethical inquiry. But he understood practical wisdom in the wide sense; he took it to be not much different from theoretical inquiry. See G. Teichmüller, "Die praktische Vernunft bei Aristoteles," Neue Studien zur Geschichte der Begriffe , vol. 3 (Gotha, 1879).

25. For although deliberation resembles other kinds of reasoning, even theoretical reasoning, it is important not to obscure the difference.

26. On at least two occasions (1142a25, 1143b5) Aristotle argues that the particulars are known by perception or intuition ( ). But even if we were to construe the reaching of particulars as a kind of deliberation, there still would be the parts of ethics dealing with the universal aspects of conduct.

27. This term may mean either "inquiry" or "method." Although in the passages I cite here it means the former, Aristotle uses it at times to mean the latter (see chap. 9 for a discussion of this matter).

28. Concerning the similarities between medicine and ethics, see D. S. Hutchinson, "Doctrines of the Mean and the Debate Concerning Skills in Fourth-Century Medicine, Rhetoric and Ethics," in R.J. Hankinson (ed.), Method, Medicine and Metaphysics: Studies in the Philosophy of Ancient Science (Edmonton: Academic Printing and Publishing, 1988).

29. This line of argument has been taken by several commentators. Thus, Burnet,

op. cit. , p. 257, and Stewart, op. cit. , vol. 2, p. 35, take Aristotle to be restricting the application of the term "knowledge" only to disciplines that deal with that which is necessary. And when he applies it to disciplines like medicine Aristotle is, according to this view, using the term rather loosely. A similar position is put forth by Greenwood, op. cit. , pp. 150-152, where he argues that the term "knowledge" or "science" is used in the N.E. "in the loose sense of 'art', 'practical science', sometimes almost 'profession', which is the popular usage.'' And he refers to 1138b26 where Aristotle calls medicine a science, but claims that " in the strict sense has nothing to do with it."

30. W. F. R. Hardie, op. cit. , p. 31.

31. See Aristotle's remarks on the highest science among theoretical sciences, i.e., the one that deals with the highest genus, as well as his claim, "For not even the mathematical sciences are all alike in this respect—geometry and astronomy deal with a certain particular kind of thing, while universal mathematics applies alike to all" ( Met. 1026a; see also 1064b).

32. See, for example, the uses that, according to Plato, pure geometry has in warfare and the upbringing of the young ( Republic 527B).

33. See Aristotle's discussion at Met. 1025b25ff. and 1064a10. When Aristotle speaks of movement most often he means change in general and not only locomotion.

34. "Mathematics also, however, is theoretical; but whether its objects are immovable and separable from matter, is not at present clear; still, it is clear that some mathematical theorems consider them qua separable from matter" ( Met. 1026a7). But at 1064a32 we are told: "Mathematics is theoretical, and is a science that deals with things that are at rest, but its subjects cannot exist apart."

35. Thus, Aristotle writes at Met. 1064a33, "Therefore about that which can exist apart and is unmovable there is a science different from both of these [i.e., from physics and mathematics], if there is a substance of this nature (I mean separable and unmovable), as we shall try to prove there is."

36. "While in the case of things done it [movement or rest] is in the doer" ( Met. 1025b25; see also E.E. 1223a5 and the rather elaborate discussion of the differences in the sources of motion or change that is due to nature and is internal, and of change that is in something external to what moves or changes at Phys. II.i).

37. Plato, as is well known, insists that there are different faculties that correspond to different types of cognitive activities and objects. The distinction between knowledge and belief in the Republic rests partly on such a claim.

38. See Met. 995a15 and the discussion in chapters 6 and 7 below.

39. Thus, Aristotle claims that the subject matter of physics is inexact but physics is nonetheless a theoretical discipline ( Met. 1025b26, 1026a7, 1064b).

40. J. Rawis, A Theory of Justice (Cambridge: Harvard University Press, 1971), p. 121, also p. 126. I take Rawls in this context to be saying that the interest in a moral geometry is a theoretical one. He certainly gives no indication that moral geometry is required by or is to be used for some practical end. Of course, others have denied that there is any knowledge whose goals are purely theoretical in the way Plato, Aristotle, and possibly Rawls claim they are.

41. See Aristotle's discussion of the architectonic structure of desires or pursuits

at N.E. I.i. We need to assume here that A is different from B and that the relation is relativized to some one agent, since it is quite possible that, while some agent desires A for the sake of B, some other agent desires B for the sake of A. See on this last point the discussion by B. Williams, "Aristotle on the Good: A Formal Sketch," The Philosophical Quarterly , vol. 12, no. 40 (1962), pp. 289-296. Of course, I am not here endorsing Aristotle's claim concerning the supposed asymmetry of the relation of subordination.

42. G. E. R. Lloyd (ed.), Hippocratic Writings (London: Penguin Books, 1978), p. 71.

43. H. H. Joachim, op. cit. , p. 16.

44. This would, of course, imply that several theoretical disciplines whose subject matter or accounts exhibit the kind of inexactness that ethics and its subject matter exhibit will also be nondemonstrative.

1. The forms that are most frequently used are the following: , (adjectival form, N.E. 1094b13, b24, Met. 1053a); , (the comparative and superlative of the adjectival form, E.E. 1231b2, N.E. 1106b14, 1107b15, 1141a9, a16); (adverb, N.E. 1104a2, 1146b25, 1164b28, 1180b17); (verb form, G.A. 778a6, Meteor. 363b32). Also the compound verb forms ( E.E. 1227a1, N.E. 1178a23), ( N.E. 1096b30, 1101b34, 1102a25, 1175a31, b14, 1180b11, H.A. 583a30) and ( N.E. 1139b17, Cael. 306b27, Polit. 1258b34, Rhet. 1369b1). Finally, ( H.A. 513a9, Met. 959a15, Polit. 1341b30, Rhet. 1361b34).

2. See , N.E. 1108a17, Top. 157a14; , G.A. 769a35; , Anim. 413a10, Phgn. 213a4; , Met. 986b4, 993a22, Cael. 303a9; , Met. 986b29, 1035b3, Cael. 286b5, PA. 692a15, N.E. 1144a21; , P.A. 647a33, TOP . 140b5, Met. 986b22; , Anim. 414b29, 416b29, N.E. 1108a18.

3. J. Barnes in his commentary on the Post. Anal. (Oxford: Clarendon Press, 1975) refers to the above passage from the Top. and claims that Aristotle glosses the term by (p. 182). I assume that Barnes means that Aristotle takes the two terms to be used at times to signify the same thing(s). That is, that the gloss is a proper one.

4. See also Polit. 1341b31, Top. 101a22, Mund. 397b12 for similar contrasts.

5. The term occurs most frequently in the dative as : Anim. 413a9, 416b30, 424a16, N.E. 1094a25, b20, 1101a27, 1104a1, 1107b14, 1113a13, 1114b27, 1117b21, 1176a31, H.A. 487a12, Met. 1029a7, Polit. 1276b19, 1302a19, 1335b5, Top. 101a22, 103a1. But also in the following forms: , N.E. 1179a34; , Polit. 1341b31; , P.A. 676b9; , Cat. 1b28, 11b20, Probl. 916a35, Top. 101a18, 103a7, 105b19; , N.E. 1129a11, H.A. 491a8, Polit. 1323a10.

6. The term occurs primarily in the phrase (to speak in summary): Anim. 433b20, N.E. 1109b11, Phys. 216a7, Polit. 1312b34, Probl. 955a28, Rhet. 1360b5. In a few instances it occurs as an adverb, (summarily): Met. 958a17, Rhet. 1415b7, 1419b31.

7. But Lidell and Scott, A Greek-English Lexicon (Oxford: Clarendon Press), correctly point out that the term is used at times as opposite of .

8. See also Mund. 397b10.

9. See also M.M. 2.1.1.5, "those things the law giver is unable to define exactly [ ] for each case, but lays down general rules [ ]."

10. J. Barnes, Aristotle's Posterior Analytics (Oxford: Clarendon Press, 1975), p. 182.

11. The idea of certainty that Barnes takes to be the common element uniting the various uses of seems to be more related to and the older adverbial form (clearly, plainly, assuredly). When used with verbs of knowing or speaking signifies something like "clearly" or "with certainty" (see Homer, Odyssey II.31; Pindar, Olympian. 8.46). Aristotle himself uses the adverbial form with verbs of speaking or saying ( Met. 989b18, 993a22) but the context makes it clear that most often certainty is not what is at issue in such cases. ' is most likely used to mean something like "certainty" where Aristotle contrasts the term in one of its grammatical forms to . As pointed out earlier, the term seems to mean something like "certainty" or "necessity'' when used in relation to proofs or arguments.

12. See Grant's discussion, The Ethics of Aristotle (New York: Arno Press, 1973), pp. 392-393, 452.

13. I have in mind here Plato's discussion of the Good in the Republic where he seems to suggest that the Good is the cause of the existence and essence of all there is and that all knowledge depends in a way on knowledge of the Good. To be sure, these are some of the most cryptic remarks in the Platonic corpus and seem to defy any interpretation. The most important recent discussion on the Good in the Republic is to be found in G. Santas, "The Form of the Good in Plato's Republic," Philosophical Inquiry , vol. 2, no. 1 (1980). Santas concentrates on what he considers to be one function of the Good in Plato's account—e.g., that its nature determines some formal features of the Forms. But it is not clear that this is the sole function the Good has in Plato's scheme of things.

14. Yet at Met. 982b5 Aristotle remarks: "And the science which knows to what end each thing must be done is the most authoritative of the sciences, and more authoritative than any ancillary science; and this end is the good of that thing, and in general the supreme good in the whole of nature. Judged by all the tests we have mentioned, then, the name in question falls to the same science; this must be a science that investigates the first principles and causes; for the good, i.e., the end, is one of the causes." The science however which, according to Aristotle, is most authoritative and investigates the first principles and causes is not ethics. It is metaphysics or first philosophy. The good this science investigates is not anything practicable, but it is what pertains to action on the other hand that ethics investigates.

15. Traditionally, metaphysics or first philosophy has been thought to be not like the ordinary Aristotelian disciplines or sciences. But M. Frede has recently argued that the study of being qua being and the study of the supreme being form a discipline or science that does not differ much from the typical Aristotelian

disciplines, e.g., mathematics or physics; see his Essays in Ancient Philosophy (Minneapolis: University of Minnesota Press, 1987), ch. 6.

16. See T. Irwin's discussion of these matters in his "The Metaphysical and Psychological Basis of Aristotle's Ethics," in A. Rorty (ed.), Essays on Aristotle's Ethics (Berkeley and Los Angeles: University of California Press, 1980), and "First Principles in Aristotle's Ethics," Midwest Studies in Philosophy , vol. 3 (1978), p. 261.

