THE THEOR Y OF PROBABILITIES. 11 



of which 



would have belonged to trials where the simple d, priori proba- 

 bility was > - : the ratio of these two expressions is ultimately 



This is the expression applied to determine the probability of a 

 common cause among similar phenomena, as in the case already 

 mentioned of the planets. 



But this application is founded on a petitio principii : we 

 assume that all the phenomena are allied : that they are the 

 results of repetitions of the same trial, that they have the same 

 simple probability ; all that, setting other objections aside, we 

 really determine, is the probability, that this simple probability 



common to all these allied phenomena is > - . 



But how does this determine the force of the presumption 

 that the phenomena are allied, or, to use Condorcet's illustration, 

 that they all come out of the same infinite lottery ? 



19. The object of this little essay being to call attention 

 to the subject rather than fully to discuss it, I have omitted 

 several questions which entered into my original design. 



The principle on which the whole depends, is the necessity 

 of recognizing the tendency of a series of trials towards regu- 

 larity, as the basis of the theory of probabilities. 



I have also attempted to show that the estimates furnished by 

 what is called the theory a posteriori of the force of inductive 

 results are illusory. 



If these two positions were satisfactorily established, the 

 theory would cease to be, what I cannot avoid thinking it now 

 is, in opposition to a philosophy of science which recognizes 

 ideal elements of knowledge, and which makes the process of 

 induction depend on them. 



