Providence vs. Miracles: same difference?

Here are some quotes from Earman’s book:

Toward the end of Part 1 [in Hume’s essay], Hume announces a ‘‘general maxim’’ […] Hume’s Maxim begs to be made precise by translating it into the language of probability theory. There should be no surprise, however, in finding that a number of inequivalent translations are possible since seemingly transparent English statements about the credibility of events turn out to be hiding ambiguities about conditional probabilities. - John Earman, Humes Abject Failure, Page 39

[…] unless testimonial evidence is allowed to overcome prior improbabilities, there is no way to underwrite the sorts of inferences made in everyday life and in science. We would not give much credence to a newspaper report of the number of the winning ticket in a fair lottery with odds of millions to one - John Earman, Humes Abject Failure, Page 33

Hume’s blunderbuss arguments against miracles are ineffective and that his ambition to provide a ‘‘proof ’’ against miracles is based on an impoverished conception of inductive inference. - John Earman, Humes Abject Failure, Page 49

[…] given some mild assumptions, which can be made plausible or at least can be motivated, results about the incremental confirmation of hypotheses about miracles and religious doctrines proper can be proved as theorems of probability. Second, given minimal assumptions about the reliability of witnesses, convergence to certainty, as the number of witnesses increases, about the occurrence of miraculous events can be proven, again as theorems of probability. Thus, if evidence driven consensus is the mark of objectivity of opinion, then objectivity can be achieved in some circumstances in natural religion as well as in science and everyday life. - John Earman, Humes Abject Failure, Page 72

I highly recommend you give it a read. I have seen it described as the most thorough and precise analysis of Hume’s essay on Miracles that exists.

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