ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 471 



But here the reasoning is really this : 



Mule. Every quadrangle is other than a triangle. 

 Case. Some figures are quadrangles. 

 Result. Some figures are not triangles. 



Inductive or synthetic reasoning, being something more than the 

 mere application of a general rule to a particular case, can never be re- 

 duced to this form. 



If, from a bag of beans of which we know that f are white, we take 

 one at random, it is a deductive inference that this bean is probably 

 white, the probability being f . We have, in effect, the following syl- 

 logism: 



Rule. The beans in this bag are f white. 



Case. This bean has been drawn in such a way that in the long 

 run the relative number of white beans so drawn would be equal to the 

 relative number in the bag. 



Result. This bean has been drawn in such a way that in the long 

 run it would turn out white f of the time. 



If instead of drawing one bean we draw a handful at random and 

 conclude that about of the handful are probably white, the reasoning 

 is of the same sort. If, however, not knowing what proportion of 

 white beans there are in the bag, we draw a handful at random and, 

 finding -| of the beans in the handful white, conclude that about f of 

 those in the bag are white, we are rowing up the current of deductive 

 sequence, and are concluding a rule from the observation of a result in 

 a certain case. This is particularly clear when all the handful turn out 

 one color. The induction then is : 



These beans were in this bag. 



These beans are white._ 



All the beans in the basr were white 



& 



Which is but an inversion of the deductive syllogism. 



Rule. All the beans in the bag were white. 



Case. These beans were in the bag 



Result. These beans are white. 



So that induction is the inference of the rule from the case and 

 result. 



But this is not the only way of inverting a deductive syllogism so 

 as to produce a synthetic inference. Suppose I enter a room and there 

 find a number of bags, containing different kinds of beans. On the 

 table there is a handful of white beans ; and, after some searching, I 

 find one of the bags contains white beans only. I at once infer as a 



