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15 - Do Infinitesimal Probabilities Neutralize the Infinite Utility in Pascal’s Wager?

from Part III - Extensions

Published online by Cambridge University Press:  28 September 2018

Paul Bartha
Affiliation:
University of British Columbia, Vancouver
Lawrence Pasternack
Affiliation:
Oklahoma State University
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Summary

In chapter 15, Sylvia Wenmackers explores the implications for Pascal’s Wager if we allow agents to have an infinitesimal probability that God exists. Pascal anticipated and rejected infinitesimal probabilities, but his reasons are not entirely clear. A number of philosophers have argued that infinitesimal probabilities are not merely permissible but sometimes rationally required. It is natural, then, to ask whether Pascal’s Wager succeeds for an agent who combines an infinitely small credence in the existence of God with infinite utility for salvation. This question only makes sense relative to some non-standard decision theory. Wenmackers argues that any such theory should satisfy a ‘harmony’ condition that allows us to combine infinite utilities and infinitesimal probabilities, and she shows that hyperreal decision theory meets this criterion. Within hyperreal decision theory, infinite utility can be ‘neutralized’ by infinitesimal probability, provided the infinitesimal is small enough. There is an interesting analogy here between hyperreal and finite-utility versions of the Wager: in both cases, success or failure depends upon the precise combination of utility and probability values. Wenmackers’ chapter also reviews important concerns about whether the hyperreal formalization is sufficiently faithful to Pascal’s original argument.
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Pascal's Wager , pp. 293 - 314
Publisher: Cambridge University Press
Print publication year: 2018

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