728 SCIENCE AND HYPOTHESIS 



of scientific applications. Two stars, for instance, are very close 

 together on the celestial sphere. Is this apparent contiguity a mere 

 effect of chance? Are these stars, although almost on the same 

 visual ray, situated at very different distances from the earth, and 

 therefore very far indeed from one another ? or does the apparent cor- 

 respond to a real contiguity? This is a problem on the probability 

 of causes. 



First of all, I recall that at the outset of all problems of probability 

 of effects that have occupied our attention up to now, we have had 

 to use a convention which was more or less justified; and if in most 

 cases the result was to a certain extent independent of this convention, 

 it was only the condition of certain hypotheses which enabled us 

 a priori to reject discontinuous functions, for example, or certain 

 absurd conventions. We shall again find something analogous to this 

 when we deal with the probability of causes. An effect may be pro- 

 duced by the cause a or by the cause b. The effect has just been ob- 

 served. We ask the probability that it is due to the cause a. This 

 is an <z posteriori probability of cause. But I could not calculate it, 

 if a convention more or less justified did not tell me in advance 

 what is the a priori probability for the cause a to come into play 

 I mean the probability of this event to some one who had not ob- 

 served the effect. To make my meaning clearer, I go back to the 

 game of ecarte mentioned before. My adversary deals for the first 

 time and turns up a king. What is the probability that he is a 

 sharper? The formulae ordinarily taught give 8-9. a result which is 

 obviously rather surprising. If we look at it closer, we see that the 

 conclusion is arrived at as if, before sitting down at the table, I 

 had considered that there was one chance in two that my adversary 

 was not honest. An absurd hypothesis, because in that case I should 

 certainly not have played with him; and this explains the absurdity 

 of the conclusion. The function on the a priori probability was un- 

 justified, and that is why the conclusion of the a posteriori prob- 

 ability led me into an inadmissible result. The importance of this 

 preliminary convention is obvious. I shall even add that if none 

 were made, the problem of the a posteriori probability would have 

 no meaning. It must be always made either explicitly or tacitly. 



Let us pass on to an example of a more scientific character. 1 

 require to detennine an experimental law; this law, when discovered, 

 can be represented by a curve. I make a certain number of isolated 

 observations, each of which may be represented by a point. When I 

 have obtained these different points, I draw a curve between them as 

 carefully as possible, giving my curve a regular form, avoiding sharp 

 angles, accentuated inflections, and any sudden variation of the ra- 

 dius of curvature. This curve will represent to me the probable law, 

 and not only will it give me the values of the functions intermediary 



