Date of publication: 2017-07-09 10:47
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On the other hand, if we were to suppose that T yields false positives 95% of the time, the epistemic status of E would look quite different. While condition (i) is still satisfied, condition (ii) would not be: since the test almost as frequently produces false positives, there is a very low probability that T would have produced a less fitting result if the patient did not have D. Accordingly, T would not count as a severe test of our hypothesis H, and so E would fail to constitute error-statistical evidence for H.
On the Bayesian view, what we need to consider are the separate effects wrought by E on the probabilities of H and A. Accordingly, the goal will be to compare P(H/E) and P(A/E), both of which can be conveniently calculated by means of Bayes' theorem:
Finally, Williamson points out that we often think of evidence as ruling out certain hypotheses. For instance, that I was in Cleveland at the time of the murder rules out the hypothesis that I was the murderer in Columbus. But evidence E rules out an hypothesis H only when the two are logically inconsistent in particular, one must be able to deduce ~H from E. And, of course, the premises in a logical deduction consist of propositions —the sort of thing that can be true or false. Indeed, a valid deduction is one such that, if the premises are true , the conclusion must also be true.
Whether or not we agree with Williamson, we shall see in the next section, where we consider the important role evidence plays—namely, as something that justifies belief—that we may have strong theoretical ground for accepting, contrary to Williamson, that experiences can also count as evidence.
" Barth, the Menardian " by American Literature author Berndt Clavier, " The misunderstood Irish composer " by Music author Majella Boland, and " Picking a fight in an empty room " by British and Irish Literature author James Moran are now available on the OUPblog.