104 THE SCIENCE OF LOGIC 



i.e. generalizing from the mere counting of instances, is admittedly 

 a hazardous process and cannot give certitude. How, then, can 

 we be certain of the uniformity of nature, and through it, of 

 our scientific inductions, if uniformity itself is grounded on this 

 hazardous process of enumeration ? Mill commences his answer 1 

 with this statement : &quot; Now, the precariousness of the method of 

 simple enumeration is in an inverse ratio to the largeness of the 

 generalization &quot;. Assuming this, he points out that the subject- 

 matter of the law of uniformity which is the &quot; largest &quot; general 

 ization of all is &quot; so widely diffused that there is no time, no 

 place, and no combination of circumstances, but must afford an 

 example of its truth or of its falsity,&quot; and that it was &quot;never 

 found otherwise than true &quot;. 2 From this he concludes that the 

 law of uniformity &quot; takes its place among the most firmly estab 

 lished as well as the largest truths accessible to science &quot;. This 

 is a plausible piece of reasoning until we advert to the fact that 

 its opening statement assumes what is to be proved. The reason 

 why we regard a wide enumerative induction as safer than a 

 narrow one, the reason why one which is found to range without 

 exception over an extensive region of time and space yields higher 

 certitude, is because we are made morally certain by it that the 

 special observed uniformity in question is not a casual but a 

 causal one, and because we ARE ALREADY CONVINCED, or ALREADY 

 ASSUME, that a CAUSAL uniformity will persist beyond and outside 

 our experience, in other words, THAT NATURE IS UNIFORM. Did 

 we not already believe in the uniformity of nature, all enumera 

 tive induction, whether wide or narrow, in fact all inference be 

 yond actual experience, would be equally hazardous. To assume 

 that we can thus differentiate between wide and narrow inductions, 

 in an attempt to prove that we can believe nature to be uniform, 

 is simply to beg the question at issue. 



Mill s attempt, therefore, to assign a rational basis for belief in 

 the uniformity of nature breaks down. And hence he is unable 

 to justify the individual scientific inductions by which we establish 

 isolated laws of nature ; for in every one of these inductions there 

 is a partial application of the principle of uniformity ; every one 

 of them transcended the actual sense experience of the individual ; 



1 Logic, III., xxi., 3. 



2 What about his previous recognition [III., iii., 2] of phenomena, which &quot; seem 

 altogether capricious,&quot; about the &quot; course of nature&quot; being &quot; not only uniform&quot; but 

 &quot;also infinitely various&quot;? Again, what about miracles? Or about the impossi 

 bility of inferring what must be, or even what will be, merely from what was or is ? 



