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432 pages, Paperback
First published January 1, 2011
P1. That A is the case provides evidence E for B’s being the case if and only if the number of times in which we have observed A, and then have observed B, is greater than the number of times in which we have observed that A was not followed by B.
P2. The strength of E is proportional to the ratio among the number of times in which we have observed A, and then have observed B, and the number of times in which we have observed that A was not followed by B.
P3. The existence of testimony of type K (henceforth K-testimony) to the effect that B was not the case provides evidence ET for the proposition that B was not the case only if the number of times in which we have received K-testimony for a proposition, and then have observed that the proposition was true, is greater than the number of times in which we have received K-testimony for a proposition and then have observed that the proposition was not true (instantiation, P1).
P4. The strength of ET is proportional to the ratio among the number of times in which we have received K-testimony for a proposition and then have observed that the proposition was true and the number of times in which we have received K-testimony for a proposition and then have observed that the proposition was not true (instantiation, P2).
P5. Whenever one’s global evidence is constituted by E1 and E2, and E1 is evidence in favor of a given p, and E2 is evidence for non-p, it is rational to believe that p only if E1 is stronger than E2, it is rational to disbelieve that p only if E2 is stronger than E1, and it is rational to withhold belief as to whether p only if the strength of E1 is the same as the strength of E2.
P6. There is K-testimony to the occurrence of a miracle M.
P7. There is a law of nature L – say that every A is followed by B – and the K-testimony is to the effect that A was not followed by B (DEF–m).
P8. It is rational to accept that M occurred (assumption for reductio).
P9. That A was the case provides evidence E* for the proposition that B was the case, which is weaker than the evidence ET, provided by the K-testimony, for the proposition that B was not the case.
P10. If it is rational to accept that M occurred, then that A was the case provides evidence E* for the proposition that B was the case, which is weaker than the evidence ET, provided by the K-testimony, for the proposition that B was not the case (instantiation, P8, P9).
P11. L has been established by a “firm and unalterable experience” of many instances of A’s that were followed by many instances of B’s without exception (DEF-1).
P12. That A was the case provides the strongest possible evidence E* for the proposition that B was the case (instantiation, P2, P11).
P13. ET is stronger than the strongest possible evidence E* (conjunction P9, P12).
C1. It is not the case that ET is stronger than E*.
C2. It is not rational to accept that M occurred (modus tollens, P10, C1).