From Miracles by C.S. Lewis:
Now of course we must agree with Hume that if there is absolutely “uniform experience” against miracles, if in other words they have never happened, why then they never have. Unfortunately we know the experience against them to be uniform only if we know that all the reports of them are false. And we can know all the reports to be false only if we know already that miracles have never occurred. In fact, we are arguing in a circle.
There is also an objection to Hume which leads us deeper into our problem: The whole idea of Probability (as Hume understands it) depends on the principle of the Uniformity of Nature. Unless Nature always goes on in the same way, the fact that a thing had happened ten million times would not make it a whit more probable that it would happen again. And how do we know the Uniformity of Nature? A moment’s thought shows, that we do not know it by experience. We observe many regularities in Nature. But of course all the observations that men have made or will make while the race lasts cover only a minute fraction of the events that actually go on. Our observations would therefore be of no use unless we felt sure that Nature when we are not watching her behaves in the same way as when we are: in other words, unless we believed in the Uniformity of Nature. Experience therefore cannot prove uniformity, because uniformity has to be assumed before experience proves anything. And mere length of experience does not help matters. It is no good saying, “Each fresh experience confirms our belief in uniformity and therefore we reasonably expect that it will always be confirmed”; for that argument works only on the assumption that the future will resemble the past–which is simply the assumption of Uniformity under a new name. Can we say that Uniformity is at any rate very probable? Unfortunately not. We have just seen that all probabilities depend on it. Unless Nature is uniform, nothing is either probable or improbable. And clearly the. assumption which you have to make before there is any such thing as probability cannot itself be probable.
The odd thing is that no man knew this better than Hume. His Essay on Miracles is quite inconsistent with the more radical, and honourable, scepticism of his main work.