1 See my ‘Bayesianism Without the Black Box; Philosophy of Science 56 48-69.

2 See my ‘Not by the Book,’ Philosophical Topics (forthcoming).

3 These conditions may not seem so modestto some. For example (they may note), it is an axiom of the probability calculus that every tautology has the maximum probability. This being so, you will count as satisfying the second condition only if you invest the maximum amount of confidence in every tautology. But, if so (they may argue), surely the second condition demands too much. The tautologies are infinite both in number and complexity. None of us possesses a sufficient amount of either logical acumen or time to recognize them all. Similar complaints can be made about the theorem that no hypothesis is more probable than any of its consequences.

But the complaint mistakes a regulative ideal for a regulation. As a regulation, the two conditions would indeed require you to succeed in investing the maximum amount of confidence in every tautology. But, as a regulative ideal, they require only that you invest maximum confidence in h if provided proof that h is a tautology. (And, likewise, that you not invest more confidence in h than in g if provided proof that h entails g.) And surely this is a requirement one can justifiably call modest.

4 See, for example, Richard W. Miller, Fact and Method (Princeton: Princeton University Press 1987), 321.

5 Clark Glymour, Theory and Evidence (Princeton: Princeton University Press 1980), 83-4

6 See Hilary Putnam, ‘Probability and Confirmation,’ in Putnam's Mathematics, Matter and Method (Cambridge: Cambridge University Press 1975).

7 See John Pollock, Contemporary Theories of Knowledge (Totowa, NJ: Rowman and Littlefield 1986), 7-8 (where the contrast between epistemic and prudential reasons is drawn by an example similar to the one I have used) and 99-100 (where an objection not unlike this one is advanced against the Dutch Book Argument).

8 And that, among the hypotheses that T entails and C does not, there are hypotheses of whose truth you are not certain.

9 1his is a paraphrase of Robert Nozick, Philosophical Explanations (Cambridge, MA: Harvard University Press 1981), 255.

10 To use Richard C. Jeffrey's phrase, from ‘Dracula Meets Wolfman: Acceptance vs. Partial Belief,’ in Marshall Swain, ed., Induction, Acceptance and Partial Belief (Dordrecht: D. Reidel1970) 157-85, at 172.

11 See Miller, ch. 6 and 7; also look at the many discussions of what it is rational to believe or accept in the face of the lottery described earlier.

12 In what follows I sketch an account of belief and methodology I first advanced (as an account of rational acceptance) in my ‘A Bayesian Theory of Rational Acceptance,’ The Journal of Philosophy 78 (1981) 305-30 and ‘Rational Acceptance,’ Philosophical Studies 40 (1981) 129-45. The defense I offer on its behalf is, however, new. The account was inspired by the one offered in Ronald B. DeSousa, ‘How to Give a Piece of Your Mind: Or, The Logic of Belief and Assent,’ The Review of Metaphysics 25 (1971) 52-79, at 62-3.

13 The view that, in determining what to accept, we seek both comprehensiveness and avoidance of error, has played a central role in the work of Isaac Levi (see Gambling with Truth [New York: Knopf 1967] and The Enterprise of Knowledge [Cambridge, MA: MIT Press 1980]). But Levi holds a variant on the view, criticized earlier, that belief is a state of certainty. (For him, maximal confidence is a necessary, though not sufficient, condition of acceptance.) So, from my point of view, Levi can be said to have taken (indeed, pioneered) a correct approach to rational methodology but to have applied it to the wrong thing. (For a more extended discussion, see my review of Levi's The Enterprise of Knowledge, The Philosophical Review 92 (1983) 310-16.)

Much more recently Patrick Maher has also construed comprehensiveness and avoidance of error as the aims of rational acceptance. But his account of what acceptance is, though it displays some affinity with the present proposal for defining belief, does not meet the Bayesian challenge. According to Maher, ‘acceptance of H is the state expressed by sincere intentional assertion of H’ (Patrick Mayer, Betting on Theories [Cambridge: Cambridge University Press 1993], 132). The trouble here is that, if dictionary definitions are to be trusted (and Maher offers no alternative), an intentional assertion counts as sincere if and only if the asserter believes her assertion to be true. But what is belief? If it is just acceptance by another name, than Maher's definition fails to meet the Bayesian challenge: it presupposes the intelligibility of acceptance. And if belief is something distinct from acceptance, then Maher's definition would seem to be mistaken. For it is a person's belief that H, not her acceptance that H, that is necessary and sufficient for her intentional assertion of H to count as sincerewhich would seem to indicate that it is the belief that H, not the acceptance of H, that sincere intentional assertion of H expresses.

14 This objection is due (independently) to Barry Loewer and Patrick Maher, each of whom pressed it upon me in correspondence. Recently the latter has committed it to print. (See Maher, 155-6.)

15 See Bas C. Van Fraassen, ‘Glymour on Evidence and Explanation,’ in John Earman, ed., Testing Scientific Theories (Minneapolis: University of Minnesota Press 1983) 165-76, where Van Fraassen argues that the very features of powerful theories that make them seem attractive make them less probable and, hence, less worthy of belief. I address his argument in ‘Believing the Improbable,’ Philosophical Studies (forthcoming).

16 See, for example, Stephen Leeds, ‘Theories of Reference and Truth,’ Erkentniss 15 (1978); and Robert Brandom, ‘Reference Explained Away,’ The Journal of Philosophy 81 (1984) 469-92.

17 I would like to thank Joan Weiner for comments on earlier drafts of this paper. The research of which this paper is, in part, a product was supported by a grant from the National Science Foundation.