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Combining Bayesian Theism with Pascal’s Wager
Stamatios Gerogiorgakis
In the light of the newest criticisms against it, Bayesian Theism appears to be an endangered
project. In order to give the Bayesian analysis of religious faith a chance independently of the
question whether these criticisms are sound or not, I propose a Bayesian reading of Pascal’s
Wager which is exclusively based on subjective probabilities. I argue that following religious
maxims for reasons which are independent from religious ethics is inconsistent. I argue,
further, that one’s following religious maxims only makes sense only under the condition
that one bets on God’s existence, i.e. has a strong faith.
1. Motivational Remarks
Swinburne’s Bayesian argument for the existence of God consists in calculating by Bayes’s
theorem the likeliness of God’s existence on the total available evidence, once we assume: 1)
some plausible value for the likeliness of the fact that would be that the evidence is made
available to us by God and 2) the ratio of the intrinsic probability of the existence of God
alone to the intrinsic probability of the evidence (without assuming that God gave us the
evidence, that is). I.e. (for h = the hypothesis that God exists; k = tautological evidence, e.g.
laws of logic and physics; e & k = the total evidence for the existence of God):
(BT)→P (h | e & k) = P (e | h & k) · P (h | k) / P (e | k).
Richard Swinburne (2004) argues that the value for P (h | e & k), i.e. the likeliness of the
hypothesis that God exists given the total evidence, approximates, nevertheless does not
reach the value 1. In other words, God is very likely to exist. The basis for Swinburne’s
calculation is set by 1) the assumption by the principle of indifference (see below) that it is as
likely for God to provide us with some evidence for His existence as it is likely that He would
not provide us with this evidence (i.e. P (e | h & k) = ½) and 2) the assumption of a value
approximating but not reaching 2 for the ratio P (h | k) / P (e | k).
As one easily sees, Swinburne’s result depends largely on probabilities which are not
calculated but assumed; in other words: on prior probabilities. 1 The principle of indifference
allows for example for assigning a priori equal probability values to alternative events, for
whose statistic frequency we are completely clueless.
Jeremy Gwiazda objected that the hypothesis that God exists (‘h’) given the necessities of
nature and thought (‘k’) is very simple, whereas our available evidence (‘e’) for the existence
of God given the same necessities is much more complex. The principle of simplicity allows to
assign simple hypotheses which are explanatory of certain events, higher prior probabilities
than more complex hypotheses which are explanatory of the same events. Gwiazda (2010,
360) feels justified to conclude from this that the ratio P (h | k) / P(e | k) must result in a
1
By contrast to the largest part of the bibliography concerning the topic objective vs. subjective
Bayesianism which uses the term “prior probability” to denote the assumed, non-calculated probability,
Swinburne (2004), 67, uses “prior” and “intrinsic” probability interchangeably and offers no specific
term for the assumed, non-calculated probability. This is a pity since assumed, non-calculated
probabilities play a great role in his analysis. By the term “prior probabilities” I am using here the
linguistic convention of the objective-vs.-subjective-Bayesianism-bibliography, not Swinburne’s usage.