Evidence and a cumulative case for God › A hypothetical update with stated assumptions

Consider a numerical illustration of the method, rather than Swinburne's estimate of God's probability. Suppose a hypothesis starts with probability one fifth. Its negation then has probability four fifths, so the odds favoring the hypothesis are one to four. Odds compare the probability of the hypothesis with the probability of its negation.

Suppose an observation is three times as likely if the hypothesis is true as if it is false. Multiplying the initial odds by that likelihood ratio gives odds of three to four. Those odds correspond to a probability of three sevenths, about 0.429. The evidence supports the hypothesis, but it has not yet made it more probable than not.

Now suppose a second observation is twice as likely given the hypothesis, after taking the first observation into account, as given its negation with that same information. The updated odds become six to four, giving probability six tenths. Under these invented assumptions, the combined evidence makes the hypothesis more probable than not.

The numbers show the difference between confirmation and an overall probable conclusion. They do not measure theism. The likelihood ratios and starting probability have been stipulated to illustrate the arithmetic. Disagreeing with their use for a religious hypothesis would require evaluating the proposed probabilities and their grounds.

The conditioning in the second step matters. If both observations merely report the same underlying fact, treating them as independent can count the same support twice. A cumulative argument can handle dependent evidence, but it must assess the additional evidence in light of what is already known. Dependence is a reason for care, not a reason to abandon cumulative reasoning.