1 This doctrine is articulated by Fraassen, Bas Van in “Belief and the Will” (here-after BW), Journal of Philosophy, 81, 5 (May 1984): 235–56CrossRefGoogle Scholar; see especially pp. 236 and 246.

2 Van Fraassen writes, “My main argument for voluntarism in epistemology is not among those given in this chapter, but remains the one in my ‘Belief and the Will.’” See Fraassen, Bas Van, Laws and Symmetry (hereafter LS) (New York: Oxford University Press, 1989), pp. 175–76.CrossRefGoogle Scholar

3 LS, especially sec. 5, chap. 7, is where Van Fraassen articulates much of the above.

4 Let us assume, not uncontroversially, that a degree of belief in a proposition represents the betting odds one would be willing to accept on that proposition. The Dutch Book theorem states that willingness to deviate from the dictates of the probability calculus when setting subjective probabilities for each proposition in a set of hypotheses inevitably leaves one vulnerable to a betting strategy that will ensure a loss of a sum of money regardless of what the truth values of the hypotheses turn out to be—i.e., a Dutch Book. In other words, one can be exploited for an unavoidable loss of money if one ignores the axioms of the probability calculus in formulating subjective probabilities and is willing to bet according to the subjective probabilities so devised. In this way, one can argue that coherence is a constraint on rationality; failure to be coherent could leave one vulnerable to a Dutch Book. For a discussion of problems associated with such Dutch Book Arguments, see Earman, John, Bayes or Bust (Cambridge: MIT Press, 1992), chap. 2.Google Scholar

Van Fraassen's DBA goes beyond attempting to motivate coherence; he also attempts to justify the Reflection principle with a DBA. The relevant DBA for consideration here is the diachronic DBA that van Fraassen constructs. Diachronic DBAs attempt to show that one subjects oneself to a Dutch Book by failing to have an appropriate strategy in place for changing beliefs. Van Fraassen's diachronic Dutch Book strategy is based on one's present degree of belief about a later degree of belief. He shows that, if one is willing to place bets about one's later degree of belief or subjective probability for an event, a Dutch Book can result if Reflection is not followed. If I consider some hypothesis H and some proposition E about my future attitude to the hypothesis as propositions about which bets can be placed, the Dutch book arises as follows. Let P(X) be the probability of X. Let x be the probability of ∼H, given E. The bookie offers me a bet that pays 1 if (∼H & E) and costs P(∼H & E), a second bet that pays x if ∼E and costs xP(∼E), and a third bet that pays (x—the bettor's subjective probability for H if E becomes true) and costs ((P(∼H & E)/ P(E))&the odds one will accept on H if E is true)P(E). A Dutch Book arises solely from my having a lack of confidence in my handicapping skills—i.e., if I give a low probability for P(∼H & E), then I shall be in a position in which a monetary loss is unavoidable. The Reflection principle is offered as a means of avoiding such Dutch Books. Van Fraassen's DBA is found in BW, pp. 240–41.

5 What I have suggested in this paragraph is similar to the suggestions made by Green, Mitchell S. and Hitchcock, Christopher R., “Reflections on Reflection: Van Fraassen on Belief,” Synthese, 98 (1994): 301–302.CrossRefGoogle Scholar

6 See, for example, Christensen, David, “Clever Bookies and Coherent Beliefs,” The Philosophical Review, 100 (1991): 229–47CrossRefGoogle Scholar; Nicholas, John, “Realism for Shopkeepers: Behaviouralist Notes on Constructive Empiricism,” in An Intimate Relation, edited by Brown, J. R. and Mittelstrass, J. (Dordrecht: Kluwer Academic Publishers, 1989): 459–76CrossRefGoogle Scholar; and Talbott, W. J., “Two Principles of Bayesian Epistemology,” Philosophical Studies, 62 (1991): 135–50CrossRefGoogle Scholar.

7 Van Fraassen (BW, p. 243) suggests that such concerns are adequately addressed in Skyrms, Brian, “higher-order Degrees of Belief,” in Prospects for Pragmatism: Essays in Honour of F. P. Ramsey, edited by Mellor, D.H. (New York: Cambridge University Press, 1980), pp. 109–37Google Scholar.

8 Pascal assures us that acting according to such a belief will eventually increase the degree of psychological certainty one feels about God's existence.

9 Descartes also invokes God's existence to endorse memory as an epistemic process that can warrant present beliefs, and to show that what he remembers demonstrating with clarity and distinctness remains certain despite the fact that he can no longer remember the proof: “Accordingly, even if I am no longer attending to the arguments which led me to judge that this is true, as long as I can remember that I clearly and distinctly perceived it, there are no counterarguments which can be adduced to make me doubt it, but on the contrary I have true and certain knowledge of it” (Descartes, Rene, Meditations, in The Philosophical Writings of Rene Descartes, Vol. 2, edited and translated by Cottingham, John, Stoothof, Robert, and Murdoch, Dugald [Cambridge: Cambridge University Press, 1984], p. 48, or AT VII, p. 70).Google Scholar

10 Numerous studies have explored the extent to which human cognizers follow Bayes's theorem when making probability judgements, and some have concluded that humans are not, as a matter of empirical fact, Bayesian agents. For instance, see Phillips, L. and Edwards, W., “Conservatism in a Simple Probability Learning Task,” Journal of Experimental Psychology, 72 (1966): 346–54CrossRefGoogle Scholar, and Kahneman, D., Slovic, P., and Tversky, A., Judgment under Uncertainty: Heuristics and Biases (Cambridge: Cambridge University Press, 1982).CrossRefGoogle Scholar

11 I use the term “Cartesian voluntarism” because of the aforementioned considerations from the Meditations, but also because of this telling statement in “Meditation One”: “My habitual opinions keep coming back, and, despite my wishes they capture my belief, which is as it were bound over to them as a result of long occupation and the law of custom… In view of this I think it will be a good plan to turn my will in completely the opposite direction and deceive myself, by pretending for a time that these former opinions are utterly false and imaginary” (Descartes, Meditations, p. 15, or AT VII, p. 15).

12 Talbott, “Two Principles,” pp. 136–37.

13 Christensen, “Clever Bookies,” pp. 234–35.

14 For discussion of what constitutes an epistemically reliable process, I refer the reader to Goldman, Alvin, Epistemology and Cognition (Cambridge: Harvard University Press, 1986), chap. 5.Google Scholar

15 See LS, p. 176.