17. For a recent discussion of the relation of ethics to politics, see J. Cooper, Reason and Human Good in Aristotle (Cambridge: Harvard University Press, 1975), especially p. 108. See also L. H. C. Greenwood, Aristotle: Nicomachean Ethics, Book VI (Cambridge: Cambridge University Press, 1909), pp. 60ff., and T. Irwin, "First Principles in Aristotle's Ethics," op. cit. , p. 258.

18. I have in mind here Aristotle's remarks at N.E. 1094b25 where he claims that there are differences in exactness between mathematics and rhetoric, the rest of the disciplines falling somewhere between these two; and the remarks at 1098a27 where he indicates that there is an exactness appropriate to the inquiry. The supposed inexactness of ethics is not however connected to the number of basic elements making up the subject matter of ethics. It is not connected to its simplicity or lack of it.

19. Aristotle's language makes it clear that we should in all cases do as ( ) the arithmetician and geometer do. We should use the mathematicians as examples of the way to abstract rather than of what to abstract.

20. Ross in his commentary on the Met. (Oxford: Oxford University Press, 1958), vol. 2, p. 417, says that since geometry abstracts from maguituide, it is above solid geometry, solid geometry is above all sciences of motion, astronomy is above sublunary kinetics, which studies noncircular movement, and still more above biology, which studies generation and corruption.

21. See Barnes, op. cit. , p. 182. The term occurs in three other places in Aristotle's writings, leaving aside the occurrence at N.E. 1122b7 where it is used to signify a type of vice that is contrasted to magnificience. In all these three occurrences it seems to mean something like "detailed" or "elaborate" treatment of a subject: e.g., a detailed treatment of the nature of blood vessels ( H.A. 513a9), a detailed discussion of the study of music ( Polit. 1341b29), a minute examination of what constitutes a happy old age ( Rhet. 1361b33). Commenting on the passage from the Met. that speaks of , Alexander of Aphrodisias in his commentary on the Met. takes the term to signify something like concern with detail, or minutiae ( , see In Aristotelis Metaphysica Commentaria 168.3).

22. Thus, at Met. 1039b27 Aristotle claims that "there is neither definition nor demonstration about sensible individual substances, because they have matter whose nature is such that they are capable both of being and of not being . . . . If then demonstration is of necessary truths and definition is a scientific process—clearly there can neither be definition of nor demonstration about sensible individuals."

23. But see below for Aristotle's claim that some properties of the good are to be proven by the mathematical sciences.

24. In the case of some of these disciplines, e.g., optics, Aristotle identifies a

level that is purely mathematical. But he identifies no such level in the case of biology. See below for a discussion of these matters.

25. And these disciplines (i.e., physics, biology, and optics) are, according to Aristotle, bona fide sciences.

26. That knowledge or understanding consists in giving explanations and determining the causes of things and that these in turn are explicated in terms of demonstration is argued for in Post. Anal. I.ii; see also Phys. 194b20, Met. 1025b, 1064a5. Aristotle of course recognizes other types of knowledge, e.g., intuition. But he restricts intuition to a grasp of the first principles of science which cannot be demonstrated. Intuition is not scientific or demonstrative knowledge; see for a discussion of these matters, M. F. Burnyeat, "Aristotle on Understanding Knowledge," in E. Berti (ed.), Aristotle on Science (Padova: Editrice Antenore, 1981), pp. 97-139.

27. But as Barnes, op. cit. , p. 154, has pointed out, Aristotle's own treatment of the rainbow is one of the most mathematically sophisticated parts of his corpus. This view is shared by T. L. Heath, Mathematics in Aristotle (Oxford: Oxford University Press, 1949), pp. 180-190.

28. Aristotle characterizes again H.A. as a desciptive discipline that is not concerned with causes at P.A. 646a8 when he writes, "I have already described with considerable detail in my Researches on Animals what and how many are the parts of which the various animals are composed. We must now leave on one side what was said there, as our present task is to consider what are the causes through which each animal is as I there described it." D. M. Balme, however, has recently questioned the view that the H.A. is a purely descriptive or nonexplanatory inquiry. Although he claims that it is Aristotle's "nearest approach to a descriptive collection of data, and it is very wide and perceptive," this is not the only aim of Aristotle's treatise. Balme claims that it is in part concerned with causes and there is evidence that portions, or perhaps all, of H.A. is later than the other biological treatises which have always been taken to provide the explanations of the phenomena described in it; see his "Aristotle's Use of Differentiae in Zoology," in J. Barnes, M. Schofield, and R. Sorabji (eds.), Articles on Aristotle (London: Duckworth, 1975), vol. 1, pp. 183-193. Balme may be right about the nature of H.A. , but this does not affect the point I wish to make: namely, that Aristotle distinguishes between descriptive and explanatory disciplines, and in fact characterizes some of his own investigations as being purely descriptive.

29. See W. D. Ross's commentary on the Post. Anal. (Oxford: Oxford University Press, 1965), p. 555, and Heath, op. cit. , pp. 58-61. See also Barnes's comments, op. cit. , p. 154, for an example of how premises from purely mathematical and observational disciplines are used to produce a demonstrative syllogism.

30. The best recent discussion of Aristotle's views on the relation of subordination among sciences is to be found in Barnes's commentary, pp. 151-155.

31. W. D. Ross, commentary on Post. Anal. , p. 555.

32. See Barnes, op. cit. , p. 154. The problem here stems partly from the fact that Aristotle recognizes no other type of explanation than the demonstrative one. There are no inductive explanations. But even if there were other types of explanations, it would not resolve the problem. For Aristotle's distinction seems to be

between explanatory and nonexplanatory disciplines. It is not the case that the latter disciplines offer explanations that are different from the demonstrative ones. They offer no explanations at all.

33. We are likely to disagree with Aristotle's claims about the possibility of children, as well as animals, being happy. Our disagreement stems partly from the fact that our conception of happiness is not exactly Aristotle's conception. But this, of course, does not affect the point under discussion: namely, that Aristotle sees his task as being partly to give explanations of what he takes the facts to be.

34. See for a discussion of this matter M. F. Burnyeat's remarks in "Aristotle on Learning to Be Good," in A. Rorty (ed.), op. cit. , pp. 71-72, and T. Irwin's comments in his translation of the N.E. While it is true that Aristotle claims at 1095b4-8 that the starting point of our investigation is the fact and what is known to us, this is not the end of ethical inquiry. Its aim is to explain the facts or to give the "causes." In speaking of causes in the present context, I do not mean to assert that Aristotelian causes are exactly the sorts of things we designate as causes. This has been pointed out by several scholars recently—Barnes, Burnyeat, Moravcsik, Sorabji. But this, of course, does not exclude the possibility that some Aristotelian causes are causes in the way we most often understand causes—namely, as efficient causes.

35. Thus, Aristotle remarks at Met. 1078a31: "Now since the good and the beautiful are different (for the former always implies conduct as its subject, while the beautiful is found also in motionless things), those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or their definitions, it is not true to say that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree."

36. This is of course not to say that Aristotle does not raise the question of exactness/inexactness in relation to second-order disciplines. He does raise such questions in the case of the logical treatises, including Rhet. and Top. Disciplines such as the logical ones have often been viewed as not being first-order disciplines.

37. Plato also speaks of the fairest and most exact ( )of material things ( Republic 529D).

38. The root of this term means "load" or "burden." Although it retains in part this meaning, Aristotle uses it often to signify the "coarse," "common," or "vulgar'' (see Polit. 1340b8, 1341b11; Rhet. 1395b1; Poet. 1462a4).

39. Thus, Alexander of Aphrodisias in his commentary on the Met. : "It even seems to some illiberal to demand in arguments [or accounts] exactness in excess and examination of little things, as is the case in exchanges" ( In Aristotelis Metaphysica Commentaria , 168.9).

40. Aristotle uses distinct terms to name the disposition and the person who has the disposition or corresponding character—for example, irascibility ( ) vs. irascible person ( ), rashness ( ) vs. rash person ( ), and

41. At E.E. 1233b20 Aristotle says that the emotion corresponding to the un-

named extreme is also unnamed. But the character is given as that of the malicious person ( ). At N.E. 1108b2 "malice" ( ) is given as the name of the extreme that in the E.E. is nameless.

42. Aristotle gives the name "insensitiveness" ( ) to this unnamed extreme (1221a) and calls the corresponding character, which he says happens to have no name, "insensitive" ( —N.E. 1107b7). But he probably finds these names too wide, for they suggest lack of sensation in general and not only in relation to pleasures.

43. See also E.E. 1231a35 for a statement of the same claim.

44. See H.A. where Aristotle says that the following lack names: the part in which touch has its natural place (489a17); the groups that have dermatous or membranous wings (490a12); the soft-shelled animals (490b10); some kinds included in the group of viviparous quadrupeds (490b31); one part of the ear (492a14); the outer surface of the hand (494a2); the upper part of the foot (494a2); and for more unnamed things see 505b29, 515b9, 525b5, 552b30, 553a1, 623b5. In the P.A. see 642b15, 644b4, 669b10, 678a9, 680a14, 683b23.

45. Among recent translators and commentators, T. Irwin has most clearly recognized the importance of Aristotle's remarks on the nameless dispositions. He correctly recognizes that an examination of the nameless dispositions is necessary for saving the validity of Aristotle's thesis even in the cases where the lack of names may suggest that the thesis is false—see T. Irwin, Aristotle: Nicomachean Ethics (Indianapolis: Hackett, 1985), p. 315. We must keep in mind, however, that Aristotle himself recognizes that "not every action or emotion however admits of the observance of a due mean." Aristotle gives the cases of malice, shamelessness, envy, adultery, theft, and murder as cases that do not admit of the mean (1107a10; see also E.E. 1221b20).

46. I agree with Irwin in adding "only" to the text, for without it Aristotle's statement makes little sense. Most translations make no such addition.

47. Aristotle insists that in all cases the mean is to be praised: "In order to discern better that in all things the observance of the mean is to be praised, while the extremes are neither right nor praiseworthy, but reprehensible" (1108a15), "it is the mean disposition that is to be praised" (1109b23), "the mean disposition is praiseworthy . . . while the various forms of excess and defect are blameworthy" (1126b5, also 1126b17).

48. At 1108b15 he writes concerning the apparent opposition between the mean and the two extremes: "So the middle states of character are in excess as compared with the defective states and defective as compared with the excessive states, whether in the case of feelings or actions. For instance, a brave man appears rash in contrast with a coward and cowardly in contrast with a rash man; similarly a temperate man appears profligate in contrast with a man insensible to pleasure and pain, but insensible in contrast with a profligate; and a liberal man seems prodigal in contrast with a mean man, mean in contrast with one who is prodigal."

49. Bonitz goes a step further and claims that in this occurrence is synonymous with (easiness of comprehension). This seems unlikely to me.

