(1) Warwick summarizes Hume's essay in this way:
In Hume’s ‘Of Miracles’ in Section X of his An Enquiry Concerning Human Understanding, he sets out what he considers a decisive case to show that we are not justified in believing in miracles. Beginning with the proposition that we should proportion our belief in accordance with the strength of the available evidence, Hume observes that the sole evidence most of us ever have for any miracle is usually that of the testimony of others. But hearsay is not particularily strong evidence. He goes on to conclude that the testimony in favour of a miracle can never balance, let alone outweigh, the evidence against it, especially when it contravenes accepted natural law.
However, this is not really quite right. First, Hume explicitly allows that testimony in favor of a miracle can outweigh the evidence against it, although he doesn't think it has actually happened. He proposes an example of eight days of darkness, witnessed by many reputable historians independently writing from many parts of the world, as such a case; in part because while the eight days of darkness are not the sort of thing we find in our experience, they are fairly analogous to things we do find in our experience, and in part because it's hard to see how there could be interfering passions biasing the reporters, especially given that we have concurrence that can't be conspiratorial. Hume explicitly qualifies his claims by saying that he only has religious miracles in view.
Further, I don't think it's actually true that Hume thinks hearsay is necessarily weak; for Hume testimony is evaluated insofar as it is an effect that can give evidence for its causes, and thus is not really different from any other sort of causal evidence (and massive amounts of our evidence for anything is causal). Again, it is only religious testimony that is problematized in Hume's argument. Why? Because it is part of a family of testimony that deals with issues that guarantee intense emotional involvement that can bias witnesses, shape testimony, and motivate lying.
(2) Warwick applies the Humean reasoning the Miracle of the Sun at Fatima, and this is entirely a good idea. Since it is a religious miracle, and since Warwick assumes it to be an astronomical phenomenon, his application of Hume's reasoning is sound: it would have to be rejected because it is contrary to uniform experience, in which the sun does not dance around, and if it did, it would wreak havoc. But this does raise a question. For it is not uncommon for proponents of the Miracle of the Sun to take it to be a meteorological phenomenon, caused by a cloud of dust or ice. Interpreting the original event in this way, it suddenly conforms much more closely to uniform experience: perihelia, anthelia, and the like are not uncommon. This at least makes it closer to the eight days of darkness scenario (as far as the issue of experience goes; the religious context would still worry Hume). More than that, it raises the question of whether the event was a preternatural miracle -- preternatural miracles are rare events entirely explicable in terms of natural laws that get their significance from associated events (in this case, the visions of Fatima). If it were a preternatural miracle, it wouldn't merely be like an ordinary meteorological phenomenon, it would simply be one (albeit perhaps still of a rare sort). Preternatural miracles do not fall under Hume's definition of miracle, although they are widely recognized (it's a standard category of miracle for Catholics, and Campbell in his response to Hume gives a Calvinist version using a somewhat different terminology).
What the application of Hume's reasoning to the Miracle of the Sun really brings out, then, is the fact that a great deal actually rests on how you interpret the purported event. Consider another hypothetical scenario Hume uses: suppose several reputable historians claim that Elizabeth I died in the presence of witnesses, then a little while after appeared again and finished out her reign. Hume says nothing in this would really induce him to believe that Elizabeth I actually died and came back to life, no matter how reputable the historians. Even granted that, however, it would still be at least reasonable to suggest that something happened that seemed to contemporaries as if Elizabeth died and came back to life -- a very cleverly done impostorship, for instance. Testimony can genuinely witness to the fact of an event, but do so under an inaccurate interpretation; and, indeed, this is quite common. Thus we always have to keep this possibility in mind, even if we are purely Humean in our approach to this sort of question.
