First, then, can there be evidence that a law of nature has been violated? It seems natural to understand, as Ninian Smart (2) does, by a violation of a law of nature, an occurrence of a non-repeatable counter-instance to a law of nature. Clearly, as Hume admitted, events contrary to predictions of formulae which we had good reason to believe to be laws of nature often occur. But if we have good reason to believe that they have occurred and good reason to believe that similar events would occur in similar circumstances, then we have good reason to believe that the formulae which we previously believed to be the laws of nature were not in fact such laws. Repeatable counter-instances do not violate laws of nature, they just show propositions purporting to state laws of nature to be false.

If the laws of nature are statistical and not deterministic, it is not in all cases so clear what counts as a counter-instance to them. How improbable does an event have to be to constitute a counter instance to a statistical law? But this problem is a general one in the philosophy of science and does not raise any issues peculiar to the topic of miracles.

It is clear that all claims about what does or does not violate the laws of nature are subject to revision. New scientific knowledge may force us to revise any such claims. But all claims to knowledge about matters of fact are correctable, and we must reach provisional conclusions about them on the evidence available to us. We have to some extent good evidence about what are the laws of nature, and some of them are so well established and account for so many data that any modifications to them which we could suggest to account for the odd counter-instance would be so clumsy and ad hoc as to upset the whole structure of science. In such cases the evidence is strong that if the purported counter-instance occurred it was a violation of the laws of nature. There is good reason to believe that the following events, if they occurred, would be violations of the laws of nature: levitation; resurrection from the dead in full health of a man whose heart has not been beating for twenty-four hours and who was, by other criteria also, dead; water turning into wine without the assistance of chemical apparatus or catalysts; a man getting better from polio in a minute.

So then we could have the evidence that an event E if it occurred was a non-repeatable counter-instance to a true law of nature L. But Hume's argument here runs as follows. The evidence, which ex hypothesis is good evidence, that L is a true law of nature is evidence that E did not occur. We have certain other evidence that E did occur. In such circumstances, writes Hume, the wise man "weighs the opposite experiments. He considers which side is supported by the greater number of experiments."(3) Since he supposes that the evidence that E occurred would be that of testimony, Hume concludes "that no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact which it endeavors to establish."(4) He considers that this condition is not in fact satisfied by any purported miracle, though he seems at times to allow that it is logically possible that it might be.

One wonders here at Hume's scale of evidence. Suppose two hundred witnesses claiming to have observed some event E, an event which, if it occurred, would be a non-repeatable counterinstance to a law of nature. Suppose these to be witnesses able and anxious to show that E did not occur if there were grounds for doing so. Would not their combined evidence give us good reason to believe that E occurred? Hume's answer which we can see from his discussion of two apparently equally well authenticated miracles is – No. But then, one is inclined to say, is not Hume just being bigoted, refusing to face facts? It would be virtually impossible to draw up a table showing how many witnesses and of what kind we need to establish the occurrence of an event which, if it occurred, would be a non repeatable counterinstance to a law of nature. Each purported instance has to be considered on its merits. But certainly one feels that Hume's standards of evidence are too high. What, one wonders, would Hume himself say if he saw such an event?