50. In a more problematic passage at Anim. 418a Aristotle writes, "But since

there are no names [ ] for the differences [in potentiality], and we have now explained that there are differences and how they differ, we must continue to use 'to be acted upon' and 'altered' as though they were ordinary [ ] names." Some translations, e.g., W. S. Hett in the Loeb Classical Series, take to mean something like "precise" and Aristotle to be concerned with using nonprecise terms to make a difference that is not marked. It is true that the terms, as Aristotle points out, do not mark the two types of potentiality he distinguishes. In that sense they are imprecise. But this term , as most translators recognize, when applied to names signifies something like "actual," "current,'' or "ordinary."

51. The instructional role of the Aristotelian treatises and of the demonstrative method in general has been most clearly recognized by J. Barnes. He gives some of the strongest arguments in support of the position that not only has the demonstrative method instructional uses but that instructional use is its sole purpose. I find Barnes's arguments quite convincing as far as the former claim is concerned but I remain unconvinced about the latter; see J. Barnes, "Aristotle's Theory of Demonstration," Phronesis 14 (1969), pp. 123-152.

52. The passages quoted above, stressing the role that the data familiar to us ( ) play in relation to investigation or inquiry, emphasize the method of inquiry that Aristotle at times refers to as the dialectical method. These passages raise important substantive issues about the elements used as starting points of investigation. This and related matters have been discussed recently by J. Barnes, "Aristotle and the Methods of Ethics," Revue Internationale de Philosophie 133-134 (1980), pp. 490-511; T. Irwin, "First Principles in Aristotle's Ethics," in op. cit. , pp. 257-259, "Aristotle's Methods in Ethics," in D.J. O'Meara (ed.), Studies in Aristotle (Washington: Catholic University of America Press, 1981), pp. 194-201, and his translation of and commentary on the N.E. , p. 398.

53. Some translators and commentators doubt that Aristotle is referring to a separate treatise on food. R. D. Hicks in his commentary on the Anim. (Amsterdam: A. M. Hakkert, 1965), p. 349, argues that most probably Aristotle is referring to such a treatise. A reference to such a treatise is also made at G.A. 784a2 when Aristotle writes, "A more detailed account of this cause [food] will be given in the treatise Of Growth and Nutrition [ ]."

54. For Aristotle's own discussion of encomia, see Rhet. I.xxxiii, xxxiv.

55. See also 1102a25: "The student of politics therefore as well as the psychologist must study the nature of the soul, though he will do so as an aid to politics, and only so far as is requisite for the objects of inquiry that he has in view: to pursue the subject in greater detail would doubtless be more laborious than is necessary for his purpose."

56. See also Anim. 402a for the claim that some knowledge is more valuable because it is of better and more wonderful things and N.E. 1141b for the claim that wisdom, the most exact knowledge, is knowledge of the things that are most honorable in nature.

57. Thus, Plato writes at Timaeus 29 B-C: "Our world must necessarily be a likeness of something . . . concerning a likeness, then, and its model we must make this distinction: an account is of the same order as the things which it sets forth—an account of that which is abiding and stable and discoverable by the aid of reason

will itself be abiding and unchangeable . . . while an account of what is made in the image of that other, but is only a likeness, will itself be but likely" (translated by F. M. Cornford); see also Republic 511E.

58. I owe this example to Professor Charles Young.

1. See also M.M. 1.5.1.3, 1.34.3.2, 1.4.10.4, 1.12.1.5, 1.13.4.4.

2. There are two more occurrences of the term in the N.E. (1094b20 and 1104a1), which I will discuss in later chapters. For even though the term is used in these occurrences to mean in part something like lack of detail or being only an outline, it also means something different.

3. The term , in a variety of forms and embedded in different phrases, is also used quite frequently by Plato (Republic 403E, 414A, 491C; Laws 718C) to mean the same thing it means in Aristotle. Its original meaning (i.e., an impression or imprint) is also in part preserved in the way Plato uses it (see also Liddell and Scott, A Greek-English Lexicon ).

4. See Liddell and Scott, op. cit. , for the meaning of .

5. It is worth noting here that the term does not occur at all in the E.E. And we also see that the number of times the other terms that signify the same kind of inexactness occur in the E.E. is considerably lower than that of their occurrences in the N.E. or Polit. Is there any significance to this? Perhaps there is. It may indicate that Aristotle places a greater emphasis on the practical nature of ethics. As we shall see below, in many cases Aristotle locates the source of the inexactness under consideration here in the goals of ethics. He, thus, often characterizes his accounts as inexact because they fail to meet the level of detail or specificity that he thinks is required by the practical goals of the discipline. The difference, then, between the number of occurrences of the terms signifying this type of inexactness in the E.E. and that in the N.E. may very well indicate a difference between a predominantly theoretical and a more practical conception of ethical inquiry.

6. What Aristotle says in this remark seems to be somewhat puzzling. Its context, being that of describing various aspects of the physical plan of the ideal city, suggests that the exactness Aristotle considers useless is detail in the description of these aspects. His use of —detail, concern with minutiae—supports this. Yet Aristotle, in claiming that such exactness is useless, contrasts the difficulty of practice relating to the physical plant to the presumed easiness of understanding or explaining ( ) whatever relates to it. Thus H. Rackham, in his translation of the Polit. , sees the contrast as being between theory and practice (Loeb Classical Library, p. 595). Is the inexactness Aristotle is willing to forego a deficiency in descriptive detail or in (theoretical?) explanation and understanding?

7. Thus Aristotle anticipates J. Cooper's complaint when the latter criticizes the functional account of the good in the following way: "Now what is disappointing about this argument . . . is that it is too abstract to be informative. It tells at most only that the excellences, whatever these may turn out to be, are the essential condition of a flourishing life, but if one is in doubt . . . then the abstract statement

in Aristotle's conclusion is not very interesting or helpful," Reason and Human Good in Aristotle (Cambridge: Harvard University Press, 1975), p. 145. Aristotle seems to be quite clear about the purposes and limitations of his account of the good from function and the relation among function, the good, and the excellences. But these limitations of Aristotle's argument from function and its conclusions do not render the argument of no interest or help. For the argument aims at providing the theoretical account of the good and its relation to the excellences that forms the foundation of the subsequent discussion in the N.E. This theoretical framework needs to be elaborated upon, but it is by no means of no interest or help.

8. For the role definitions play in Aristotelian demonstrations, see Post. Anal. and our discussion in chapter 2: Definitions are some of the basic propositions from which, together with the axioms and common principles, the various properties that belong to a kind are demonstrated or proved to belong to the kind.

9. The use of ge to modify at 1094a25 (5.1) adds support to the idea that inexact accounts may be sufficient for Aristotle's purposes: we should try to attain accounts that are at least in outline. But it also suggests that this is all that can be expected in such contexts: we should try to attain an account of the good even though it will be inexact.

10. This is a rather obscure passage in which Aristotle claims that accounts of the particulars are more inexact than those of the more general or universal aspects of conduct. I shall discuss this matter in a later chapter (8), but it is clear that the type of exactness/inexactness Aristotle has in mind in this passage cannot be the one we have isolated in this chapter—detail or specificity/lack of detail or generality. For Aristotle says that the accounts of particulars are more inexact than the ones of the general or universal aspects of matters of conduct.

11. The example Aristotle uses can be very easily interpreted as meaning the particular in the strict sense. It is the sort of thing one can learn from experience of particular instances. I agree, however, with Irwin here that what Aristotle contrasts in this passage is knowledge of general types to knowledge of more determinate types (see Irwin's comments on this passage in his translation of N.E. , p. 343). But there are, as Irwin points out, passages where it is not clear what Aristotle means when he speaks of particulars (p. 418).

12. Aristotle: The Nicomachean Ethics (Cambridge: Loeb Classical Library, 1962), p. 120. The best discussion on Aristotle's views regarding the ontology of actions is to be found in D. Charles, Aristotle's Philosophy of Action (Ithaca, N.Y.: Cornell University Press, 1986).

13. Although Aristotle does not explicitly discuss this, both types of actions consist of action-tokens or spatio-temporally located individuals. For with both types, and regardless of what they deal with, we can at least specify the agent, place, and time.

14. Actually, what Aristotle writes here is that the physician does not study the health of the species man ( ), but that of the individual.

15. Aristotle, as Plato did earlier, is at times concerned about the difficulty law presumably has in reaching what he considers to be the required level of detail. See, for example, N.E. V.x, Polit. II.vii, and Rhet. I.xiii. 11-14. Plato discusses this problem in both the Republic and Statesman .

16. There is somewhat of a problem in determining with certainty what Aristotle means when he says about the accidents of life that "to distinguish between them in detail [ ] . . ." Some translators take him to be concerned with distinguishing each individual accident, while others with distinguishing the various types of accidents. Thus, W. D. Ross, "to discuss each [event] in detail . . .," H. G. Apostle, ''to discuss each [fortune] of them individually. . ."; but H. Rackham, "to distinguish between them [the accidents] in detail . . .," T. Irwin, "to differentiate all the particular cases [of fortunes] . . ." In all probability Aristotle is not speaking of the individual accidents, events, or misfortunes. The term in this occurrence probably means the more specific. And the use of (divide, distinguish) makes it more likely that he is thinking of distinguishing the various types of accidents, dividing them into smaller classes in terms of some distinguishing feature that each class possesses. A discussion of the accidents of life that distinguished the various types or divided them into smaller classes would be less general and in outline than one that did not but instead spoke in general about them, or did not distinguish the various types at all or sufficiently, or did not divide them into classes at all or not far enough. What Aristotle goes on to do after he tells us that a detailed account of the accidents of life is not possible, and that one that is in outline may be sufficient, confirms this interpretation. Aristotle proceeds to distinguish the various misfortunes or divide them into smaller classes in terms of some of their features: for example, their weight and influence on our lives, the relation the person to whom they happen has to us (e.g., whether they happen to our friends), and so forth. Such an account can, however, fail to be exact by not reaching some desired level of specificity—hence Aristotle is correct in viewing his own account as one that is in outline only.

17. See Post. Anal. I.viii and the comments of W. D. Ross and J. Barnes on this chapter in their respective commentaries. Ross takes Aristotle to be saying that "we do not strictly prove that or explain why the moon is eclipsed, because it is not an eternal fact that the moon is eclipsed but only that which has an opaque body interposed between it and its source light is eclipsed; the moon sometimes incidentally has the latter attribute because it sometimes incidentally has the former." Yet in his comments on I.xxxi, where Aristotle argues that perception does not give us demonstrative knowledge, Ross writes "but the principles thus grasped [by intuitive induction] may become premises from which the particular facts may be deduced." But Aristotle need not necessarily be speaking here of demonstration of particular facts, if what is meant are individual occurrences. What he seems rather to be concerned with is proving or showing that the nature of the phenomenon of the eclipse of the moon in general is such and such, which is of course a more particular case of the even more general phenomenon of interposing an opaque object between another object and the latter's source of light. And knowledge of the wider universal (knowledge of the eclipse) may provide us with the means of showing what the nature of the narrower universal (the eclipse of the moon) is.

