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 asks my advice. If I give it him, I use the calculus of probabilities; but I shall not guarantee success. That is what I shall call subjective probability. In this case we might be content with the explanation of which I have just given a sketch. But assume that an observer is present at the play, that he knows of the coup, and that play goes on for a long time, and that he makes a summary of his notes. He will find that events have taken place in conformity with the laws of the calculus of probabilities. That is what I shall call objective probability, and it is this phenomenon which has to be explained. There are numerous Insurance Societies which apply the rules of the calculus of probabilities, and they distribute to their shareholders dividends, the objective reality of which cannot be contested. In order to explain them, we must do more than invoke our ignorance and the necessity of action. Thus, absolute scepticism is not admissible. We may distrust, but we cannot condemn en bloc. Discussion is necessary.

I. Classification of the Problems of Probability.—In order to classify the problems which are presented to us with reference to probabilities, we must look at them from different points of view, and first of all, from that of generality. I said above that probability is the ratio of the number of favourable to the number of possible cases. What for want of a better term I call generality will increase with the number of possible cases. This number may be finite, as, for instance, if we take a throw of the