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[The following passage is from C. S. Lewis’ Miracles, 1947.]

Probability is founded on the presumption of a resemblance between those objects of which we have had experience and those of which we have had none; and therefore it is impossible that this presumption can arise from probability.

HUME, Treatise of Human Nature, I, iii, vi.

The argument up to date shows that miracles are possible and that there is nothing antecedently ridiculous in the stories which say that God has sometimes performed them. This does not mean, of course, that we are committed to believing all stories of miracles. Most stories about miraculous events are probably false: if it comes to that, most stories about natural events are false. Lies, exaggerations, misunderstandings and hearsay make up perhaps more than half of all that is said and written in the world. We must therefore find a criterion whereby to judge any particular story of the miraculous. In one sense, of course, our criterion is plain. Those stories are to be accepted for which the historical evidence is sufficiently good. But then, as we saw at the outset, the answer to the question, ‘How much evidence should we require for this story?’ depends on our answer to the question, ‘How far is this story intrinsically probable?’ We must therefore find a criterion of probability.

The ordinary procedure of the modern historian, even if he admits the possibility of miracle, is to admit no particular instance of it until every possibility of ‘natural’ explanation has been tried and failed. That is, he will accept the most improbable ‘natural’ explanations rather than say that a miracle occurred. Collective hallucination, hypnotism of unconsenting spectators, widespread instantaneous conspiracy in lying by persons not otherwise known to be liars and not likely to gain by the lie—all these are known to be very improbable events: so improbable that, except for the special purpose of excluding a miracle, they are never suggested. But they are preferred to the admission of a miracle.

Such a procedure is, from the purely historical point of view, sheer midsummer madness unless we start by knowing that any Miracle whatever is more improbable than the most improbable natural event. Do we know this?

We must distinguish the different kinds of improbability. Since miracles are, by definition, rarer than other events, it is obviously improbable beforehand that one will occur at any given place and time. In that sense every miracle is improbable. But that sort of improbability does not make the story that a miracle has happened incredible; for in the same sense all events whatever were once improbable. It is immensely improbable beforehand that a pebble dropped from the stratosphere over London will hit any given spot or that any one particular person will win a large lottery. But the report that the pebble has landed outside such and such a shop or that Mr So-and-So has won the lottery is not at all incredible. When you consider the immense number of meetings and fertile unions between ancestors which were necessary in order that you should be born, you perceive that it was once immensely improbable that such a person as you should come to exist: but once you are here, the report of your existence is not in the least incredible. With probability of this kind—antecedent probability of chances—we are not here concerned. Our business is with historical probability.

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 Miracle; 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 timetable 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 timetable’s being altered? To find that out you must eavesdrop in the masters’ common-room. It is no use studying the timetable.

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