1 This formulation of (LE1) might be regarded as implausible since it entails that all analytic propositions are knowable. Some have claimed, for example, that it is possible that some analytic propositions are too complex for human comprehension and, hence, not knowable. Such claims raise issues about how to understand the modality in (LE1) which I will not address in this paper. I propose to grant that all analytic propositions are knowable and to focus exclusively on the issue of whether there is any good reason to suppose that they are knowable a priori. If one finds this concession troubling, one can understand the subject of (LE1) to involve an implicit restriction to knowable analytic propositions. The same point applies to the related principles (LE4) and (LE1*).

2 Putnam, Hilary in ‘There Is At Least One A Priori Truth,’ in Philosophical Papers, Vol. 3 (Cambridge: Cambridge University Press 1983)Google Scholar, and Kitcher, Philip in The Nature of Mathematical Knowledge (Oxford: Oxford University Press 1983)Google Scholar, ch. 4, both challenge (LE1) on the grounds that (1) if p is knowable a priori then p is rationally unrevisable, and (2) analytic propositions are rationally revisable. I do not find this challenge compelling since (1) is extremely implausible. For a defense of this claim, see my ‘Revisability, Reliabilism, and A Priori Knowledge,’ Philosophy and Phenomenological Research 49 (1988) 187-213.

3 For a discussion of these problems, see Casullo, A. ‘A Priori/ A Posteriori,’ in Dancy, J. and Sosa, E. eds., A Companion to Epistemology (Oxford: Basil Blackwell forthcoming).Google Scholar

4 Quinton, Anthony ‘The A Priori and the Analytic,’ in Sleigh, R.C. Jr ed., Necessary Truth (Englewood Cliffs, NJ: Prentice-Hall 1972), 90-1.Google Scholar For a lucid and more comprehensive discussion of this concept, see Butchvarov, PanayotThe Concept of Knowledge (Evanston: Northwestern University Press 1970), ch. 2.Google Scholar

5 Kripke, Saul in Naming and Necessity (Cambridge: Harvard University Press 1980)Google Scholar and ‘Identity and Necessity,’ in Munitz, M.K. ed., Identity and Individuation (New York: New York University Press 1971)Google Scholar, makes a similar point with respect to the concepts of a priori knowledge and necessary truth. For a critical discussion of Kripke’s view on the relationship between the a priori and the necessary, see my ‘ripke on the A Priori and the Necessary,’ Analysis 37 (1977) 152-9CrossRefGoogle Scholar, reprinted in Moser, P. ed., A Priori Knowledge (Oxford: Oxford University Press 1987).Google Scholar Some related issues are discussed in my ‘Actuality and the A Priori,’ Australasian Journal of Philosophy 66 (1988) 390-402.CrossRefGoogle Scholar

6 It is somewhat ironic that in Naming and Necessity, Kripke makes it a matter of stipulation that’ … an analytic statement is, in some sense, true by virtue of its meaning and true in all possible worlds by virtue of its meaning. Then something which is analytically true will be both necessary and a priori’ (39). Clearly, on this account, it is trivially true that all analytic statements are necessary. It is not clear, however, why Kripke thinks that it follows from this stipulation that analytic statements are a priori.

7 Ayer, A.J.Language, Truth and Logic, 2nd ed., (London: Gollancz 1946), ch. 4;Google Scholar and Hempel, Carl ‘On the Nature of Mathematical Truth,’ in Sleigh, R.C. Jr ed., Necessary TruthGoogle Scholar

8 Hempel entertains a third option, that mathematical propositions require no justification because they are self-evident, which he quickly rejects as too subjective. He may be viewing this option as a version of rationalism.

9 Hempel, 35-6. See Ayer, 75-6, for a similar argument. Ayer’s, argument is critically evaluated in my ‘Necessity, Certainty, and the A Priori,’ Canadian Journal of Philosophy 18 (1988) 43-66.Google Scholar

10 Analogous considerations establish the implausibility of rejecting (GCE) for other types of evidence. For example, if a proof of a mathematical proposition that p from a certain set of axioms confirms that p, it would be implausible to maintain that a proof of not-p from the same set of axioms does not disconfirm that p. Similarly, if it is maintained that one’s seeming to remember that one last revised this paper on Thursday confirms the proposition that one last revised this paper on Thursday, it would be implausible to also maintain that one’s seeming to remember that one last revised this paper on Wednesday does not disconfirm that proposition.

