Evidence and a cumulative case for God › What Bayesian reasoning contributes

Bayesian reasoning distinguishes a hypothesis's probability before the evidence under consideration from its probability after that evidence. The first is a prior probability; the second is a posterior probability. A prior is relative to an evidential starting point. It need not represent what someone believed before encountering any experience whatsoever.

The likelihood of evidence given a hypothesis concerns how probable that evidence would be if the hypothesis were true. It differs from the probability that the hypothesis is true given the evidence. An explanation's ability to accommodate an observation does not by itself confirm it; confirmation requires comparing how probable the observation is under the hypothesis and under its negation.

For evidence to favor a hypothesis against its negation, it must be more probable given the hypothesis than given its negation, provided the relevant probabilities are defined and nondegenerate. A proposed explanation gains no advantage merely because the observation is compatible with it. The comparison asks whether the observation is more to be expected on that explanation.

For theism, this raises questions about divine intentions. An all-powerful being could produce many different worlds. To claim that a world like ours is probable given God, one needs reasons for thinking God would choose something relevantly like it. Power establishes ability; it does not by itself establish a likelihood of acting.

Swinburne appeals to goods God would have reason to realize, including conscious life and responsible agency. This supplies a proposed connection between the hypothesis and the evidence. A critic can question either the proposed goods or the inference from their value to what God would probably create. The probability framework makes that disagreement visible without deciding it.