The Inductive Theories. 23 



Turning to the theory of Mill we find a definition of induc- 

 tion more nearly like that with which our investigation began. 

 " Induction " according to him, " is that operation of the mind 

 by which we infer that what we know to be true in a case or 

 cases is true in all cases which resemble the former in certain 

 assignable respects." The conclusion of an Induction is a uni- 

 versal proposition: and there are two elements in the inductive 

 process; one the discovery of the generalization, the other its 

 proof. To which correspond two branches of the Logic of In- 

 duction, one concerned with the process of discovery, the other 

 with the conditions under which generalization is legitimate; 

 the Logic in a word of Discovery and of Proof. 



To the subject of inductive validity, that is the Logic of 

 Proof, Mill devotes special attention. Let us endeavor to 

 sketch his view of the conditions under which an observation 

 of particular fact warrants a general conclusion. 



In the first place a process which ends in the establishment 

 of universal propositions implies that Nature is such that uni- 

 versally true assertions can be made regarding it. 



Conceiving of the universe, therefore, as a realm of Law 

 throughout, we may proceed to investigate the conditions un- 

 der which we may form generalizations with respect to it. 



Along with the uniformity that Nature exhibits is exhibited 

 also most immense variety. While certain kinds of phenomena 

 occur with complete regularity, others show a less degree, and 

 in many we can discover no uniformity whatever. Generaliza- 

 tions from various kinds of phenomena will therefore possess 

 very different degrees of trustworthiness. But if in our inves- 

 tigations we are led to see that a given uniformity A is so con- 

 cerned with a uniformity of a mere regular kind, B, that B must 

 be false if A is, A becomes at once a generalization of the same 

 value as B. Such a standard generalization is supplied, 

 according to Mill, by the principle of causation. Of the two 

 ways in which phenomena may accompany one another in time, 

 co-existence and sec^uence, the latter has been observed to exhi- 

 bit complete regularity. The Principle of Causation is the 

 statement of the fact that events are not combined indefinitely 



