Given ht as the hypothesis of theism, hm as the hypothesis of materialism, and e as the evidence of a complex life-bearing universe, Swinburne presents these arguments in his "The Existence of God" (2004):
(1) That this ordered universe is a priori improbable (2004, p49, p150, 1991, p304 et seq.), given the stringent requirements for life (cf. Leslie, 2000, p12), and the Second Law of Thermodynamics (Giancoli, p396);
(2) That this universe’s structure is evidence for theism, and that theism therefore explains this universe. Swinburne argues that that because P(e| ht) > P(e| hm), it follows that P(ht |e) > P(hm |e). (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| ht) > P(e). I draw a number of conclusions, most pertinently, that Hacking's Total Probability Rule (TPR), for cases of mutually exclusive hypotheses [ht v hm] and evidence e entails that any h can only be confirmed if P(e|~h) is low. I also conclude that if we follow TPR for Swinburne's argument, we achieve the result that theism is at best slightly improbable, or equiprobable with materialism.