18. Aristotle often concludes a topic of discussion in the biological treatises by indicating that the account he has just given is complete, and thus without suggesting that it is in some way or other inexact: "I have now described the arrange-

ment of the external parts" ( H.A. 494b20), "We have now given a description of the parts, both internal and external, of man . . ." (497b), "We have now described blood-vessel, sinew, and skin; fibres and membrane . . ." (519b25; see also 527a35, 527b35, 538b28, and so on). And where he indicates that his account of some phenomenon is inexact and refers us to another treatment that is presumably more exact the latter may not provide any greater detail. See, for example, his treatment of menstruation at G.A. I.xx, which Aristotle finds inexact (728b13). He refers us there to a more exact treatment of the topic in H.A. But the treatment of this topic at H.A. 572b29ff. does not provide an account that is significantly more exact.

19. J. Lukasiewicz, Aristotle's Syllogistic (Oxford: Clarendon Press, 1967), p. 2

20. Met. 1026b10. At Post. Anal. 75b15 Aristotle writes about accidental attributes of geometrical objects: "Nor can geometry prove that anything belongs to lines not as lines and as from their proper principles—e.g., whether the straight line is the most beautiful of lines or whether it is the contrary to the curved."

21. See Post. Anal. 79a15. As I said earlier, it is not clear that there is a geometrical proof of this proposition.

22. As we saw above, at N.E. 1107a30 Aristotle claims that the accounts "that are more specific are more true, since actions deal with particulars and our accounts must agree with them."

23 I am not, of course, saying that there are no problems with following rules or applying general statements to particulars. As Wittgenstein has pointed out, there are many problems with the most common explanations we give of how we understand, follow, or apply any rule. Yet I am not convinced that Aristotle's problems are, as J. McDowell has argued, the skeptical problems Wittgenstein has raised about rule-following; see J. McDowell, "Virtue and Reason," The Monist , vol. 62, no. 3 (1979).

1. In 6.2 Aristotle says that we should be content ( ), when dealing with subject matter that is for the most part, with conclusions that are of the same kind. Aristotle does not mean merely that we should be satisfied when we reach a certain level of exactness, but rather that, given the nature of the subject matter, a high degree of exactness is not possible. We should therefore be satisfied when we reach that level that is commensurate with the nature of the subject matter.

2. I shall discuss the nature and implications of difference or variations ( ) in chapter 8.

3. The term occurs at N.E. 1155a20 where Aristotle writes: "We may see even in our travels [ ] how near and dear every man is to every man."

4. When Aristotle speaks of bravery in this context he probably means something like the psychological trait of fearlessness rather than the virtue of courage as he defines it. This use of the term is rather common in Greek, and indeed Socrates uses it in this manner in some of the Socratic Dialogues. At Meno 88, for example, he speaks of the harm that comes at times from bravery or quickness of mind.

5 See N.E. 1134b25: "What is by nature is immutable and has the same validity anywhere, as fire burns both here and in Persia, but what is just is seen to vary."

6. This phrase, , is best rendered in English as "for the most part" or "in most cases" and not, as is sometimes rendered, as "in generality," "in general," or "speaking in general'' (Grant, Rackham). For Aristotle is clearly concerned with what does not hold in all cases or is in a certain way in most cases. He is not concerned with what is a generality which is often contrasted to what is in detail or possesses specificity. It certainly should not be rendered as "speaking in general" or "generally speaking" if we mean by this "speaking without knowledge of specifics or details." For what Aristotle wishes to say is that we know how things are and certain things are such that they exhibit some property for the most part. As we shall see later, when Aristotle characterizes something as being for the most part he is not making an epistemic claim.

7. In claiming that the exactness/inexactness under consideration here is a formal feature and that it pertains to the truth of an account, I do not mean to assert that truth itself is a formal property, if we mean by this that it is a syntactic feature. Truth is considered to be a semantic property, and Aristotle himself conceives of it as a relation between an account and what the account is about. But an account can be exact or inexact in virtue of the way it satisfies this relation, e.g., in all cases, for the most part, roughly, and so forth.

8. See also Met. 1027a11 where Aristotle says that, outside the domain of matters of conduct as well, most things are for the most part

9. As a matter of fact Aristotle does not need to assume that all of the premises of a syllogism have to be for the most part in order that its conclusion be also for the most part (see below for this point)

10. Aristotle defines wealth at N.E. 1119b26 as follows: "By wealth we mean everything whose value is measured by money." He gives no evidence in this context that he thinks there is some problem with the nature or essence of wealth. The definition is clearly intended as holding true in all cases. In chapter 8, I shall discuss in some detail several examples of things whose definitions are, according to Aristotle, problematic because their nature is problematic. The concept beard , for example, may be vague and therefore difficult to define. But we should not assume that this is necessarily the reason that "Males have a beard" is true for the most part. For even if the definition of the concept beard posed no problem, it still could be the case that "Males have a beard" is true only for the most part.

11. Aristotle sees this clearly when at Pr. Anal. 43b35 he remarks that "And propositions that are for the most part are [derived] from syllogisms with premises that are for the most part, either all or some of them."

12. The way I have quoted 6.11 may give the impression that the for-the-most-part locution does not occur in Aristotle's text. Actually 6.11 is a continuation of 6.10, and it is quite clear that the for-the-most-part locution which appears at the beginning of 6.10 applies to both: "One ought for the most part to return services . . . [6.10] just as [ ] one ought to pay back a loan [6.11]." In both examples Aristotle's concern is with the exceptions to these two statements. In 6.12, however, Aristotle does not use the locution. But here again the concern is with what is true

for the most part, what has exceptions or fails to hold in all cases: "As a general rule [ ] . . . but they may not be best for a particular case."

13. I append here one example from M.M. : "If for the most part and at most times left retains the familiar character of life, and right of fight, the distinction [between left and right hand] is a natural one" (1.33.20.7). On the other two occasions where the author of M.M. uses the phrase "for the most part" (1.33.21.4, 2.8.2.4) he gives no particular examples of things that are for the most part or propositions that are true for the most part but instead makes some observations about the nature of being for the most part.

14. Some of the examples from the logical treatises may not be examples of things that Aristotle actually takes to be for the most part or propositions that he considers to be true for the most part. They could be only examples for the purpose at hand, namely, to illustrate some logical features. They seem, however, not to be any different from the examples he gives elsewhere. It is reasonable to conclude that most probably Aristotle views them as examples of things that are for the most part or propositions that are true for the most part.

15. For additional things that are for the most part, see G.A. 725b17, 727b13, 728a3, 739a32, 750b33, 768a24, 774b9, P.A. 663b30, 690a10, H.A. 508b2, 522a3, 522a12, 545b4, b18, b22, 553a6, 560b20, 562b4, b15, and so forth.

16. It may seem in this context that Aristotle is putting forth a view that can best be described as act-consequentialism. For he seems to be suggesting that, regardless of the contracts or debts one has entered into or incurred, what is proper for him to do depends on the consequences of the action and not on previous contracts or agreements. But this is not so. Aristotle takes the general rule stating that we are required to pay our debts to be true: "For a debtor ought to pay what he owes" (1163b20). His point, of course, is that there are exceptions to such rules.

17. This suggestion was made to me in conversations with Professors Charles Young and Mikael Karlsson.

18. The view that Aristotle links what is always with what is by necessity has been forcefully defended by J. Hintikka, "Necessity, Universality and Time in Aristotle," Ajatus 20 (1957), pp. 65-90, and more recently by S. Waterlow, Passage and Possibility (Oxford: Clarendon Press, 1982).

19. Richard Sorabji, Necessity, Cause and Blame (London: Duckworth, 1980), especially pp. 128-135.

20. Kant argues that there is no real distinction between universality and necessity in the Critique of Pure Reason , especially B 3-4.

21. I owe this example to Professor Charles Young.

22. Aristotle refers to such assertoric syllogisms at Rhet . 1356b17: "But when, certain things being posited, something different results from them, from their being true universally or for the most part, in Dialectic such reasoning is called a syllogism, in Rhetoric an enthymeme."

1. Among the ancient commentators, Eustratius and Alexander of Aphrodisias are clearly among those who concluded that the inexactness of ethics makes it non-demonstrative. The latter, in particular, thought that there could be no syllogisms whose premises consist of for-the-most-part propositions (see below). More recently, the view has, in one form or another, been defended by W. Jaeger, Aristotle: Fundamentals of the History of His Development (Oxford: Oxford University Press, 1948), especially, pp. 228-258; C. J. Rowe, The Eudemian and Nicomachean Ethics: A Study in the Development of Aristotle's Thought (Cambridge: Proceedings of the Cambridge Philological Society, 1971), especially pp. 63-76; J. Burnet, who in his commentary on the N.E. (London: Methuen, 1900) maintains that inexactness implies that Aristotle's own treatise is not demonstrative but dialectical throughout (especially pp. v-xvi); L. H. G. Greenwood, who, although critical of some of Bur-net's views, nonetheless agrees with him that ethics is dialectical because its propositions are not necessary or universally true—see his Aristotle: Nicomachean Ethics, Book VI (Cambridge: Cambridge University Press, 1909), especially pp. 131-133; H. H. Joachim, who also concludes from the supposition that ethical propositions are not necessary that ethics cannot be demonstrative—see his Aristotle: The Nicomachean Ethics (Oxford: Clarendon Press, 1955), especially p. 15. W. F. R. Hardie argues against the views of Burnet, Greenwood, and Joachim and does not take inexactness to imply that ethics cannot be demonstrative. Yet he remarks that, "It is reasonable to think that, in holding this view [that ethical statements have exceptions or are true for the most part], Aristotle is right as against those philosophers who have believed that moral rules can be demonstrated as in geometry, a company which includes Locke as well as Spinoza," Aristotle's Ethical Theory (Oxford: Clarendon Press, 1968), p. 32. Last, T. Irwin, who at times claims that ethics is an inexact science (see next note), on at least one occasion argues that because ethical propositions are about what is for the most part, ethics cannot be a science: "Concern with the usual [what is for the most part] deprives ethics of exactness, and prevents it from being a science"—see his translation of and commentary on the N.E. (Indianapolis: Hackett, 1985), p. 430. The view that ethics cannot be a science is not confined to Aristotelian scholars; it is accepted by many philosophers who at times appeal to Aristotle's authority. Thus H. Putnam, invoking Aristotle's remarks at N.E. 1094b19-27, claims that, "In fact, there is no prospect of a 'science' of ethics, whether in the sense of a laboratory science or of a deductive science;'' see his Reason, Truth and History (Cambridge: Cambridge University Press, 1984), p. 135.

