7 i 8 THE POPULAR SCIENCE MONTHLY. 



is here the appearance of these different beans) is involved in the con- 

 dition of experience. The condition of this special experience is that 

 all these beans were taken from that bag. According to Kant's princi- 

 ple, then, whatever is found true of all the beans drawn from the bag 

 must find its explanation in some peculiarity of the contents of the 

 bag. This is a satisfactory statement of the principle of induction. 



When we draw a deductive or analytic conclusion, our rule of 

 inference is that facts of a certain general character are either in- 

 variably or in a certain proportion of cases accompanied by facts of 

 another general character. Then our premise being a fact of the 

 former class, we infer with certainty or with the appropriate degree 

 of probability the existence of a fact of the second class. But the 

 rule for synthetic inference is of a different kind. When we sample 

 a bag of beans we do not in the least assume that the fact of some 

 beans being purple involves the necessity or even the probability of 

 other beans being so. On the contrary, the conceptualistic method 

 of treating probabilities, which really amounts simply to the deduc- 

 tive treatment of them, when rightly carried out leads to the result 

 that a synthetic inference has just an even chance in its favor, or in 

 other words is absolutely worthless. The color of one bean is en- 

 tirely independent of that of another. But synthetic inference is 

 founded upon a classification of facts, not according to their charac- 

 ters, but according to the manner of obtaining them. Its rule is, that a 

 number of facts obtained in a given way will in general more or less 

 resemble other facts obtained in the same way ; or, experiences whose 

 conditions are the same will have the same general characters. 



In the former case, we know that premises precisely similar in 

 form to those of the given ones will yield true conclusions, just once 

 in a calculable number of times. In the latter case, we only know 

 that premises obtained under circumstances similar to the given ones 

 (though perhaps themselves very different) will yield true conclusions, 

 at least once in a calculable number of times. We may express this 

 by saying that in the case of analytic inference we know the proba- 

 bility of our conclusion (if the premises are true), but in the case of 

 synthetic inferences we only know the degree of trustworthiness of 

 our proceeding. As all knowledge Comes from synthetic inference, 

 we must equally infer that all human certainty consists merely in our 

 knowing that the processes by which our knowledge has been derived 

 are such as must generally have led to true conclusions. 



Though a synthetic inference cannot by any means be reduced to 

 deduction, yet that the rule of induction will hold good in the long 

 run may be deduced from the principle that reality is only the object 

 of the final opinion to which sufficient investigation would lead. 

 That belief gradually tends to fix itself under the influence of inquiry 

 is, indeed, one of the facts with which logic sets out. 



