268 THE PRINCIPLES OF SCIENCE. [CHAP 



degrees of probability proportionate to the probabilities 

 that they would give the same results. 



So far we have treated only of the process by which 

 we pass from special facts to general laws, that inverse 

 application of deduction which constitutes induction. 

 But the direct employment of deduction is often com- 

 bined with the inverse. No sooner have we established 

 a general law, than the mind rapidly draws particular 

 consequences from it. In geometry we may almost seem 

 to infer that because one equilateral triangle is equiangular, 

 therefore another is so. In reality it is not because one is 

 that another is, but because all are. The geometrical con- 

 ditions are perfectly general, and by what is sometimes 

 called parity of reasoning whatever is true of one equilateral 

 triangle, so far as it is equilateral, is true of all equilateral 

 triangles. 



Similarly, in all other cases of inductive inference, 

 where we seem to pass from some particular instances to 

 a new instance, we go through the same process. We 

 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 almost certainly true, and 

 other hypotheses, though conceivable, may be so im- 

 probable as to be neglected without appreciable error. 



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 