2. Many scholars have glossed Aristotle's own words by claiming that ethics is not an exact or strict science. Most recently, T. Irwin has made such a claim in his commentary on the N.E. : "For the same reason, ethical truths are only usual [for the most part] and hence lack the exactness that would be needed for a science in the strict sense. . . . This lack of exactness [having exceptions] means that ethics cannot meet Aristotle's strictest criteria for science," Nicomachean Ethics (Indianapolis: Hackett, 1985), pp. 398, 399.

3. Most translators and commentators have assumed that Aristotle takes ethics

to be like rhetoric or the exactness of ethical investigations to be that proper to rhetorical practice or activity.

4. This is most often overlooked by those concerned with Aristotle's conception of the natural sciences, and in particular of the ones studying biological phenomena. But such phenomena are, according to Aristotle, quite inexact and therefore pose the same problems in relation to demonstration that matters of conduct or medical phenomena do. Thus, in his excellent article on the axiomatic-demonstrative character of P.A. , A. Gotthelf seems to overlook this problem altogether; see his "First Principles in Aristotle's Parts of Animals ," in A. Gotthelf and J. Lennox (eds.), Philosophical Issues in Aristotle's Biology (Cambridge: Cambridge University Press, 1987). I agree, however, with Gotthelf that, contrary to Barnes's claims, the P.A. is implicitly an axiomatic-deductive treatise.

5. By insisting that not every valid and sound inference is an explanation, Aristotle avoids the problem empiricists face by identifying explanation with such an inference and analyzing cause in terms of it—namely, the problem of having to admit that the inference from the length of the shadow of a tower to the height of the tower is a causal explanation of the height of the tower.

6. Aristotle, of course, recognizes different kinds of induction. Besides ordinary or enumerative induction, he also speaks of intuitive or rational induction, the cognitive activity he associates with grasping the basic principles of the various disciplines (see Post. Anal. II.xix). Aristotle argues at length that this latter kind of induction is not demonstration; it does not prove anything. But enumerative or ordinary induction has always been thought to resemble in some respects demonstrative reasoning that produces scientific knowledge or explanation (see Post. Anal. 71a5, 81a40). The question, however, is whether ordinary induction can be a proof in the way a demonstrative syllogism presumably is or can produce knowledge of the kind produced by such a syllogism.

7. The necessity Aristotle speaks of here is most probably that which he associates with the relation of premises to conclusion in a valid argument and not that of the necessity of the premises or of the conclusion. His point is that the person who uses division does not make a deductive inference, whereas demonstration is a deductive inference (71b18).

8. The view that the term Aristotle uses when he speaks of demonstration encompasses anything that shows or reveals that something is the case has been defended by J. Barnes, "Aristotle's Theory of Demonstration," Phronesis 14 (1969), pp. 123-152. Barnes's view has been criticized by J. Hintikika in his "On the Ingredients of an Aristotelian Science," Nous , vol. 6, no. 4 (1972), pp. 55-69, where he argues that the term Aristotle uses for demonstration has a core of meaning that excludes a variety of ways or means that we may be willing to designate as means or ways of showing that something is the case. Most interpreters of Aristotle's account of demonstration or demonstrative science hold views that differ from those of Barnes on this issue. See, in particular, H. Scholz, "The Ancient Axiomatic Theory,'' in J. Barnes, M. Schofield, and R. Sorabji (eds.), Articles on Aristotle , vol. 1 (London: Duckworth, 1975), and M. Burnyeat, "Aristotle on Understanding Knowledge," in E. Berti (ed.), Aristotle on Science (Padova: Editrice Antenore, 1981).

9. As Barnes says, "A demonstration is a species of modal syllogism. In a demonstration all the propositions are necessary . . .", Aristotle's Posterior Analytics (Oxford: Claredon Press, 1975), p. xvi. Barnes's way of explicating Aristotle's notion

of demonstration rules out the possibility that there are demonstrations with premises that are not necessary or that are true for the most part. Aristotle, I believe, does not share this view. What Barnes says is true of strict or absolute demonstration only and not of all demonstration.

10. J. Barnes, "Aristotle's Theory of Demonstration," Phronesis 14 (1969), pp. 123-152. But Aristotle need not necessarily share Barnes's views on this matter, for he seems to think that some demonstrations are better or "more truly demonstrations" than others (see below).

11. For a discussion concerning the assumptions about teleology, rationality, and so on that underlie Aristotle's opening statements in the N.E. about the good and the structure of desire and pursuits, see B. Williams, "Aristotle on the Good: A Formal Sketch," The Philosophical Quarterly , vol. 12, no. 49 (1962), pp. 289-296. Concerning action and teleology, see D. Charles, Aristotle's Philosophy of Action (Ithaca, N.Y.: Cornell University Press, 1986).

12. Thus J. L. Austin has remarked that "the relation between 'being ' and 'being desired' is one of the most baffling puzzles in Aristotle's, or for that matter Plato's, ethical theory"; see his "Agathon and Eudaimonia in the Ethics of Aristotle," in J. M. E. Moravcsik (ed.), Aristotle (Garden City, N.J.: Anchor Books, 1967), p. 296. Austin's paper is a response to H. A. Prichard's "The Meaning of Agathon in the Ethics of Aristotle,'' in J. M. E. Moravcsik, op. cit. Prichard argues that the relation between "being " and "being desired" is one of meaning.

13. P. Shorey takes Plato to have anticipated G. E. Moore's thesis that Good is indefinable; see his comments in his translation of Plato's Republic (Cambridge: The Loeb Classical Library, 1969), vol. 2, p. 95.

14. The classic discussions on these issues are to be found in Poincaré's essays, "Mathematics and Logic" and "Why Space Has Three Dimensions" in his Mathematics and Science: Last Essays and "Intuition and Logic in Mathematics" in his The Value of Science . See also in this connection the discussion of some of these issues by M. Steiner, Mathematical Knowledge (Ithaca, N.Y.: Cornell University Press, 1975).

15. Professor Mark Wilson has also pointed out to me that the same problem arises when we try to formalize in a systematic way the informal Peano axioms for natural numbers.

16. R. Gale, The Language of Time (London: Routledge & K. Paul, 1968).

17. On at least two occasions when Aristotle defines "syllogism" he appears to rule out suppressed premises, for he insists that the conclusion of a syllogism follows from the propositions that have been laid down as premises ( Pr. Anal. 24b20; Top. 100a18). Elsewhere, however, he recognizes syllogisms whose premises may not have all been laid down. In this connection, see M. Frede's discussion of some features of Aristotle's account of syllogistic reasoning, "Stoic vs. Aristotelian Syllogistic," Archiv für Geschichte der Philosophie 56 (1974), pp. 1-32.

18. This view of the role of enthymematic reasoning is stated throughout the Rhet . and at times in the Top.

19. J. Barnes, Aristotle's Posterior Analytics (Oxford: Clarendon Press, 1975), p. 135.

20. I have in mind Quine's discussion of necessity in "Two Dogmas of Empiricism." Quine has, of course, attacked the whole idea of necessity, but what he says about the way some propositions stand fast or are less likely to be revised can

be looked upon as offering a notion of necessity that admits of degrees. Putnam suggests that there can be degrees of necessity in his "The Analytic and the Synthetic" in his Mind, Language, and Reality (Cambridge: Cambridge University Press, 1975). The view is, however, explicitly stated and defended in his "It Ain't Necessarily So," in his Mathematics, Matter and Method (Cambridge: Cambridge University Press, 1975), where he argues that statements about species (e.g., "Cats are animals") are less necessary than purely analytic statements (e.g., ''Bachelors are not married").

21. That the essence cannot be demonstrated is the main topic of discussion in Post. Anal. II.iii-x, as well as Met. 1025b14, 1064a.

22. See Anim. 422b26, 436b3; E.E. 1229b; G.A. 722b32, 741b11, 782a, etc.

23. This tendency in Plato's thought is most strongly expressed in the Middle Dialogues, especially the Phaedo and the Republic (see Republic 529); at least Aristotle understood him as excluding the world of the senses from the domain of knowledge (see Met. 987a34).

24. Alexandri in Aristotelis Analyticorum Priorum Librum I Commentarium, 169.5; J. Lukasiewicz, Aristotle's Syllogistic (Oxford: Clarendon Press, 1967), p. 203.

25. J. Barnes, Aristotle's Posterior Analytics (Oxford: Clarendon Press, 1975), p. 184, and see also his "Aristotle's Theory of Demonstration," Phronesis 14 (1969), especially p. 133ff.

26. Barnes claims that Aristotle pursues this line of argument at Post. Anal. 75b33-6 and 98b29 and refers to H. H. Joachim's discussion of the topics of these passages in the latter's edition of the Gen. et Corr. (see Barnes, "Aristotle's Theory of Demonstration"). But what Aristotle is concerned with in the first passage is the relation of demonstration to intermittent events, e.g., the occurrence of an eclipse. In the second passage Aristotle is concerned with the problem of whether a cause is commensurate with its effects. And these are the topics Joachim discusses in the introduction to his edition of Gen. et Corr. (Oxford: Oxford University Press, 1922).

27. "The Science of Medicine," in G. E. R. Lloyd (ed.), Hippocratic Writings (London: Penguin Books, 1978), p. 142.

28. See Barnes, op. cit., and Pr. Anal. 25b14 and Rhet. 1357a37. Barnes has also suggested that Aristotle sometimes "treats 'for the most part' as a quasi modal operator . . . and uses it to express laws of nature. . . . From By nature C's are B and by nature B's are A it does not obviously not follow that By nature C's are A "; see his Aristotle's Posterior Analytics (Oxford: Clarendon Press, 1975), p. 184. I think Barnes is correct. I also argued earlier that Aristotle takes what is for the most part to be a component of the regularities of nature. And there is no doubt that the conclusions of some such syllogisms where "for the most part" is treated as being equivalent to "by nature" are true. Such syllogisms are nonetheless not valid. To use an example from Aristotle, the premises of the syllogism, "By nature fissepedes produce many offspring and by nature the elephant is a fissepede, therefore by nature the elephant produces many offspring," are true, but the conclusion is not (see below).

29. This is not to say that Aristotle does not recognize inductive reasoning. He does, but he tends to restrict its use to purposes that are different from those he

assigns to demonstrative reasoning, i.e., different from explanation or scientific understanding.

30. As Barnes has pointed out, Aristotle does not distinguish between propositions which express truths that are necessary, e.g., "Every man is an animal," and propositions which express the necessity of truths, e.g., "Necessarily: every man is an animal" (see his Aristotle's Posterior Analytics , pp. 112-113). Similarly, he does not distinguish between propositions that are true for the most part and propositions asserting that something is true for the most part. Aristotle almost invariably thinks in terms of the former.

