Traditional act utilitarianism judges an action permissible just in case it produces as much aggregate utility as any alternative. It is often supposed that utilitarianism faces a serious problem if the future is infinitely long. For in that case, actions may produce an infinite amount of utility. And if that is so for most actions, then utilitarianism, it appears, loses most of its power to discriminate among actions. For, if most actions produce an infinite amount of utility, then few actions (...) produce non-maximal utility, and so most actions are permissible.1 I will argue that potentially infinite futures create no major problems for utilitarianism. Utilitarianism has, I argue, the resources to distinguish among actions all of which produce infinite amounts of utility -- judging some permissible and some impermissible. For brevity of expression I will focus on act utilitarianism, but all the points apply equally well to many other traditional forms of utilitarianism. (shrink)

On what grounds will the rational man become a Christian? It is often assumed by many, especially non-Christians, that he will become a Christian if and only if he judges that the evidence available to him shows that it is more likely than not that the Christian theological system is true, that, in mathematical terms, on the evidence available to him, the probability of its truth is greater than half. It is the purpose of this paper to investigate whether or (...) not this is a necessary and sufficient condition for the rational man to adopt Christianity. (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)

"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, _Journal of Philosophy_.

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.

Gambling on God brings together a superb collection of new and classic essays that provide the first sustained analysis of Pascal's Wager and the idea of an infinite utility as well as the first in-depth look at moral objections to the Wager.

000000001. Introduction Call a theory of the good—be it moral or prudential—aggregative just in case (1) it recognizes local (or location-relative) goodness, and (2) the goodness of states of affairs is based on some aggregation of local goodness. The locations for local goodness might be points or regions in time, space, or space-time; or they might be people, or states of nature.1 Any method of aggregation is allowed: totaling, averaging, measuring the equality of the distribution, measuring the minimum, etc.. Call (...) a theory of the good finitely additive just in case it is aggregative, and for any finite set of locations it aggregates by adding together the goodness at those locations. Standard versions of total utilitarianism typically invoke finitely additive value theories (with people as locations). A puzzle can arise when finitely additive value theories are applied to cases involving an infinite number of locations (people, times, etc.). Suppose, for example, that temporal locations are the locus of value, and that time is discrete, and has no beginning or end.2 How would a finitely additive theory (e.g., a temporal version of total utilitarianism) judge the following two worlds? Goodness at Locations (e.g. times) w1:..., 2, 2, 2, 2, 2, 2, 2, 2, 2, ..... w2:..., 1, 1, 1, 1, 1, 1, 1, 1, 1, ..... Example 1 At each time w1 contains 2 units of goodness and w2 contains only 1. Intuitively, we claim, if the locations are the same in each world, finitely additive theorists will want to claim that w1 is better than w2. But it's not clear how they could coherently hold this view. For using standard mathematics the sum of each is the same infinity, and so there seems to be no basis for claiming that one is better than the other.3 (Appealing to Cantorian infinities is of no help here, since for any Cantorian infinite N, 2xN=1xN.). (shrink)