402 INDUCTION. 



of the original unscientific induction ; and on this diversity (as observed in 

 the fourth chapter of the present book) depend the rules for the improve- 

 ment of the process. The improvement consists in correcting one of these 

 inartificial generalizations by means of another. As has been already point- 

 ed out, this is all that art can do. To test a generalization, by showing 

 that it either follows from, or conflicts with, some stronger induction, some 

 generalization resting on a broader foundation of experience, is the begin- 

 ning and end of the logic of induction. 



§ 3. Now the precariousness of the method of simple enumeration is in 

 an inverse ratio to the lai'geness of the generalization. The process is 

 delusive and insufiicient, 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 princi- 

 ples 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 re- 

 cently 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 preceding chapters. When a fact has been observed a cer- 

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

 false, if we at once aifirra that fact as a universal truth or law of natui-e, 

 without either testing it by any of the four methods of induction, or de- 

 ducing it from other known laws, we shall in general err grossly ; but we 

 are perfectly justified in affirming it as an empirical law, true within cer- 

 tain limits of time, place, and circumstance, provided the number of coin- 

 cidences be greater than can with any probability be ascribed to chance. 

 The reason for not extending it beyond those limits is, that the fact of its 

 holding true within them may be a consequence of collocations, which can 

 not be concluded to exist in one place because they exist in another; or 

 may be dependent on the accidental absence of counteracting agencies, 

 which any variation of time, or the smallest change of circumstances, may 

 possibly bring into play. If we suppose, then, the subject-matter of any 

 generalization to be so widely diffused that there is no time, no place, and 

 no combination of circumstances, but must afford an example either of its 

 truth or of its falsity, and if it be never found otherwise than true, its 

 truth can not be contingent on any collocations, unless such as exist at all 

 times and j^laces ; nor can it be frustrated by any counteracting agencies, 

 unless by such as never actually occur. It is, therefore, an empirical law 

 co-extensive with all human experience ; at which point the distinction be- 

 tween empirical laws and laws of nature vanishes, and the proposition 

 takes its place among the most firmly established as well as largest truths 

 accessible to science. 



Now, the most extensive in its subject-matter of all generalizations 

 which experience warrants, respecting the sequences and co-existences of 

 phenomena, is the law of causation. It stands at the head of all observed 

 uniformities, in point of universality, and therefore (if the preceding ob- 

 servations are correct) in point of certainty. And if we consider, not what 

 mankind would have been justified in believing in the infancy of their 

 knowledge, but what may rationally be believed in its present more ad- 

 vanced state, we shall find ourselves warranted in considering this funda- 

 mental law, though itself obtained by induction from particular laws of causa- 



