Criticisms of Pascal

The argument assumes that the same decision matrix applies to everybody. However, perhaps the relevant rewards are different for different people. Perhaps, for example, there is a predestined infinite reward for the Chosen, whatever they do, and finite utility for the rest, as Mackie 1982 suggests. Or maybe the prospect of salvation appeals more to some people than to others, as Swinburne 1969 has noted.

Even granting that a single 2 x 2 matrix applies to everybody, one might dispute the values that enter into it. This brings us to the next two objections.

2. The utility of salvation could not be infinite

One might argue that the very notion of infinite utility is suspect---see for example Jeffrey 1983 and McClennen 1994. Hence, the objection continues, whatever the utility of salvation might be, it must be finite. Strict finitists, who are chary of the notion of infinity in general, will agree---see. Dummett 1978 and Wright 1987. Or perhaps the notion of infinite utility makes sense, but an infinite reward could only be finitely appreciated by a human being.

3. There should be more than one infinity in the matrix

There are also critics of the Wager who, far from objecting to infinite utilities, want to see more of them in the matrix. For example, it might be thought that a forgiving God would bestow infinite utility upon wagerers-for and wagerers-against alike---Rescher 1985 is one author who entertains this possibility. Or it might be thought that, on the contrary, wagering against an existent God results in negative infinite utility. (As we have noted, some authors read Pascal himself as saying as much.) Either way, f₂ is not really finite at all, but or - as the case may be. And perhaps f₁ and f₃ could be or -. Suppose, for instance, that God does not exist, but that we are reincarnated ad infinitum, and that the total utility we receive is an infinite sum that does not converge.

4. The matrix should have more rows

Perhaps there is more than one way to wager for God, and the rewards that God bestows vary accordingly. For instance, God might not reward infinitely those who strive to believe in Him only for the very mercenary reasons that Pascal gives, as James 1956 has observed. One could also imagine distinguishing belief based on faith from belief based on evidential reasons, and posit different rewards in each case.

5. The matrix should have more columns: the many Gods objection

If Pascal is really right that reason can decide nothing here, then it would seem that various other theistic hypotheses are also live options. Pascal presumably had in mind the Catholic conception of God---let us suppose that this is the God who either ‘exists’ or ‘does not exist’. By excluded middle, this is a partition. The objection, then, is that the partition is not sufficiently fine-grained, and the ‘(Catholic) God does not exist’ column really subdivides into various other theistic hypotheses. The objection could equally run that Pascal’s argument ‘proves too much’: by parallel reasoning we can ‘show’ that rationality requires believing in various incompatible theistic hypotheses. As Diderot 1875-77 puts the point: "An Imam could reason just as well this way".

Go to Alternative Formulation

Reference:

1.http://plato.stanford.edu/entries/pascal-wager/#1

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