Bill takes the Humean position that, given the very concept of a "law of nature," it is absurd to say that there can be "exceptions" to such laws. For a law of nature is just an "exceptionless regularity." Any event, therefore, that appears to violate the laws of nature must really be only be following those laws in a way we don't yet understand. But if that's the case, then to say that such events lack any "natural" explanation is merely to say that we're not, at present, in a position to provide such an explanation. Such is the "epistemic" conception of miracles. If that conception is adequate, then miracles lack the sort of evidentiary value that would facilitate or confirm religious belief.
Clearly, the difficulty here is conceptual. But I don't think it useful to begin with the concept of a "law of nature," a concept of which philosophers of science lack a consensual account. For the present purpose, I believe, one must first adduce a conception of miracle common to those theological traditions which assign evidentiary value to miracles.
Contemporary theologians almost always insist that miracles, if they occur in a theologically significant sense, can only be recognized as such by the eyes of faith. That is because miracles, precisely as such, function as manifestations of divine agency for the purpose of eliciting or confirming faith in God beyond that which is or can be elicited by reason alone. And that viewpoint seems to be confirmed by Scripture itself. Given as much, the best definition of 'miracle' I know of is that of St. Thomas Aquinas, as offered in Summa Contra Gentiles, Book III: "...those things are properly called miracles which are done by divine agency beyond the order commonly observed in nature (praeter ordinem communiter observatum in rebus)." Thus miracles are "super"-natural whether or not some are also "anti"-natural. What's essential to an event's being a miracle, therefore, is not that it be a "violation" of the laws of nature, but that it depart from the order of nature "commonly observed" in such a way as to manifest divine agency of a sort beyond that manifested by Nature alone. And such agency would be, at least in part, the object of faith.
I don't have time at the moment to do more than propose such a definition of 'miracle' for discussion. But I am confident that such a definition would frame the question more fruitfully than we often see. A book which does that well, in my opinion, is Stanley Jaki's Miracles and Physics.
