720 SCIENCE AND HYPOTHESIS 



gases, a well-known hypothesis wherein each gaseous molecule is sup- 

 posed to describe an extremely complicated path, but in which, 

 through the effect of great numbers, the mean phenomena which are 

 all we observe obey the simple laws of Mariotte and Gay-Lussac. 

 All these theories are based upon the laws of great numbers, and the 

 calculus of probabilities would evidently involve them in its ruin. 

 It is true that they have only a particular interest, and that, save 

 as far as interpolation is concerned, they are sacrifices to which we 

 might readily be resigned. But I have said above, it would not be 

 these partial sacrifices that would be in question; it would be the 

 legitimacy of the whole of science that would be challenged. I quite 

 see that it might be said : We do not know, and yet we must act. As 

 for action, we have not time to devote ourselves to an inquiry that 

 will suffice to dispel our ignorance. Besides, such an inquiry would 

 demand unlimited time. We must therefore make up our minds 

 without knowing. This must be often done whatever may happen, 

 and we must follow the rules although we may have but little confi- 

 dence in them. What I know is, not that such a thing is true, but 

 that the best course for me is to act as if it were true. The calculus 

 of probabilities, and therefore science itself, would be no longer of 

 any practical value. 



Unfortunately the difficulty does not thus disappear. A gambler 

 wants to try a coup, and he 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 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 scepti- 

 cism 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 favorable 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, 



