72 INDUCTION. 



occurrence. Why, in tossing up a halfpenny, do we 

 reckon it equally probable that we shall throw cross 

 or pile ? Because experience has shown that in any 

 great number of throws, cross and pile are thrown 

 about equally often; and that the more throws we 

 make, the more nearly the equality is perfect. We 

 call the chances even, because if we stake equal sums, 

 and play a certain large number of times, experience 

 proves that our gains and losses will about balance 

 one another ; and will continue to do so, however long 

 afterwards we continue playing : while on the contrary, 

 if we give the slightest odds, and play a great number 

 of times, we are sure to lose ; and the longer we con- 

 tinue playing, the greater losers we shall be. If expe- 

 rience did not prove this, we should proceed as much at 

 haphazard in staking equal sums as in laying odds ; 

 we should have no more reason for expecting not to 

 be losers by the one wager than by the other. 



It would indeed require strong evidence to per- 

 suade any rational person that by a system of opera- 

 tions upon numbers, our ignorance can be coined 

 into science ; and it is doubtless this strange pre- 

 tension which has driven a profound thinker, M. 

 Comte, into the contrary extreme of rejecting alto- 

 gether a doctrine which, however imperfectly its 

 principles may sometimes have been conceived, 

 receives daily verification from the practice of insur- 

 ance, and from a great mass of other positive expe- 

 rience. The doctrine itself is, I conceive, sound, but 

 the manner in which its foundations have been laid by 

 its great teachers is most seriously objectionable. 

 Conclusions respecting the probability of a fact rest 

 not upon a different, but upon the very same basis, as 

 conclusions respecting its certainty ; namely, not our 

 ignorance, but our knowledge : knowledge obtained 



