70 



CHAPTER XVIII. 

 OF THE CALCULATION OF CHANCES. 



1. "PROBABILITY," says Laplace*, " has refer- 

 ence partly to our ignorance, partly to our knowledge. 

 We know that among three or more events, one, and 

 only one, must happen ; but there is nothing leading 

 us to believe that any one of them will happen rather 

 than the others. In this state of indecision, it is 

 impossible for us to pronounce with certainty on their 

 occurrence. It is, however, probable that any one of 

 these events, selected at pleasure, will not take place ; 

 because we perceive several cases, all equally possible, 

 which exclude its occurrence, and only one which 

 favours it." 



Such is this great mathematician's statement of 

 the logical foundation upon which rests, according to 

 him, the theory of chances : and if his unrivalled 

 command over the means which mathematics supply 

 for calculating the results of given data, necessarily 

 implied an equally sure judgment of what the data 

 ought to be, I should hardly dare give utterance to 

 my conviction, that in this opinion he is entirely 

 wrong ; that his foundation is altogether insufficient 

 for the superstructure erected upon it; and that there 

 is implied, in all rational calculation of the probabilities 

 of events, an essential condition, which is either over- 

 looked in Laplace's statement, or so vaguely indicated 



* Essai Philosophique sur les Probabilites, fifth Paris edition, 



P. 7. 



