SCIENCE AND DEMONSTRATION 247 



misses alone account for the conclusion. It may be that we do not yet under 

 stand why they must be true, not having so far found an &quot; explanation &quot; or 

 &quot; proof&quot; of them, but the facts revealed in the conclusion force us to believe 

 that they are de facto true ; and that they alone are true compatibly with these 

 facts. The establishing of such reciprocal relations between &quot; cause &quot; and 

 &quot; effect,&quot; between &quot; antecedent &quot; and consequent,&quot; is an ideal at which induc 

 tion aims (212). 



The attainment of this ideal involves a higher degree of precision in these 

 latter concepts and terms than they possess in ordinary thought and language. 

 Hence, while the canons of formal inference, following the wider usage which is 

 consistent with plurality of &quot; causes,&quot; or &quot; reasons,&quot; or &quot; antecedents,&quot; forbids 

 us to infer the antecedent from the consequent, induction aims at reaching such 

 an exact knowledge of the causal or rational relation, and its terms, as will 

 make the relation reciprocal, and so enable us to infer from consequent to ante 

 cedent as well as from antecedent to consequent (221). We have seen already 

 that induction does not often realize this ideal of knowledge ; but at all events, 

 starting from facts as consequents, it establishes the truth of causal laws as ante 

 cedents, by this kind of consideration : that these antecedents are true because 

 they account satisfactorily for their consequents, and are the only ones that 

 account for them so far as observation and experiment can inform us. And 

 inductive science has no other and no better &quot; explanation &quot; to offer for its ulti 

 mate generalizations than the superior success of these latter in accounting for 

 the facts of our experience (230) : &quot; Many explanations are put forward,&quot; says 

 Mr. Joseph, 1 &quot; which do not appeal only to principles already known, but have it 

 as their avowed object to prove one or more of the principles which they employ. 

 Explanation then figures as an instrument of induction ; and J. S. Mill spoke 

 accordingly of a deductive method of induction, and rightly attributed great 

 scientific importance to the process which he called by that name. No better 

 instance . . . can be given than the familiar instance of the . . . theory of 

 gravitation . . . [which Newton] proved for the first time by his use of it in 

 explanation.&quot; 



We have now to note that deductive science does not rely on any con 

 sideration of this kind for the proof of its antecedents : it does not prove its 

 antecedents by showing that they alone can account for the consequents in 

 ferred from them. It proves them by deriving them from self-evident first 

 principles. And as a matter of fact the antecedents so proved are, perhaps for 

 the most part, not the only antecedents from which the consequents actually 

 inferred can be derived. In the demonstrative proofs by which conclusions 

 are derived from first principles in the deductive sciences, the antecedents are 

 regarded as sufficient grounds, but not necessarily as the only or indispensable 

 grounds, of the consequents (213). This is noteworthy that in order to estab 

 lish a conclusion deductively by a &quot; causal &quot; demonstration (252), it is required 

 indeed that the middle term give some &quot; cause &quot; which will necessitate the 

 conclusion, but not that it give the only or indispensable &quot; cause &quot; of the latter. 

 In other words, a causal proof is recognized as a strict demonstration even 

 although it does not give the only possible cause of the conclusion : for one 

 and the same conclusion there may be a plurality of antecedents, a plurality 

 of distinct lines of demonstration, each connecting the conclusion in some 

 l op. cit., p. 477. 



