UNI FORM IT Y OF NA TURE 1 03 



made. We arrive at this universal law by generalization from 

 many laws of inferior generality. . . . As, however, all rigorous 

 processes of induction presuppose the general uniformity, our 

 knowledge of the particular uniformities from which it was first 

 inferred was not, of course, derived from rigorous induction, but 

 from the loose and uncertain mode of induction/^ enumerationem 

 simplicem&quot; * 



And of this latter process he had already said : &quot;It consists 

 in ascribing the character of general truths to all propositions 

 which are true in every instance that we happen to know of. ... 

 In science it carries us but a little way. We are forced to begin 

 with it ; we must often rely on it provisionally, in the absence 

 of means of more searching investigation.&quot; 2 There is here, ap 

 parently, no rational basis assigned, on which this &quot; loose&quot; process 

 can produce scientific certitude. Yet, it is by this process we 

 ascend to the &quot; particular uniformities,&quot; and, by a second applica 

 tion of it, from these to the &quot; general uniformity,&quot; on which 

 the validity of the whole inductive process is to be based. The 

 principle so obtained must necessarily be, as Professor Welton 

 expresses it, &quot; untrustworthy in a twofold degree ; for it is an in 

 ference, uncertain in its very essence, from other inferences of the 

 same dubious character. . . . Mill s argument on this point is 

 indeed nothing but a petitio pn ncipii. We are, he says, to con 

 sider no minor generalization as proved except in so far as the 

 law of causation confirms it (III., xxi., 3), and yet that law is to 

 be derived from those very same minor generalizations which it is 

 called upon to confirm .&quot; 3 



Mill is, of course, mistaken in thinking that we cannot make 

 a strict, scientific induction without hav mg previously justified our 

 belief in the general uniformity of nature. We have pointed out 

 above that this is not necessary ; that we may accept the principle 

 provisionally and base our scientific inductions upon it. Mill, 

 however, thinks we can only make &quot; enumerative &quot; inductions ; 

 and upon these alone he endeavours to base our belief in that 

 general uniformity, which will then turn around and confirm 

 them. His attempt to avoid the charge of inconsistency in basing 

 the validity of the &quot; rigorous &quot; process upon the &quot; loose and un 

 certain &quot; process, reveals once more a rather naive petitio prindpii. 

 The difficulty he had to face was this : Enumerative induction, 



1 Logic, III., xxi., 2. 2 ibid., iii., 2. 



3 WELTON, Logic, ii., pp. 42, 43. C/~. JOSEPH, op. cit., pp. 388, 391. 



