xii.] THE INDUCTIVE OR INVERSE METHOD. 267 



number of particular verifications of a supposed law will 

 render that law certain. In short, certainty belongs only 

 to the deductive process, and to the teachings of direct 

 intuition ; and as the conditions of nature are not given 

 by intuition, we can only be certain that we have got a 

 correct hypothesis when, out of a limited number con- 

 ceivably possible, we select that one which alone agrees 

 with the facts to be explained. 



In geometry and kindred branches of mathematics, 

 deductive reasoning is conspicuously certain, and it would 

 often seem as if the consideration of a single diagram 

 yields us certain knowledge of a general proposition. 

 But in reality all this certainty is of a purely hypothetical 

 character. Doubtless if we could ascertain that a sup- 

 posed circle was a true and perfect circle, we could be 

 certain concerning a multitude of its geometrical pro- 

 perties. But geometrical figures are physical objects, and 

 the senses can never assure us as to their exact forms. 

 The figures really treated in Euclid's Elements are 

 imaginary, and we never can verify in practice the 

 conclusions which we draw with certainty in inference ; 

 questions of degree and probability enter. 



Passing now to subjects in which deduction is only 

 probable, it ceases to be possible to adopt one hypothesis 

 to the exclusion of the others. We must entertain at the 

 same time all conceivable hypotheses, and regard each 

 with the degree of esteem proportionate to its probability. 

 We go through the same steps as before. 



(1) We frame an hypothesis. 



(2) We deduce the probability of various series of pos- 

 sible consequences. 



(3) We compare the consequences with the particular 

 facts, and observe the probability that such facts would 

 happen under the hypothesis. 



The above processes must be performed for every con- 

 ceivable hypothesis, and then the absolute probability of 

 each will be yielded by the principle of the inverse 

 method (p. 242). As in the case of certainty we accept 

 that hypothesis which certainly gives the required results, 

 so now we accept as most probable that hypothesis which 

 most probably gives the results; but we are obliged to 

 entertain at the same time all other hypotheses with 