31. Barnes writes, "And the paradigm demonstrative mood is Barbara . . . . Aristotle never sets this paradigm out with any clarity or emphasis; and in several passages whether deliberately or by oversight, he lets the fetters of necessity relax and is even unfaithful to Barbara . For all that, it is, I think, surely right to take the syllogism in Barbara with necessary components as the model of demonstrative reasoning" ( Aristotle's Posterior Analytics , p. xvi).

32. Aristotle's example comes from Euripides' Hecuba , 858.

33. Aristotle takes matter to be capable of being otherwise, to lack necessity ( Met. 1039b27). And if universality in truth implies necessity, lack of necessity, as pointed out earlier, will imply lack of universality of truth.

34. Ross, in his commentary on this passage, speaks of mathematical proof, and 1 take him to be thinking of demonstrative proofs of the rigor encountered in mathematics and not of proofs that involve elements of mathematics. These are, of course, different kinds of things.

35. Met. 1080b25: "The case of lines, planes, and solids is similar. For some think that those which are the objects of mathematics are different from those which come after the Ideas; and of those who express otherwise some speak of the objects of mathematics and do so mathematically [ ]—viz. those who do not make the Ideas numbers or say that Ideas exist . . . mathematically." The phrase, then, "to speak mathematically," that Aristotle uses in the above passage and in the one quoted in the text (995a6) when he speaks of the kinds of proofs demanded by listeners can, and does, mean ''to use the language of mathematics." Notice, also, the identical grammatical structure of "speaking mathematically" ( ) and "speaking by example" ( ) in Aristotle's text.

36. That physics is a theoretical and demonstrative science is asserted at Met. 1025b26, 1026a7, 1064b.

37. So G. E. R. Lloyd, Aristotle: The Growth and Structure of His Thought (Cambridge: Cambridge University Press, 1968), p. 204, even translates Aristotle's words in 7.4 as saying, "It is inappropriate to demand demonstration in ethics," whereas what Aristotles says is that it is foolish to demand demonstrations from a rhetorician. In fact, we see that Aristotle does not even say that the rhetorician gives no proofs—perhaps sometimes he does or at least he can—but that it is unreasonable, inappropriate, or foolish to demand proofs from him. We must also keep in mind that when Aristotle speaks of the rhetorician in the present context he means someone who practices rhetoric and not someone who investigates the nature of rhetorical phenomena. And whereas it may be inappropriate to demand proofs

from the former it may not be from the latter, for their activities and purposes are different (see chap. 9). In any case, the important point to stress is that Aristotle does not say that ethics is like the practice of rhetoric or that it does not give proofs.

38. That several of Aristotle's propositions about the good and happiness and their relation to goals or desires are necessary propositions is maintained by B. Williams, op. cit. , p. 294; see also my "Aristotle on Function and the Attributive Nature of the Good," in D. Depew (ed.), The Greeks and the Good Life (Indianapolis: Hackett, 1980).

39. As I said earlier, the technique of restricting the universal or the subject is used by Plato. That Aristotle also uses it has been recognized by W. F. R. Hardie, op. cit. , p. 33.

40. See also 771a20 where Aristotle explains why size is the cause.

1. Aristotle takes children to have debts toward their fathers: "Hence it would appear that a son never ought to disown his father, although a father may disown his son; for a debtor ought to pay what he owes, but nothing a son can do comes up the benefits he has received, so that a son is always in his father's debt. But a creditor may discharge his debtor, and therefore a father may disown his son" (1163b18).

2. H. L. Hart in his The Concept of Law (Oxford: Clarendon Press, 1961), pp. 122-126, points to problems with formulating laws or rules that are similar to the ones Aristotle identifies. But Hart argues that such problems may stem from two different sources. One is the use in formulating rules or laws of general terms that often defy precise definitions. The other, however, is what he calls "our relative indeterminacy of aims." And the indeterminacy of aims results, in turn, in an indeterminacy of our rules. So that the indeterminacy of a law concerning the distribution of land may not necessarily result from the indeterminacy of the term "land" or the concept land , but from the indeterminacy of our aims regarding land.

3. F. Waismann, "Verifiability," in A. Flew (ed.), Logic and Language , First Series (Garden City, N.J.: Anchor Books, 1965). The most detailed examination of the notion of open texture is to be found in J. M. Brennan, The Open-Texture of Moral Concepts (New York: Macmillan, 1977). Brennan makes some important distinctions in his discussion of open texture, but at times he seems to identify open texture with so many and quite different features of our moral concepts that he almost undercuts the usefulness of the notion (see especially pp. 116-134).

4. At Polit. 1326a35 Aristotle remarks, "But there is a due measure of magnitude for a city-state as there also is for all other things—animals, plants, tools; each of these if too small or excessively large will not possess its own proper efficiency, but in the one case will have entirely lost its true nature and in the other will be in a defective condition; for instance, a ship a span long will not be a ship at all, nor will a ship a quarter mile long, and even when it reaches a certain size, in the one case smallness and in the other excessive largeness will make it sail badly."

Aristotle seems to be saying that our concepts provide us with answers even in situations that are similar to those Waismann imagines.

5. G. Frege, "On the Concept of Number," in H. Hermes, F. Kambartel, and F. Kaulbach (eds.), Frege: Posthumous Writings (Chicago: University of Chicago Press, 1979), p. 77.

6. G. Evans, "Can There Be Vague Objects?" Analysis 38 (1978); N. U. Salmon, Reference and Essence (Princeton, N.J.: Princeton University Press, 1981), p. 243ff.; P. Unger, "There Are No Ordinary Things," Synthese 41 (1979), pp. 117-154; S.C. Wheeler, "On That Which Is Not," Synthese 41 (1979), pp. 155-173.

7. Op . cit. , p. 166.

8. P. Geach and M. Black (eds.), Translations from the Philosophical Writings of Gottlob Frege (New York: Rowman and Littlefield, 1952), p. 139. Wittgenstein responds to Frege's claim at Philosophical Investigations I.71 as follows: "Frege compares a concept to an area and says that an area with vague boundaries cannot be called an area at all. This presumably means that we cannot do anything with it.—But is it senseless to say: 'Stand roughly there?' Suppose that I were standing with someone in a city square and said that. As I say it I do not draw any kind of boundary, but perhaps point with my hand—as if I were indicating a particular spot. And this is just how one might explain to someone what a game is" (see also 76, 77).

9. Thus, M. Black, Margins of Precision (Ithaca, N.Y.: Cornell University Press, 1970), writes "So far as I can see all empirical concepts are 'loose' in the sense which I have explained" (p. 6) and "Now if all empirical concepts are loose, as I think they are . . ." (p. 7).

10. For a discussion of the claim that knowledge of the definition of F is necessary for knowing that some x is F and of the Socratic Fallacy in general, see chap. 2 and the references in notes 8 and 29 of that chapter. See also J. L. Austin's discussion of this issue in his "Are There A Priori Concepts?" in his Philosophical Papers (Oxford: Oxford University Press, 1970).

11. This line of argument is developed by G. Ryle in his The Concept of Mind (London: Hutchinson University Library, 1949).

12. The most important criticisms of the claim that any definition of F is by itself sufficient for determining whether something is an F are those developed by Wittgenstein in the Philosophical Investigations . Wittgenstein, by examining the conditions that need to be met for applying a rule correctly, concludes that no rule is by itself sufficient for determining anything. A whole system of beliefs and practices is, according to him, presupposed or required in applying any rule.

13. See Aristotle's discussion of this matter in Post. Anal. II.xix and Anim. II and the perceptive comments of M. Wedin in his "Aristotle on the Mechanics of Thought," Ancient Philosophy 9 (1989), especially pp. 80-81.

14. See the discussion by M. Black, op. cit. , pp. 11-12.

15. For the problem of the identity of vague objects, see G. Evans and N. U. Salmon, op. cit. The problem with the transitivity of identity of such objects has been discussed by S. Kripke, Naming and Necessity (Oxford: Oxford University Press, 1980), p. 51.

16. Thus, Frege writes that "The law of the excluded middle is really just another

form of the requirement that the concept should have a sharp boundary," op. cit. , p. 139.

17. B. Russell, "Vagueness," Australasian Journal of Psychology and Philosophy I (1923), p. 88. See Wittgenstein's criticisms of this view in Philosophical Investigations I, 104, 105, 106, 107.

18. This point has been made by J. Lear, Aristotle and Logical Theory (Cambridge: Cambridge University Press, 1980), pp. 110-111.

19. Black, who agrees with Aristotle that all empirical concepts are "loose" or that "nothing perceptible can be precisely defined," points to the unwelcome consequence of denying the possibility of valid reasoning with imprecise or vague concepts: "Now if all empirical concepts are loose, as I think they are, the policy becomes one of abstention from any reasoning from empirical premises. If this is a cure, it is one that kills the patient" ( op. cit. , p. 7). Black goes on to argue along lines that Aristotle would probably have found congenial: "In using a loose concept, I must know that there are instances that are indisputably 'clear' and must be able to recognize such cases; and I must also be able to recognize 'borderline cases'. I must understand that the use of the customary logical principles presupposes an ad hoc demarcation, somewhere in the region of cases that are not indisputably clear; and, finally, I must understand that there are no rules for drawing such lines. Provided I understand all this, I may properly use a loose concept and reason with it, even at times about cases which are not indisputably clear" ( op. cit. , p. 12).

20. See Post. Anal. I.xxvii and Met. A.3, as well as the discussion in chap. 4 above.

21. It may be objected in this connection that Aristotle takes the moral virtue (vice) of courage (cowardice) not to be simply a natural disposition, since, according to him, it cannot exist without practical wisdom ( N. E. VI.xiii). But we cannot conclude from this that no causal-explanatory account of the moral virtue (vice) of courage (cowardice) can be given. For, among other reasons, it is not obvious that no causal-explanatory account cannot be given in the case of practical wisdom itself.

22. I do not, of course, mean that there are no causal explanations purporting to explain why cities come into being or why they grow the way they do. I am only questioning whether the causal explanation of these kinds of phenomena about cities is relevant to the question concerning the vagueness or indefiniteness of "city" or of the concept city .

23. A. Grant, The Ethics of Aristotle (New York: Arno Press, 1973), p. 488, and Eustratius' commentary in G. Heylbut (ed.), Eustratii et Michaelis et Anonyma in Ethica Nicomachea Commentaria (Berlin: Reimer, 1892), p. 126.

24. Aristotle himself defines art (craft) in a few lines at N.E. 1140a20 while he devotes most of the Poet. to defining tragedy. Concerning the problems with defining tragedy, see the discussion by B. Vickers, Towards Greek Tragedy (London: Longman, 1973), especially chs. 1 and 2.

25. For a discussion of the problem of trying to make ethical concepts more exact by assigning to them numerical values, see K. Baier, The Moral Point of View (Ithaca, N.Y.: Cornell University Press, 1958), pp. 66-72.

