Chapter 1 of the Mackie book covers Hume's account of miracles, which we discussed in our Hume epistemology episode. One of our blog commenters here mentioned offhand that he thought that argument had been long discredited, which was a surprise to me.
You can review the argument at Wikipedia here. Basically it boils down to "extraordinary claims require extraordinary evidence." We have plenty of experience of people lying, but (and this is an appeal to your own experience) no experience of the laws of nature being evidently contravened for special happenstances. Though miracles may in fact occur, we're never epistemically justified in believing them. Though Hume nominally leaves room for revelation being a route to bypass normal epistemic procedures, Mackie for one just thinks Hume was doing lip service to this principle to minimize his political trouble.
Mackie thinks that arguing for miracles is especially tricky because you have to both argue that there are laws of nature, and that these can be contravened divinely. It's not enough that there might be some experienced regularities, but that we're ignorant of the mechanism behind these and so could run into apparent exceptions to the rules we've established. It's that, yes, these are laws working deterministically within a closed system, yet God can set them aside at will. From p. 26:
Where there is some plausible testimony about the occurrence of what would appear to be a miracle, those who accept this as a miracle have the double burden of showing both that the event took place and that it violated the laws of nature. But it will be very hard to sustain this double burden. For whatever tends to show that it would have been a violation of natural law tends for that very reason to make it most unlikely that it actually happened. Correspondingly, those who deny the occurrence of a miracle have two alternative lines of defence. One is to say that the event may have occurred, but in accordance with the laws of nature. Perhaps there were unknown circumstances that made it possible; or perhaps what were thought to be the relevant laws of nature are not strictly laws; there may be as yet unknown kinds of natural causation through which this event might have come about. The other is to say that this event would indeed have violated natural law, but that for this very reason there is a very strong presumption against its having happened, which it is most unlikely that any testimony will be able to outweigh. Usually one of these defences will be stronger than the other. For many supposedly miraculous cures, the former will be quite a likely sort of explanation, but for such feats as the bringing back to life of those who are really dead the latter will be more likely. But the fork, the disjunction of these two sorts of
explanation, is as a whole a very powerful reply to any claim that a miracle has been performed.
For one point of view in contrast to Hume's, I was just looking at a description of Scottish philosopher George Campbell (1719-1796) in the Stanford Encyclopedia of Philosophy:
Campbell's opening move against this argument is to reject Hume's premiss that we believe testimony solely on the basis of experience. For, according to Campbell, there is in all of us a natural tendency to believe other people. This is not a learned response based on repeated experience but an innate disposition. In practice this principle of credulity is gradually finessed in the light of experience. Once testimony is placed before us it becomes the default position, something that is true unless or until proved false, not false unless or until proved true. The credence we give to testimony is much like the credence we give to memory. It is the default position as regards beliefs about the past, even though in the light of experience we might withhold belief from some of its deliverances.
Because our tendency to accept testimony is innate, it is harder to overturn than Hume believes it to be. Campbell considers the case of a ferry that has safely made a crossing two thousand times. I, who have seen these safe crossings, meet a stranger who tells me solemnly that he has just seen the boat sink taking with it all on board. The likelihood of my believing this testimony is greater than would be implied by Hume's formula for determining the balance of probabilities.
I personally don't find Campbell's response at all convincing: as Mackie points out, our judgments of likelihood are based on a body of background knowledge, so the antecedent improbability of a miracle is much greater than that of a ferry sinking (which was presumably not unheard of for ferries, even if one had never personally witnessed this happening). If readers have additional online sources they wish to point out against Hume's point, feel free to post some links and/or arguments as comments to this post.