Ever since Hume's famous Essay it has been believed that historical statements about miracles are the most intrinsically improbable of all historical statements. According to Hume, probability rests on what may be called the majority vote of our past experiences. The more often a thing has been known to happen, the more probable it is that it should happen again; and the less often the less probable. Now the regularity of Nature's course, says Hume, is supported by something better than the majority vote of past experiences: it is supported by their unanimous vote, or, as Hume says, by "firm and unalterable experience." There is, in fact, "uniform experience" against miracles; otherwise, says Hume, it would not be a Miracle. A miracle is therefore the most improbable of all events. It is always more probable that the witnesses were lying or mistaken than that a miracle occurred.
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.
The question, "Do miracles occur?" and the question, "Is the course of Nature absolutely uniform?" are the same question asked in two different ways. Hume, by sleight of hand, treats them as two different questions. He first answers "Yes," to the question whether Nature is absolutely uniform: and then uses this "Yes" as a ground for answering, "No," to the question, "Do miracles occur?" The single real question which he set out to answer is never discussed at all. He gets the answer to one form of the question by assuming the answer to another form of the same question.
Probabilities of the kind that Hume is concerned with hold inside the framework of an assumed Uniformity of Nature. When the question of miracles is raised we are asking about the validity or perfection of the frame itself. No study of probabilities inside a given frame can ever tell us how probable it is that the frame itself can be violated. Granted a school time-table with French on Tuesday morning at ten o'clock, it is really probable that Jones, who always skimps his French preparation, will be in trouble next Tuesday, and that he was in trouble on any previous Tuesday. But what does this tell us about the probability of the time-table's being altered? To find that out you must eavesdrop in the masters' common-room. It is no use studying the time-table.
If we stick to Hume's method, far from getting what he hoped (namely, the conclusion that all miracles are infinitely improbable) we get a complete deadlock. The only kind of probability he allows holds exclusively within the frame of uniformity. When uniformity is itself in question (and it is in question the moment we ask whether miracles occur) this kind of probability is suspended. And Hume knows no other. By his method, therefore, we cannot say that uniformity is either probable or improbable; and equally we cannot say that miracles are either probable or improbable. We have impounded both uniformity and miracles in a sort of limbo where probability and improbability can never come. This result is equally disastrous for the scientist and the theologian; but along Hume's lines there is nothing whatever to be done about it.
C. S. Lewis