26. I have in mind here Aristotle's argument from function at N.E. I.vii where he concludes that the "human good turns out to be activity of soul in conformity with excellence [or virtue]" (1098a15).

27. J. Rawls, A Theory of Justice (Cambridge: Harvard University Press, 1972), p. 399.

28. W. D. Ross, The Right and the Good (Oxford: Oxford University Press, 1930), p. 67.

1. See Post. Anal. I.xii, xxvii, and discussion above (chap. 4).

2. W. F. R. Hardie, Aristotle's Ethical Theory (Oxford: Clarendon Press, 1968), p. 31, for instance, claims that "what methods and procedures are proper in a science depends on its purpose . . ." but stops short of concluding that the method of ethics is nondemonstrative.

3. Post. Anal. 71b16, 92b19, 93a10, 98a20; Anim. 402a. The term , however, is often used to mean simply the way something is done, which may have nothing to do with the method an inquiry or investigation uses—e.g., Top. 156a15, Pr. Anal. 32b8.

4. Aristotle uses this term most often to signify the manner of obtaining the elements or premises of a syllogism, e.g., Pr. Anal. 53a2, 43a21. At other times, however, he uses it to signify something that is closer to the way or method of proving something, e.g., Pr. Anal. 46b24, Post. Anal. 82b30. But in many instances what Aristotle considers to be different methods are really different syllogistic forms.

5. Aristotle, using the same term, speaks again of the way to the first principles at Post. Anal. 84b23.

6. For the use of see N.E. 1099b14 (where some inquiry that studies matters pertaining to the gods is distinguished from the inquiries of ethics and politics), 1102a12, 1146b14. For the use of , see E.E. 1217a3, Top. 152b12, and for that of , N.E. 1096a11, 1112b21, Anim. 403b25.

7. At E.E. 1216b35-39 Aristotle writes, "And in every investigation [or method, ] arguments [accounts] stated in philosophical form are different from those that are not philosophical . . . since that is the philosophical way in every investigation [ ]." Although it is not altogether certain that the term means "inquiry" in its first occurrence, it most probably does. The term is, however, used at 1214a14 to clearly mean "field of inquiry."

8. See Polit. 1260b35, 1279b12, 1289a25, 1293b29, 1295a1, 1317a18, b33, 1324a2, a21.

9. M. Sintonen, The Pragmatics of Scientific Explanation (Helsinki: Acta Philosophica Fennica, vol. 37, 1984), p. 29. I quote Sintonen's statement below.

10. W. F. R. Hardie, op. cit. , p. 31, claims that "what methods and procedures are proper in a science depends on its purpose, on what are the questions to which answers are sought . . ." (my italics).

11. What Aristotle says in this passage (1098b) is not without its problems. He urges that we do not demand the cause in the same way in all cases ( ). Aristotle's words have been rendered in a variety of ways: "In all matters alike . . . an explanation of the reason why" (Rackham), "The cause in all things alike" (Apostle), "The cause in all matters alike" (Ross), "The same demand

for an explanation in all cases" (Irwin). Rackham and Irwin, in rendering as explanation, express agreement with the view defended recently by several scholars that Aristotelian causes are to be understood in terms of explanation-see J. Barnes, Aristotle's Posterior Analytics (Oxford: Clarendon Press, 1975) and R. Sorabji, Necessity, Cause, and Blame (London: Duckworth, 1980). Apostle and Ross, however, take Aristotle to be speaking about causes. These translators also go on to render differently what Aristotle says about what we might do if we are not to seek the "causes." Aristotle says that in some cases, and in particular in the case of the principles, it is sufficient to show adequately that something is so ( ). Most translators render Aristotle's words in such a way that they distinguish, as Aristotle seems to want to do, between proving or explaining (by giving the causes of) the principles on the one hand and in some way showing or establishing (Rackham, Ross) or indicating (Apostle) them on the other. Irwin, however, renders Aristotle's words by saying, "It is enough to prove that something is true without explaining why it is true." There is, at least prima facie, something puzzling with the idea that it is possible to prove something without explaining it.

12. See Eustratius's discussion, op. cit. , pp. 73-74, where he contrasts sharply what the builder does by using the T-square, the carpenter's orthogonal triangle, and the leaden weight for obtaining a straight line or a right angle to what the geometrician does.

13. "And after having given an art a single name in what has preceded, thereby making us think that it was a single art, does not the discussion now assume that the same art is two and ask whether the art as practiced by the philosopher or the non-philosopher was the more exact?" (57C).

14. Sometimes Plato's words at Philebus 57B are translated as follows: "Well, had not the discussion already found in what preceded that the various arts had various purposes [ ] and various degrees of exactness" (translated by H. N. Fowler, Loeb Classical Library). But actually what Plato says in this passage is that "different arts, dealing with different things [ ]" possess different degrees of exactness. R. Hackforth's rendering of this passage in which he attributes variation in exactness to the differences of the objects arts or disciplines deal with is the correct one— Plato's Examination of Pleasure (Indianapolis: The Library of Liberal Arts, 1945).

15. Its goals are, as Plato and Aristotle often insist, purely theoretical; it aims at knowledge for the sake of knowledge.

16. Grant in his commentary on 1098a30 (9.2) seems to me to have something like this in mind when he points to the different aspects or conditions of demonstration and the possibility that ethics may differ from mathematics because it does not satisfy all of these conditions or at least not to the degree or in the way mathematics does.

17. I do not mean to claim here that Aristotle does not identify any methods other than demonstration for investigating into certain domains or for discovering the basic principles. He clearly does. In Post. Anal. II.xix he argues that some type of induction, and not demonstration, is the way by which the basic principles are to be grasped. At Top. 101a37 he argues that the starting points of the sciences are arrived at by using dialectic. And at N.E. 1098b3 he claims that principles "are

studied by means of induction, perception, habituation and other means." But these methods, as G. E. L. Owen has pointed out, are not methods of explaining, proving, or producing scientific understanding—see G. E. L. Owen, "Aristotle: Method, Physics, Cosmology," in C. C. Gillespie (ed.), Dictionary of Scientific Biography (New York: Scribner, 1970).

18. See Post. Anal. 79a15, 88b13; Met. 1025a, 1064a.

19. See his commentary on this passage in his translation of the N.E. (Dordrecht: D. Reidel, 1975).

20. This translation is by P. Shorey in the Loeb Classical Library edition. Shorey, commenting on Plato's use of the word "ludicrous" to characterize the language of doing that is employed by some in relation to geometry, says that "the very etymology of 'geometry' implies the absurd practical conception of the science." Why the conception is, however, absurd is not obvious. Plato himself did not remove geometry from any and all practical applications (see below).

21. The goal of eliminating from mathematics the kind of language or proofs that Plato finds ludicrous has always been a part of the ideal of mathematical knowledge, even in the earliest stages of the history of the discipline of mathematics. This is brought out quite clearly in the comments of T. L. Heath on Euclid's Elements . Heath quotes the following from Schopenhauer: "I am surprised that, instead of the eleventh axiom [the Parallel-Postulate], the eight is not rather attacked: 'Figures which coincide are equal to one another.' For coincidence is either mere tautology, or something entirely empirical, which belongs, not to pure intuition, but to external sensuous experience. It presuposes in fact the mobility of figures; but that which is movable in space is matter and nothing else. Thus this appeal to coincidence means leaving pure space, the sole element of geometry, in order to pass over to the material and empirical" ( Die Welt als Wille und Vorstellung , vol. 2, 2d edition, p. 130). Euclid himself expresses reservations about the use of superposition of figures in geometry, but, as Heath observes, superposition is fundamental in geometry and an inseparable element of some of the common notions or axioms, especially 1.4—"Things which coincide with one another are equal to one another"—: "But seeing how much of the Elements depends on 1.4, directly or indirectly, the method can hardly be regarded as being, in Euclid, of only subordinate importance; on the contrary, it is fundamental. Nor, as a matter of fact, do we find in the ancient geometers any expression of doubt as to the legitimacy of the method," Euclid's Elements (New York: Dover Publications, 1956), vol. 1, p. 225. The problems associated with interpreting Plato's views on the nature of mathematical and scientific knowledge in general have been recently discussed by G. Vlastos, "The Role of Observation in Plato's Conception of Astronomy," and A. Mourelatos, "Plato's Real Astronomy: Republic VII 527D-531D,'' in J. P. Anton (ed.), Plato on Science and the Sciences (New York: Eidos Books, 1980); see also my discussion of these papers in "Plato on the Sciences," Inquiry 26 (1983), pp. 237-246.

22. According to Heath, op. cit. , p. 226, Aristotle accepts the method of superposition in geometry. But it would not be true to accuse Aristotle of failing to understand the nature of mathematical knowledge and of mathematical propositions—that is, of confusing them with empirical propositions on the basis of the

fact that he accepts the kinds of proofs that presumably Plato rejects. For he draws a sharp distinction between the proof one uses and the nature of what one proves—"the geometrician does not infer anything from the existence of the particular line which he himself has mentioned, but only from the facts which his diagrams illustrate" ( Post. Anal. 77a). See also Met. 1078a20, 1089a25, and Heath's discussion of Aristotle's views in his A History of Greek Mathematics (New York: Dover Publications, 1981), vol. 1, pp. 336-337.

23. Aristotle argues at Post. Anal. 72a30 and N.E. 1139b32 that our knowledge of the basic principles of a science must be superior to our knowledge of the propositions derived from them (its theorems).

24. See Met. 1027a: "And that the builder produces health is an accident, because it is the nature not of the builder but of the doctor to do this—but the builder happened to be a doctor. Again, a confectioner, aiming at giving pleasure, may make something wholesome, but not in virtue of the confectioner's art; and therefore we say 'it was an accident', and while there is a sense in which he makes it, in the unqualified sense he does not. For to some things correspond faculties productive of them."

25. The point here is not affected by the fact that Aristotle is mistaken about the function of the brain.

26. See in this connection the important discussion by R. Kraut in his "The Peculiar Function of Human Beings," Canadian Journal of Philosophy 9 (1979), pp. 467-478. Aristotle has at times been criticized for assuming that things have unique functions or for equating the function of something with any activity that might be unique to it; see, for example, T. Nagel, "Aristotle on Eudaimonia ," in A. Rorty (ed.), Essays on Aristotle's Ethics (Berkeley and Los Angeles: University of California Press), pp. 7-14.

27. For a discussion of Putnam's example see below. That an inexact explanation, instruction, or concept may he what is required in certain contexts or for certain purposes is a view put forth by Wittgenstein in the Philosophical Investigations . Our language, Wittgenstein often argues, is just the way it should be if it is to serve the purposes it serves: "If I tell someone 'stand roughly here'—may not this explanation work perfectly? And cannot every other one fail too? But isn't it an inexact explanation?—Yes; why shouldn't we call it 'inexact'? Only let us understand what 'inexact' means. For it does not mean 'unusable' " ( Philosophical Investigations , I, 88).

