In this second of two essays responding to critical discussion of my " Divine Hiddenness and Human Reason," I show how an ' accommodationist ' strategy can be used to defuse objections that were not exposed as irrelevant by the first essay. This strategy involves showing that the dominant concern of reasons for divine withdrawal can be met or accommodated within the framework of divine - human relationship envisaged by the hiddenness argument. I conclude that critical discussion leaves the argument (...) very much alive and kicking, and indeed strengthened as it moves into its second decade of life. (shrink)

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we (...) want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

Only one traditional objection to Pascal's wager is telling: Pascal assumes a particular theology, but without justification. We produce two new objections that go deeper. We show that even if Pascal's theology is assumed to be probable, Pascal's argument does not go through. In addition, we describe a wager that Pascal never considered, which leads away from Pascal's conclusion. We then consider the impact of these considerations on other prudential arguments concerning what one should believe, and on the more general (...) question of when and why belief formation ought to be based solely on the evidence. (shrink)

The late John L. Mackie, formerly of University College, Oxford.

Many think that Pascal’s Wager is a hopeless failure. A primary reason for this is because a number of challenging objections have been raised to the wager, including the “many gods” objection and the “mixed strategy” objection. We argue that both objections are formal, but not substantive, problems for the wager, and that they both fail for the same reason. We then respond to additional objections to the wager. We show how a version of Pascalian reasoning succeeds, giving us a (...) reason to pay special attention to the infinite consequences of our actions. (shrink)

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.

In this paper I will address a few of the many questions that fall under the general heading of “the ethics of belief.” In section I I will discuss the adequacy of what has come to be known as the “deontological conception of epistemic justification” in the light of our apparent lack of voluntary control over what we believe. In section II I’ll defend an evidentialist view about what we ought to believe. And in section III I will briefly discuss (...) apparent conflicts between epistemic considerations and moral or other considerations. (shrink)

Abstract: This paper argues that instances of what are typically called ‘epistemic irresponsibility’ are better understood as instances of moral or prudenial failure. This hypothesis covers the data and is simpler than postulating a new sui generis form of normativitiy. The irresponsibility alleged is that embeded in charges of ‘You should have known better!’ However, I argue, either there is some interest at stake in knowing or there is not. If there is not, then there is no irresponsibility. If there (...) is, it is either the inquirer's interests—in which case it is a prudential shortcoming—or someone else's interests are at stake—in which case it is a moral shortcoming. In no case, I argue, is there any need to postulate a form of normativity in epistemology other than the traditional epistemological norm that one's attitudes should fit the evidence one has. (shrink)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

A. Pascal's statement of his wager argument is couched in terms of the theory of probability and the theory of games, and the exposition is unclear and unnecessarily complicated. The following is a ‘creative’ reformulation of the argument designed to avoid some of the objections which have been or might be raised against the original.

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)