Dr. Richard C. Miller On Fantasy, Bayes and the Impossibility of Miracles

Dr. Miller recently began blogging at Hume's Bible, an important resource for the rest of us. In his most recent post he writes On the Impossibility of Miracles. This is something I've been addressing.

Miller starts by saying, "We measure human rational sanity by one’s consistent success in distinguishing clearly between fantasy and reality" and then gives an example with regard to alleged miracle claims. "Miracles, by very definition, are natural, rational impossibilities." "For, if a claim had empirical support, would we not classify such a proposal as indeed natural, not supernatural?" So he goes on to say, following Hume,
Here we may choose to end the argument, claiming a quite reasonable conclusive victory. Miracles, by very definition, are natural, rational impossibilities. When someone claims a miracle has occurred, we respond by saying that “there must be some rational explanation.” By doing this, we are implicitly recognizing as a society that miraculous claims are essentially irrational, i.e., a miraculous proposition contains one or more a priori contradictions with regard to its constituent terms (Italics mine).
This last phrase of his is very interesting. If we wish to assign a non-zero mathematical prior probability to a miracle claim, we cannot do it. For doing so means assigning a mathematical probability to something that is contradictory. Reading his explanation is worth the price of a click and a share.