28. M. Sintonen, op. cit. , p. 29; see also pp. 92-100. For "es-questions" and "se-answers" read "Explanation-seeking questions" and "Scientific-explanatory answers,'' respectively.

29. H. Putnam, Mind, Language and Reality (Cambridge: Cambridge University Press, 1975), p. 295.

30. Op. cit. , p. 296.

30. Op. cit. , p. 296.

31. Ibid.

32. H. Putnam, Meaning and the Moral Sciences (London: Routledge & K. Paul, 1979), p. 47.

33. M. Scriven, "Explanations, Predictions, and Laws," in H. Feigle and G. Maxwell (eds.), Minnesota Studies in the Philosophy of Science , vol. 3 (Minneapolis: University of Minnesota Press, 1962), p. 196.

34. B.C. van Fraassen, "Salmon on Explanation," The Journal of Philosophy , vol. 82, no. 11 (1985), p. 640.

35. The view that mathematics can, and in fact does, use less rigorous types of proofs, e.g., inductive evidence, has been recently defended by M. Steiner, Mathematical Knowledge (Ithaca, N.Y.: Cornell University Press, 1975), especially ch. 3.

36. See on this point my "Aristotle on Function and the Attributive Nature of the Good," in D. Depew (ed.), The Greeks and the Good Life (Indianapolis: Hackett, 1980).

37. The goals of ethics, then, are not merely psychological, as Hardie suggests, op. cit. , p. 31. Or, at least, they are not psychological in the sense we often understand this term, i.e., as implying something that is merely subjective.

37. The goals of ethics, then, are not merely psychological, as Hardie suggests, op. cit. , p. 31. Or, at least, they are not psychological in the sense we often understand this term, i.e., as implying something that is merely subjective.

38. Wittgenstein remarks at Philosophical Investigations , I, 88:" 'Inexact' is really a reproach, and 'exact' is praise. And that is to say that what is inexact attains its goal less perfectly than what is more exact. Thus the point here is what we call the 'goal'. Am I inexact when I do not give our distance from the sun to the nearest foot or tell a joiner the width of a table to the nearest thousandth of an inch?" In some cases, of course, the exact is what attains its goals—e.g., as Aristotle claims, an account in ethics is exact if it attains the level of detail or specificity that is needed in order to attain the goals of the discipline. It is also true, however, that sometimes we designate certain accounts, descriptions, or explanations as inexact because they fail to meet certain standards of exactness—e.g., Aristotle considers explanations in ethics to fail to meet the exactness of the explanations we give in mathematics. But, Wittgenstein retorts, "No single ideal of exactness has been laid down; we do not know what we should be supposed to imagine under this head—unless you yourself lay down what is to be so called. But you will find it difficult to hit upon such a convention; at least any that satisfies you" ( ibid. ).

39. For Aristotle's use of geometric proportion in his account of distributive justice, see the excellent discussion of D. Keyt, "Distributive Justice in Aristotle's Ethics and Politics ," Topoi 4 (1985), pp. 23-45.

40. This is, of course, Plato's line of argument in the Gorgias , where he argues in support of the view that rhetoric, medicine, cooking, and so forth cannot be left to mere sophistic treatment or guesswork. Too much depends on such arts, and if we go wrong when using them the effects can be at times fatal.

41. J. de Romilly, Magic and Rhetoric in Ancient Greece (Cambridge: Harvard University Press, 1975). See also the comments of T. Irwin in his translation of the Gorgias (Oxford: Clarendon Press, 1979).

42. H. H. Joachim, Aristotle: The Nicomachean Ethics (Oxford: Clarendon Press, 1955), p. 16.

1. When speaking of principles in the present context I shall sometimes mean general or universal statements, and not necessarily what Aristotle often has in mind when he speaks of principles—namely, the basic propositions of a discipline.

2. See Sartre's discussion of the place or role of general principles in ethical choice in his essay "Existentialism," in his Existentialism and Human Emotions (New York: Philosophical Library, 1957), p. 25ff.

3. J. McDowell, "Virtue and Reason," The Monist , vol. 62, no. 3 (1979), p. 336.

4. Op. cit. , p. 343.

4. Op. cit. , p. 343.

5. Ibid.

6. A. Baier, Postures of the Mind (Minneapolis: University of Minnesota Press, 1985), p. 218ff. See also the somewhat similar views of P. Foot in her "Moral Arguments," Mind 67 (1958), pp. 502-513, and "Moral Beliefs," Proceedings of the Aristotelian Society 59 (1958-1959), pp. 83-104.

7. A. Baier, op. cit. , p. 274. The "negative" rules Baier refers to here are some of the Ten Commandments of the Old Testament.

8. B. Williams, Ethics and the Limits of Philosophy (Cambridge: Harvard University Press, 1985), especially chs. 1 and 2; see also his "Ethical Consistency," Proceedings of the Aristotelian Society , suppl. 29 (1965), pp. 103-124, and "Consistency and Realism," Proceedings of the Aristotelian Society , suppl. vol. 40 (1966), pp. 1-22. For a critical discussion of Williams's views, see P. Foot, "Moral Realism and Moral Dilemma," The Journal of Philosophy , vol. 80, no. 7 (1983), pp. 379-398.

9. See M. Nussbaum, Aristotle's "De Motu Animalium" (Princeton: Princeton University Press, 1978), especially essay 4, and The Fragility of Goodness (Cambridge: Cambridge University Press, 1986), pp. 298-307. Nussbaum stresses Aristotle's concern with the universal aspects of ethical theory in her "Nature, Function, and Capability," Oxford Studies in Ancient Philosophy , suppl. vol. 1 (1988), pp. 145-184, and "Non-Relative Virtues: An Aristotelian Approach," Midwest Studies in Philosophy 13(1988), pp. 32-53.

10. T. Irwin, Aristotle: Nicomachean Ethics (Indianapolis: Hackett, 1985), p. 430.

11. A. Jonsen and S. Toulmin, The Abuse of Casuistry: A History of Moral Reasoning (Berkeley and Los Angeles: The University of California Press, 1988).

12. Unlike Plato, Aristotle has often been looked upon as having no interest in theory or as failing to develop a theory about something or other. Thus, J. L. Ackrill claims, "He [Aristotle] does not direct his gaze steadily upon the questions 'What is an action?' and 'What is an action?' " Ackrill concludes that, although Aristotle had the means of developing a theory of action, he does not; see his "Aristotle on Action," Mind , vol. 88, no. 348 (1978), pp. 595-601. For Aristotle's theory of action, see D. Charles, Aristotle's Philosophy of Action (Ithaca, N.Y.: Cornell University Press, 1986).

13. See also 1142a15 where Aristotle writes, "The reason is that practical wisdom in addition [ ] is concerned with the particular . . ." The in this phrase is omitted by one of the manuscripts (M ^b ) but all the editors of Aristotle's text agree on its inclusion. The context makes it clear that Aristotle is again contrasting theoretical knowledge (e.g., geometry or arithmetic) that deal only with the universal to practical knowledge that deals with both the universal and the particular.

14. Aristotle is often concerned with what he takes to be the insufficiency of the knowledge of what is virtuous or what is healthy to produce virtuous actions or healthy and vigorous conditions respectively (1105b10, 1143b25). He is thus critical of the Socratic thesis that virtue is knowledge. But the problem Aristotle sees with the Socratic thesis about virtue is different from the more narrow question of whether the knowledge required for action is of the universal or particular kind.

15. Among the commentators, Burnet, Stewart, and Grant seem to emphasize knowledge of the particular. H. G. Apostle even translates as "he knows what he does," which suggests that the agent knows the particular circumstances, although it may also mean that he knows the nature of his action. H. Rackham thinks that both kinds of knowledge are involved.

16. See also N.E. 1105a30 and 1144a18.

17. I do not, of course, mean to endorse Aristotle's claim about the alleged inability of animals to form general concepts or rules. Aristotle's claim is, indeed, a puzzling one, for it seems to imply that a dog has no general concept or precept of, for example, cat, but only images of individual cats. It also implies that, in contrast to what Aristotle says about the shading of nutritive soul into the sensitive soul (see the discussion in chap. 8 about the gradations in nature and the "dualizing" between being a plant and an animal of certain living things), there is no shading of the sensitive into the intellectual soul (or faculty). Yet at other times Aristotle seems to be of different mind about this. Thus, at Protrept . B29 he remarks, "Animals have some small sparks of reason [ ] and practical wisdom [intelligence, prudence— ] but are entirely deprived of theoretical wisdom." And at G.A. 731a32 he claims that "all animals have in addition, some measure of knowledge of a sort [ ] . . . because they have sense-perception, and sense-perception is, of course, a sort of knowledge." Finally, at N.E. 1141a27 he claims that ''even some of the lower animals are said to have practical wisdom [or intelligence, ], namely those which display a capacity of forethought as regards their own life."

18. J. McDowell, op. cit. , p. 344.

19. Op. cit. , p. 347.

20. And for the reasons Aristotle gives and that I discussed above.

21. See Post. Anal. 85b26 where Aristotle claims that "therefore, the universal is the cause" and see also 88a5.

22. The most sustained argument against any explanatory role for ethical theory has been developed by G. Harman in his The Nature of Morality (New York: Oxford University Press, 1977). Harman's argument, however, rests on a rather narrow empiricist conception of causal explanation—a conception that has little to do with Aristotle. For critical discussion of Harman's argument see, W. Quinn, "Truth and Explanation in Ethics," Ethics , vol. 96, no. 3 (1986), pp. 524-544, and G. Sayre-McCord, "Moral Theory and Explanatory Impotence," in G. Sayre-McCord (ed.), Essays on Moral Realism (Ithaca, N.Y.: Cornell University Press, 1988).

23. Baier, op. cit. , p. 273.

24. Compare the views of Ayer, Carnap, and Stevenson on this matter. All deny that ethical judgments have truth values, but for different reasons.

25. G. Ryle, The Concept of Mind (London: Hutchinson University Library, 1949), ch. 5.

26. S. C. Wheeler, "On That Which Is Not," Synthese 41 (1979), pp. 164-165.

27. B. Russell, "Vagueness," Australasian Journal of Psychology and Philosophy 1 (1923).

28. J. Lukasiewicz, Aristotle's Syllogistic (Oxford: Clarendon Press, 1957), p. 204.

29. See T. Kuhn, "Logic of Discovery or Psychology of Research," in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge (Cambridge: Cambridge University Press, 1970), pp. 171, 206; B. van Fraassen, The Scientific Image (Oxford: Oxford University Press, 1980), ch. 1; N. Cartwright, "The Truth Doesn't Explain Much," American Philosophical Quarterly , vol. 17, no. 2 (1980), pp. 159-163.