102 INDUCTION. 



the results of the original unscientific Induction ; and on this 

 diversity (as observed in the fourth chapter of the present 

 book) depend the rules for the improvement of the process. 

 The improvement consists in correcting one of these inartifi- 

 cial generalizations by means of another. As has been already 

 pointed out, this is all that art can do. To test a generaliza- 

 tion, by showing that it either follows from, or conflicts with, 

 some stronger induction, some generalization resting on a 

 broader foundation of experience, is the beginning and end of 

 the logic of Induction. 



. 



3. Now the precariousness of the method of simple 

 enumeration is in an inverse ratio to the largeness of the 

 generalization. The process is delusive and insufficient, exactly 

 in proportion as the subject-matter of the observation is 

 special and limited in extent. As the sphere widens, this 

 unscientific method becomes less and less liable to mislead ; 

 and the most universal class of truths, the law of causation for 

 instance, and the principles of number and of geometry, are 

 duly and satisfactorily proved by that method alone, nor are 

 they susceptible of any other proof. 



With respect to the whole class of generalizations of which 

 we have recently treated, the uniformities which depend on 

 causation, the truth of the remark just made follows by 

 obvious inference from the principles laid down in the pre- 

 ceding chapters. When a fact has been observed a certain 

 number of times to be true, and is not in any instance known 



their generalizations did not imply that there was uniformity in everything, 

 but only that as much uniformity as existed within their observation, existed 

 also beyond it. The induction, Fire burns, does not require for its validity 

 that all nature should observe uniform laws, but only that there should be 

 uniformity in one particular class of natural phenomena : the effects of fire on 

 the senses and on combustible substances. And uniformity to this extent 

 was not assumed, anterior to the experience, but proved by the experience. 

 The same observed instances which proved the narrower truth, proved as much 

 of the wider one as corresponded to it. It is from losing sight of this fact, and 

 considering the law of causation in its full extent as necessarily presupposed in 

 the very earliest generalizations, that persons have been led into the belief that 

 the law of causation is known d priori, and is not itself a conclusion from 

 experience. 



