### Hume and the Independent Witnesses

Arif Ahmed
2015 Mind
A longstanding and widely accepted objection to the neo-Humean argument concerning miracles is that sufficiently numerous independent testimonies to a miracle should make one almost certain of it. The paper argues that this objection fails. Even witnesses who are known to be (i) sincere (ii) reliable (iii) causally independent of one another and (iv) causally independent of anything relevant other than the supposed miracle itself, might fail to satisfy the very demanding and highly implausible
more » ... ort of independence that the anti-Humean objection actually requires. Sections 1-5 argue for this claim. Section 6 turns aside from that argument to investigate conditions under which non-independent witness ensembles should be convincing. Here the conclusion is at best equivocally Humean. There are apparently reasonable doxastic positions in which one should reject even arbitrarily extensive uniform testimony to a miracle. But there may be others in which such testimony is rationally compelling. So given the individual positive testimony, one's Bayes-appropriate degree of belief that the miracle has occurred (one's posterior degree of belief in this) is now one's prior Cr (Mt). And one's Bayes-appropriate posterior that it has not occurred is one's prior Cr (Mt). So one's correct posterior odds on M, written O (Mt) = def. Cr (Mt) / Cr (Mt), is given by: (3) O (Mt) = [Cr (tM) Cr (M)] / [Cr (tM) Cr (M)] Consider the right hand side of (3). It follows from (1) that this is approximately [Cr (tM) Cr (M)] / Cr (tM), from the probability calculus that this quantity is no greater than Cr (M) / Cr (tM), and from (2) that the latter quantity is very small. Hence the left hand side of (3), one's rational posterior odds on the miracle, should also be very small. So notwithstanding testimony t affirming it, one should remain very confident that M is false. This argument depends only on premises (1) and (2) , which are reasonable assumptions in any context where we have only a single eyewitness's testimony to a miracle. So it is reasonable to call it an a priori argument against believing such individual testimony.