11 Hempel, 36. Ayer offers a similar defense.

12 This claim is defended in more detail in my ‘Necessity, Certainty, and the A Priori.’

13 Hempel, 36. Mark Steiner, in ‘Mathematics, Explanation, and Scientific Knowledge,’ Nous 12 (1975) 17-28, defends the view that all arithmetical identities follow from stipulations and maintains that any apparent empirical disconfirmation of such an identity statement should be attributed to’ … the failure of a certain physical procedure to determine the number in the union of two disjoint sets’ (25). He does not, however, consider the point stressed in the text that claims to the effect that certain empirical procedures fail to determine the number of objects in a set are themselves subject to empirical confirmation or disconfirmation.

14 For a discussion of these issues, see Quine, W.V.Philosophy of Logic (Englewood Cliffs, NJ: Prentice-Hall 1970), ch. 5;Google ScholarPutnam, Hilary ‘Philosophy of Logic,’ sect. III, in Philosophical Papers, Vol. II (Cambridge: Cambridge University Press 1979);Google Scholar and Steiner, MarkMathematical Knowledge (Ithaca: Cornell University Press 1975), ch. 2.Google Scholar

15 For a discussion of this issue, see Parsons, Charles ‘Frege’s Theory of Number,’ in Black, Max ed., Philosophy in America (Ithaca: Cornell University Press 1965); and Steiner, ch. 1.Google Scholar

16 See Hempel, 41, for a discussion of this issue.

17 It might be thought that since some proponents of logicism held that logical truths are constitutive of every linguistic framework or, more generally, all rational thought, the question of their justification does not arise. But this is a mistake. Even if one of these accounts is correct, a person still could believe a logical truth for bad reasons and, hence, not be justified in holding that belief. For example, if p is a logical truth but my only reason for believing that p is the testimony of an individual whom I know to be unreliable on such matters, then I am not justified in believing that p.

18 Hempel, 42-3

19 Ibid., 44-5, note

20 Quine W.V. proposes and defends a similar account of necessary and sufficient conditions for a definition to conform to customary meaning: ‘For such conformity [to traditional usage] it is necessary and sufficient that every context of the sign which was true and every context which was false under traditional usage be construed by the definition as an abbreviation of some other statement which is correspondingly true or false under the established meanings of its signs’ (see ’Truth by Convention,’ in The Ways of Paradox [Cambridge: Harvard University Press 1976], 79).

21 See Carnap, RudolfLogical Foundations of Probability, 2nd ed. (Chicago: University of Chicago Press 1962), 5-8, for a discussion of the requirements for an adequate explication.Google Scholar

22 Ibid., 16

23 Ibid., 17

24 Ibid.

25 Although Carnap maintains that’ … in spite of practical skill in usage, people in general, and even mathematicians before Frege, were not completely clear about the meaning of numerical words …’ he, nevertheless, also maintains that ‘To demonstrate the adequacy of his explications, he [Frege) had to show that the numerals and the other arithmetical signs, as defined by him, had the properties customarily ascribed to them in arithmetic.’ See Carnap, Rudolf ‘Replies and Systematic Expositions,’ in Schilpp, P.A. ed., The Philosophy of Rudolf Carnap (LaSalle: Open Court 1963), 935 and 939.Google Scholar For a more extensive discussion of the role of criteria of adequacy in Carnap’s method of explication, see Pap, ArthurSemantics and Necessary Truth (New Haven: Yale University Press 1958), ch. 14.Google Scholar

26 Steiner, 62-3

27 Ibid., 66

28 Ayer, 78

29 I do not consider here the view that analytic propositions are true in virtue of abstract meanings. Such platonist accounts of mathematical truth, or of necessary truth in general, raise their own distinctive episternic problems. I discuss some of these in ‘Causality, Reliabilism, and Mathematical Knowledge,’ Philosophy and Phenomenological Research 52 (1992) 557-84.

30 Ayer, 78-9

31 Quinton, 90

32 It is also true by stipulation on the narrow reading of ‘a priori’ that (K*) All necessary statements are a priori. (K*), together with Quinton’s further claim that the categories of the necessary and the analytic are coextensive, entails (Q*) All analytic statements are a priori.

33 For a critical discussion of Kant’s argument, see my ‘Necessity, Certainty, and the A Priori.’

34 Quinton, 92. Quinton considers a challenge to the assumption that all contingent statements are empirical which is based on employing conclusive falsifiability by experience as an epistemic criterion of the empirical. In response to it, he drops the wider notion of the a priori from further consideration and maintains that ’ … the essential content of the thesis [Q] is that all necessary truths are analytic’ (93).

35 Swinburne, R.G. ’Analyticity, Necessity, and Apriority,’ in Moser, P. ed., A Priori Knowledge, 184Google Scholar

36 Ibid., 185

37 Ibid., 186

38 Ibid., 187

39 I would like to thank Robert Audi, Panayot Butchvarov, Philip Hanson, Philip Hugly, Bruce Hunter, Michael Jubien, Penelope Maddy and Joseph Mendola for their helpful comments on earlier versions of this paper.