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.

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)

How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments for (...) the existence of God, and theories on how to evaluate scientific and historical hypotheses. It is explained how Pascal and Fermat's work on chance arose out of legal thought on aleatory contracts. The book interprets pre-Pascalian unquantified probability in a generally objective Bayesian or logical probabilist sense. (shrink)

In Pascal's Wager: A Study Of Practical Reasoning In Philosophical Theology ,[1] Nicholas Rescher aims to show that, contrary to received philosophical opinion, Pascal's Wager argument is "the vehicle of a fruitful and valuable insight--one which not only represents a milestone in the development of an historically important tradition of thought but can still be seen as making an instructive contribution to philosophical theology".[2] In particular, Rescher argues that one only needs to adopt a correct perspective in order to see (...) that Pascal's Wager argument is a good argument. Moreover, there seems to be a certain amount of contemporary support for Rescher's claim that Pascal's Wager argument can be seen to be a good argument when properly construed .[3] However, despite this recent trend to adopt a more sympathetic stance towards Pascal's Wager argument, I propose to defend the traditional view that Pascal's Wager argument is almost entirely worthless--at least from the theological standpoint. (No doubt, it has historical significance from the standpoint of decision theory; but that's a separate matter.). (shrink)

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.

“Pascal's Wager” is the name given to an argument due to Blaise Pascal for believing, or for at least taking steps to believe, in God. The name is somewhat misleading, for in a single paragraph of his Pensées, Pascal apparently presents at least three such arguments, each of which might be called a ‘wager’ — it is only the final of these that is traditionally referred to as “Pascal's Wager”. We find in it the extraordinary confluence of several important strands (...) of thought: the justification of theism; probability theory and decision theory, used here for almost the first time in history; pragmatism; voluntarism (the thesis that belief is a matter of the will); and the use of the concept of infinity. (shrink)

The standard version of Pascal’s Wager suffers from serious problems. In this paper I present a modified version of a Wager-style argument that avoids several of the most serious objections to the standard version, viz., the objections of Duff and Hájek relating to infinite utilities, moral objections concerning the use of pragmatic considerations, and the many-gods objection. I argue that a serious commitment to living a Christian life is rational (and the failure to make such a commitment is irrational) if (...) one is rational in assigning a credence to Christianity of at least one-half. The upshot is that considerations of practical rationality dramatically lower the bar for natural theology. (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.

Pascal’s wager and Leibniz’s theory that this is the best of all possible worlds are latecomers in the Faith-and-Reason tradition. They have remained interlopers; they have never been taken as seriously as the older arguments for the existence of God and other themes related to faith and reason.

A person who does not have good intellectual reasons for believing in God can, depending on his probabilities and values for consequences of believing, have good practical reasons. Pascalian wagers founded on a variety of possible probability/value profiles are examined from a Bayesian perspective central to which is the idea that states and options are pragmatically reasonable only if they maximize subjective expected value. Attention is paid to problems posed by representations of values by Cantorian infinities. An appendix attends to (...) Robinsonian hyperreals. Another appendix presents for comparison Newcomb's Problem and a problem in some ways like it suggested, I think, by ideas of John Calvin. (shrink)

Pascal a croise le jeu a plusieurs reprises. En reflechissant sur des parties de cartes (ou de des) interrompues, le mathematicien jette les bases de ce qui deviendra ulterieurement le calcul des probabilites. L'auteur des Pensees, qui concoit ses lecteurs sous les traits de libertins et joueurs notoires, leur presente une societe entierement soumise au hasard; il en sonde les lois comme des regles de jeu. L'objet de cette etude n'est pas d'etablir une thematique du jeu dans l'oeuvre de Pascal, (...) mais de proposer cette notion de jeu comme un modele, un prisme a travers lequel un certain nombre de realites incompatibles coexistent neanmoins. Le modele du jeu rend compte ainsi de quelques-uns des paradoxes les plus stimulants sur lesquels roulent les Pensees: comment le conservatisme politique de Pascal s'accompagne d'une mise en cause radicale des lois, comment le monde en proie au jeu est un monde a la fois fondamentalement desordonne et admirablement regle. Quant au Pari, qui fascine et embarrasse depuis plusieurs siecles, une etude attentive des notions mathematiques qui le sous-tendent permet d'eclairer quelques obscurites du texte, et de poser une fois encore, mais sur de nouvelle bases, la question de sa portee et de sa validite. (shrink)