Can Bayes’ Theorem, given the evidence of this universe, be used to support theism?

Abstract

Given h_t as the hypothesis of theism, h_m as the hypothesis of materialism, and e as the evidence of a complex life-bearing universe, Richard Swinburne presents these arguments in The Existence of God: (1) that this ordered universe is a priori improbable, given the stringent requirements for life and the Second Law of Thermodynamics; (2) that this universe’s structure is evidence for theism, and that theism therefore explains this universe; Swinburne argues that because P(e|h_t) > P(e|h_m>), it follows that P(h>_t|e) > P(h_m|e); and (3) a theistic explanation for the universe is more probable because it is simpler; therefore it is more likely that God exists than not. As I have addressed (3) in a prior paper, this paper will address the Bayesian argument that Swinburne offers in (2), i.e. that P(e|h_t) > P(e). In the paper I draw a number of conclusions, most pertinently, that Hacking’s Total Probability Rule (TPR) for cases of mutually exclusive hypotheses [h_t vs h_m] and evidence e entails that ht can only be confirmed if P(e|~h_t) is low. I also conclude that if we follow the TPR for Swinburne’s argument, we achieve the result that theism is at best slightly improbable, or equiprobable with materialism.

South African Journal of Philosophy 2013, 32(2): 163–172