The Two Envelopes Problem is a beautiful and quite confusing problem in decision theory which is ca. 35 years old and has provoked at least 150 papers directly addressing the problem and displaying a surprising variety of different responses. This paper finds decisive progress in an approach of Priest and Restall in 2003, contends that the recent papers having appeared since did not really go beyond that paper, argues further that Priest’s and Restall’s solution is still not complete, and proposes (...) a completion of their solution. If the analysis is correct, this work has the potential of laying the Two Envelopes Problem at rest. (shrink)

Pascal’s Wager does not exist in a Platonic world of possible gods, abstract probabilities and arbitrary payoffs. Real decision-makers, such as Pascal’s “man of the world” of 1660, face a range of religious options they take to be serious, with fixed probabilities grounded in their evidence, and with utilities that are fixed quantities in actual minds. The many ingenious objections to the Wager dreamed up by philosophers do not apply in such a real decision matrix. In the situation Pascal addresses, (...) the Wager is a good bet. In the situation of a modern Western intellectual, the reasoning of the Wager is still powerful, though the range of options and the actions indicated are not the same as in Pascal’s day. (shrink)

Pascal's wager is an argument in support of religious belief taking its name from the seventeenth century polymath Blaise Pascal. Unlike more traditional arguments for the existence of God, Pascal's wager is a pragmatic argument, concluding not that God exists but that one should wager for God; that is, one should live as if God exists. After an introduction to the elements of decision theory needed to understand the wager, I discuss the interpretation of Pascal's reasoning in the Infini rien (...) fragment of the Pensees, in which he presents several versions of a wager-style argument. Recent discussions of the role of the wager within Pascal's overall project of Christian apologetics are also examined. I then review contemporary formulations of, attacks on, and objections to Pascal's wager. Recent authors have pressed moral objections, epistemological objections, objections relating to infinite utilities, the many Gods objection, and objections to the expectation rule, among others. After an examination of this literature, I conclude with a brief discussion of noncanonical versions of the wager, including Jeff Jordan's Jamesian wager. (shrink)

Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the objections (...) and Hájek's philosophical worries disappear, however, if we represent our preferences using relative utilities rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager. (shrink)

This paper argues that Pascal's formulation of his famous wager argument licenses an inference about God's nature that ultimately vitiates the claim that wagering for God is in one's rational self-interest. In particular, it is argued that if we accept Pascal's premises, then we can infer that the god for whom Pascal encourages us to wager is irrational. But if God is irrational, then the prudentially rational course of action is to refrain from wagering for him.

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

I argue that if one accepts the existence of a multiverse model that posits the existence of all possible realities, and also wants to maintain the existence of a God who exemplifies omnipotence, omnibenevolence and omniscience then the brand of God that he should ascribe to is one of deism rather than the God of classical theism. Given the nature and construct of such a multiverse, as well as some specific interpretations of the divine attributes, this points us to a (...) God who is inactive in the natural world, not one who is. This deistic conception of God not only sits better with the idea of a multiverse and is also compatible with many arguments for theism, but it also responds to certain arguments for atheism better than the classical conception of God. I ultimately argue that deism ought to be given consideration as a plausible alternative conception to the classical conception of God, given the acceptance of a multiverse. (shrink)

The orthodoxy that conditional probabilities reflect what are for a subject evidential bearings is seconded. This significance suggests that there should be principles equating rationally revised probabilities on new information with probabilities reached by conditionalizing on this information. Several principles, two of which are endorsed, are considered. A book is made against a violator of these, and it is argued that there must be something wrong with a person against whom such books can be made. Appendices comment on Popper-functions, elaborate (...) on bets and odds, and relate dutch books and strategies to conditions of inconsistency (Ramsey's idea) and imperfection. (shrink)

In the Infini-Rien fragment of his Pensées, Blaise Pascal develops an argument for the rationality of faith in God, which posthumously became known as Pascal’s Wager and at the same time represents a cornerstone of modern probability theory. While this betting argument has been the subject of much philosophical investigation, the contribution of this paper lies in the following: On the one hand, the bet is reconstructed in its basic features as well as its structure with the help of modern (...) decision and probability theory tools. Thus, it is shown that Pascal’s betting argument, in distinction to Hacking 1972 for instance, has the form of an a fortiori argument. On the other hand, as far as objections to Pascal’s argument are concerned, it is true that the premises have often been called into doubt, more or less convincingly. On the other hand, this article is dedicated to the question, often emphatically – especially in Hacking 1972 – and perhaps carelessly affirmed in Pascal research, whether Pascal’s premises imply his conclusion at all. (shrink)