322 THE SCIENCE OF LOGIC 



ment which is true only on the assumption that natural causes act uni 

 formly) : so that when the domain of generalization embraces all experience, 

 as it does in the case of this principle, enumerative induction can beget certitude, 

 and &quot; the distinction between empirical laws and laws of nature vanishes &quot; 

 (Logic, III., xxi., 3). But how does he prove, without assuming uniformity in 

 nature, the assertion that the safeness of the generalization grows with the 

 extent of its domain f His only attempt at proof is the observation that the 

 wider the field of experience on which a generalization is based the more likely 

 we are to meet with adverse instances, if any such occurred. But this already 

 supposes belief in uniformity, for why should we attempt at all to generalize 

 beyond experience did we not believe in uniformity ? Granted this belief, an 

 adverse instance would convince us that our supposed causal connexion was 

 not really causal, because not uniform ; but without such belief an adverse 

 instance would be really devoid of all significance for us. Granted the uni 

 formity of nature, the wider our actual uncontradicted experience of a given 

 sequence, the more likely it is to be a causal sequence ; but if we have yet 

 to prove that natural causes must act regularly, not capriciously and chaotically, 

 how can any such experience of itself guarantee any generalization, even a 

 single step beyond itself ? Or what can be the use of comparing all actual 

 experience in time and space, no matter how extensive, with all possible ex 

 perience, in the hope of concluding directly from the former to the latter ? Yet 

 this is what Mill does : &quot; If we suppose, then, the subject-matter of any 

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

 combination of circumstances [within or beyond actual experience] but must 

 afford an example either of its truth or of its falsity, and if it be never found 

 [within actual experience] otherwise than true, its truth cannot be contingent 

 on any collocations, unless such as exist at all times and places [even outside 

 actual experience] &quot; (ibid.) In other words, the domain of experience to 

 which the principle refers is so wide, being all possible experience, that every 

 time and place must afford an instance either of its truth or of its falsity ; 

 but it has been found to be true at all times and in all places within actual ex 

 perience ; therefore it is true of all times and places beyond our experience ! 

 The premisses give no right to any such conclusion. 



0) UNDUE ASSUMPTION OF AXIOMS. All proof presupposes, 

 and proceeds ultimately from, self-evident truths, called principles 

 or axioms : some of which are &quot; common &quot; principles, of universal 

 application, while others are &quot;proper&quot; to the subject-matter of 

 this or that special science (252). Now axioms are indemon 

 strable ; their evidence is immediate, i.e. embodied in themselves ; 

 so that their truth must be apprehended by an act of intellectual 

 intuition or vision. The theory of all this is easy enough. Noth 

 ing could be more reasonable, or more necessary, than the demand 

 of logic, that truths which are really axioms ought to be ad 

 mitted by all to be such, and that, conversely, no judgment 

 which is not really an axiom should be accepted or allowed to 

 pass current as such. The violation of this latter demand involves 



