By Peter Achinstein
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8 that it would land heads on the 1001st toss. 8). Accordingly, Salmon's version of the frequency theory, together with the positive relevance definition of evidence, yields the following thesis concerning the relationship between evidence and belief: If e is evidence that h, given b, then e together with b constitutes a good (nonveridical) reason to believe h to a higher degree than does b without e. Using the high probability definition, we get If e is evidence that h, given b, then e constitutes a good (nonveridical) reason to believe h to a higher degree than not-h.
Lewis's view also leads to a consequence on the high probability definition of evidence that may seem questionable. Let us imagine a situation in which John buys just 1 ticket, not 999. m . today, and none later. And let us suppose that, as luck would have it, John wins with this ticket, so that h is again true. Then, on Lewis's conception, C our world,noon (h) = 1. Again, if chances are probabilities, it follows that C our world,noon (h/e′) = 1. So on the high-probability definition of evidence, e′, the fact that John buys just 1 ticket in a 1000 ticket lottery, is evidence that he wins the lottery, given the way the world is at noon.
But he may say that they can and should all be rendered a priori by packing enough information into them to make them empirically complete. My response is that even if it could be done, why do so? No doubt rendering a claim a priori is one way of establishing its truth (or falsity). But it is not the only way or necessarily the best. Thomson discovered the falsity of Hertz's (potential) evidence claim not by turning it into a (false) a priori claim, but by conducting the experiments he did. 13.