THE INDUCTIVE OR INVERSE METHOD. 311 



form an hypothesis as to the logical conditions under 

 which the given instances might occur; we calculate 

 inversely the probability of that hypothesis, and com- 

 pounding this with the probability that a new instance 

 would proceed from the same conditions, we gain the 

 absolute probability of occurrence of the new instance in 

 virtue of this hypothesis. But as several, or many, or 

 even an infinite number of mutually inconsistent hypo- 

 theses may be possible, we must repeat the calculation for 

 each such conceivable hypothesis, and then the complete 

 probability of the future instance will be the sum of the 

 separate probabilities. The complication of this process 

 is often very much reduced in practice, owing to the fact 

 that one hypothesis may be nearly certainly true, and 

 other hypotheses, though conceivable, may be so im- 

 probable as to be neglected without appreciable error. 

 But when we possess no knowledge whatever of the con- 

 ditions from which the events proceed, we may be unable 

 to form any probable hypotheses as to their mode of 

 origin. We have now to fall back upon the general 

 solution of the problem effected by Laplace, which consists 

 in admitting on an equal footing every conceivable ratio 

 of favourable and unfavourable chances for the production 

 of the event, and then accepting the aggregate result as 

 the best which can be obtained. This solution is only to 

 be accepted in the absence of all better means, but like 

 other results of the calculus of probabilities, it comes 

 to our aid where knowledge is at an end and ignorance 

 begins, and it prevents us from over-estimating the know- 

 ledge we possess. The general results of the solution are 

 in accordance with common sense, namely, that the more 

 often an event has happened the more probable, as a 

 general rule, is its subsequent occurrence. With the 

 extension of experience this probability indefinitely in- 

 creases, but at the same time the probability is slight 



