Bayesian Arguments for God's Existence

Swinburne begins with Bayes's theorem: the posterior probability of a hypothesis given evidence equals the prior probability of the hypothesis times the probability of the evidence given the hypothesis, divided by the overall probability of the evidence. Applied to theism, this means: given the evidence we have, how probable is the hypothesis that God exists? Swinburne argues that we should assess this cumulatively — each phenomenon (the existence of the universe, its lawfulness, consciousness, morality, religious experience) contributes its share of evidential weight to the overall probability.

Before any evidence is introduced, Swinburne argues that theism has a relatively high prior probability because it is a supremely simple hypothesis. Simplicity is a scientific virtue: all else being equal, simpler theories are more likely to be true. Theism posits a single entity — God — with infinite properties (omnipotence, omniscience, etc.), which Swinburne argues is simpler (in the relevant sense) than hypotheses that posit multiple natural laws or the brute inexplicable existence of the universe without any explanation. Infinite properties are simpler than large finite ones precisely because they require no specific finite degree to be specified.

The evidence Swinburne marshals is extensive: the existence of the universe (cosmological argument), the orderliness of nature and the fine-tuning of physical constants (teleological argument), the existence of conscious beings with mental properties that are not reducible to physical ones (consciousness argument), the widespread experience of moral obligations (moral argument), and — most heavily weighted — the occurrence of religious experience across cultures and centuries. Each argument is assessed for how much it raises the probability of theism over naturalism. Swinburne concludes that the conjunction of all this evidence makes the existence of God more probable than not.

The Existence of God was first published in 1979 and revised in 2004. It is the second volume of Swinburne's trilogy on rational theism. His probabilistic methodology is explained and justified in The Justification of Induction (1974).