The Argument from Bayes' Theorem A. The theorem enables to calculate the posterior probability of a hypothesis, given some new piece of evidence: P(h/e). P(h/e) = P(h)P(e/h)/P(e) B. We need three inputs: (1) the prior probability of h, P(h), (2) the likelihood of the evidence, assuming the truth of the hypothesis, P(e/h), (3) the prior probability of the evidence. For P(h/e) to be high, we want P(h) and P(e/h) to be fairly high, and P(e) to be very low. C. We can compute the probability of P(e) by the formula: P(e) = P(e/h)P(h) + P(e/-h)P(-h) Since we want P(e/h) to be high, P(e/-h) must be very low. That is, the evidence e must be something that would be very unlikely (surprising) if the hypothesis were false. D. If P(e/h) > P(e/-h), and P(h) ’ 0, then we say that the evidence e confirms hypothesis h. That is, e raises the probability of h: P(h/e) > P(h), the posterior probability of h is higher than the prior probability of h. E. Swinburne's h = the existence of the God of classical theism (an infinite, uncaused, perfectly
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