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Indeed, any Bayesian analysis of the question of justified belief in miracles must be otiose until the difficult and essential questions concerning "evidence" in relation to an allegedly miraculous occurrence are resolved — at which point any Bayesian analysis will add little except the technical complexity of a formal apparatus that may or may not "clarify" the structure of Hume's argument.
The balancing of probabilities is of no use until it is decided what goes into the balance — that is, what constitutes the evidence that is to be subject to the balancing of probabilities. The point is this; apart from independent philosophical arguments — arguments that would in effect undermine the relevance of a Bayesian analysis to the question of the credibility of reports of the miraculous — no such analysis can, in principle, prove that no testimony can (or cannot) establish the credibility of a miracle.
http://plato.stanford.edu/entries/miracles/
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I would agree with the author that Bayes’ Theorem is not a good tool to show that belief in all miracles is unreasonable. Just as a magnifying glass does not help with blurry images, Bayes’ Theorem does not work well with ill-formed hypothesis and nebulous evidence. It is not at all clear that Hume’s argument can be formulated in such a way that would satisfy the requirements of Bayes’ Theorem. That said if well-formed hypotheses and concrete evidence are present, Bayes’ Theorem seems well suited to evaluate particular miracle claims.
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