Defeaters Without Confirmation — 38

Demonstrating the incoherence of a competing ideology can defeat that ideology, and in a closed Bayesian partition it may even raise the absolute probability of Christianity by redistributing the rival’s prior probability among surviving hypotheses. But it does not, by itself, positively confirm Christianity over the remaining alternatives. A rival-elimination argument becomes evidentially serious only when it specifies the hypothesis space, assigns non-arbitrary priors, and shows that the defeating evidence is more expected on Christianity than on the surviving alternatives. This paper develops a formal constraint on negative apologetics. The motivating question is simple: if one demonstrates the incoherence of a competing ideology, does Christianity thereby become more probable? The answer is mixed. There is a narrow probabilistic sense in which eliminating a rival can raise Christianity’s posterior probability. Yet the increase is inherited from the eliminated rival; it is not positive support for Christianity’s distinctive content. Without a justified contrast class, negative apologetics risks confusing local defeat with global confirmation.