INDUCTION. 149 



Induction of Partial Identities. 



We found in the last section that the simple identity of 

 two classes is almost always discovered not by direct 

 observation of the fact, but by first establishing two 

 partial identities. There are also a great multitude of 

 cases in which the partial identity of one class with an- 

 other is the only relation to be discovered. Thus the most 

 common of all inductive inferences consists in establishing 

 the fact that all objects having the properties of A have 

 also those of B, or that A = AB. To ascertain the truth 

 of a proposition of this kind it is merely necessary to 

 assemble together, mentally or physically, all the objects 

 included under A, and then observe whether B is present 

 in each of them, or, which is the same, whether it would 

 be impossible to select from among them any not-B. 

 Thus, if we mentally assemble together all the heavenly 

 bodies which move with apparent rapidity, that is to say 

 the planets, we find that they all possess the property of 

 not scintillating. We cannot analyse any vegetable sub- 

 stance without discovering that it contains carbon and 

 hydrogen, but it is not true that ah 1 substances containing 

 carbon and hydrogen are vegetable substances. 



The great mass of scientific truths consists of propo- 

 sitions of this form A = AB. Thus in astronomy we 

 learn that all the planets are spheroidal bodies ; that 

 they all revolve in one direction round the sun ; that 

 they all shine by reflected light ; that they all obey 

 the law of gravitation. But of course it is not to be 

 asserted that all bodies obeying the law of gravitation, 

 or shining by reflected light, or revolving in a particular 

 direction, or being spheroidal in form, are planets. In 

 other sciences we have immense numbers of propositions 

 of the same form, as for instance that all substances in 



