DEMONSTRATION, AND NECESSARY TRUTHS. 329 



and easiest cases of generalization from the facts 

 furnished to us by our senses or by our internal 

 consciousness. 



While the axioms of demonstrative sciences thus 

 appeared to be experimental truths, the definitions, as 

 they are incorrectly called, of those sciences, were 

 found by us to be generalizations from experience 

 which are not even, accurately speaking, truths ; 

 being propositions in which, while we assert of some 

 kind of object, some property or properties which 

 observation shows to belong to it, we at the same 

 time deny that it possesses any other properties, 

 although in truth other properties do in every indi- 

 vidual instance accompany, and in most or even in 

 all instances, modify, the property thus exclusively 

 predicated. The denial, therefore, is a mere fiction, 

 or supposition, made for the purpose of excluding the 

 consideration of those modifying circumstances, when 

 their influence is of too trifling amount to be worth 

 considering, or adjourning it, when important, to a 

 more convenient moment. 



From these considerations it would appear that 

 Deductive or Demonstrative Sciences are all, without 

 exception, Inductive Sciences; that their evidence is 

 that of experience, but that they are also, in virtue of 

 the peculiar character of one indispensable portion of 

 the general formulae according to which their induc- 

 tions are made, Hypothetical Sciences. Their conclu- 

 sions are only true upon certain suppositions, which 

 are, or ought to be, approximations to the truth, but 

 are seldom, if ever, exactly true; and to this hypothe- 

 tical character is to be ascribed the peculiar certainty, 

 which is supposed to be inherent in demonstration. 



What we have now asserted, however, cannot be 

 received as universally true of Deductive or Demon- 



