ABSTRACT
It is generally recognized that the inferences of science and common sense differ from those of deductive logic and mathematics in a very important respect, namely, that, when the premisses are true and the reasoning correct, the conclusion is only probable. We have reasons for believing that the sun will rise to-morrow, and everybody is agreed that, in practice, we can behave as if these reasons justified certainty. But when we examine them we find that they leave some room, however little, for doubt. The doubt that is justified is of three sorts. As regards the first two: on the one hand there may be relevant facts of which we are ignorant; on the other hand, the laws that we have to assume in order to predict the future may be untrue. The former reason for doubt does not much concern us in our present inquiry, but the latter is one which demands detailed investigation. But there is a third kind of doubt, which arises when we know a law to the effect that something happens usually, or perhaps in an overwhelming majority of instances, though not always; in this case we have a right to expect what is usual, though not with complete confidence. For example, if a man is throwing dice, it very seldom happens that he throws double sixes ten times running, although this is not impossible; we have therefore a right to expect that he will not do so, but our expectation ought to be tinged with doubt. All these kinds of doubt involve something that may be called “probability”, but this word is capable of different meanings, which it will be important to us to disentangle.
