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- P. Bartha (2007). Taking Stock of Infinite Value: Pascal's Wager and Relative Utilities. Synthese 154 (1):5 - 52.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 (Philosophical Review 112, 2003) 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 (generalized utility ratios) 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.
Similar books and articles
Perhaps the best known criticism of Pascal’s wager is the many Gods objection. As so often with anglophone criticisms of Pascal, the many Gods objectiontypically treats the wager in isolation from the rest of Pascal’s thought. In this case, the truncated reading has issued in the view that Pascal was indifferent toor ignorant of the possibility that Gods other than the one described by Catholic theology might exist. This view is false. Even a cursory glance beyond the wagerfragment reveals that Pascal considers a number of religious and philosophical positions and argues that, given the nature and needs of the human being, onlya God of a specific description could count as God for the human being and, so, be the object of the wager. This essay sketches Pascal’s view to show that the many Gods objection is not sufficient to address his argument meaningfully.
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.).
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.).
“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.
I defend Pascal's Wager from a particular way of evading it, the mixed strategy approach. The mixed strategies approach suggests that Pascal's Wager does not obligate one to believe in God, because one can get the same infinite expected utility from other strategies besides the strategy of believing in God. I will show that while there's nothing technically wrong with the mixed strategy approach, rationality requires it to be applied in such a way that Pascal's Wager doesn't lose any force.
In "To Bet The Impossible Bet", Harmon Holcomb III argues: (i) that Pascal's wager is structurally incoherent; (ii) that if it were not thus incoherent, then it would be successful; and (iii) that my earlier critique of Pascal's wager in "On Rescher On Pascal's Wager" is vitiated by its reliance on "logicist" presuppositions. I deny all three claims. If Pascal's wager is "incoherent", this is only because of its invocation of infinite utilities. However, even if infinite utilities are admissible, the wager is defeated by the "many gods" and "many wagers" objections. Moreover, these objections do not rely on mistaken "logicist" presuppositions: atheists and agnostics traditionally and typically hold that they have no more--or at any rate, hardly any more--reason to believe in the traditional Christian God than they have to believe in countless alternative deities.
Pascal's wager attempts to provide a prudential reason in support of the rationality of believing that God exists. The wager employs the idea that the utility of theistic belief, if true, is infinite, and in this way, the expected utility of theism swamps that of any of its rivals. Not surprisingly the wager generates more than a good share of philosophical criticism. In this essay I examine two recent objections levelled against the wager and I argue that each fails. Following this, I argue that a transfinite version of the wager -- one using the idea of an infinite utility -- is incompatible with standard axiomatic constructions of decision-theory and, as a consequence, the Pascalian would be well-advised to give up the idea of an infinite utility and employ only a finite version of the wager. The consequences of limiting the wager to finite utilities are also explored.
Discussion of P. Bartha, Taking stock of infinite value: Pascal's Wager and relative utilities
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