8 THE SCIENCE OF LOGIC 



pounding, or building uf&amp;gt; its conceptions, so to speak, into more 

 and more complex wholes, synthesizing its gradually acquired 

 truths into a logical, harmonious, and progressive system. 



Throughout this whole work of elaboration, the student of the 

 pure deductive sciences has no need to call in the aid of sense 

 experience, of observation or experiment : he might conceivably 

 become the greatest pure mathematician in the world without 

 ever leaving his library. He would, of course, need charts or 

 blackboards to aid his imagination in establishing the complex 

 spatial or numerical relations he might desire to examine between 

 the notions with which he deals. But it is from the primary 

 notions, not from the figures or symbols before him, that he de 

 duces even his remotest and most complex conclusions. 



If, however, it is true that such quiet seclusion and abstract 

 speculation can produce a great mathematician, is it not equally 

 true that they can never produce a great physical scientist ? A 

 knowledge of the physical world implies actual, positive contact 

 with Nature and its activities. The discovery of its laws is con 

 ditioned by the observation of its concrete phenomena, and even 

 by experimenting with these latter. It is the result of a long 

 analytic process that has been called Induction : hence the designa 

 tion, physical or positive or inductive sciences. 



When a science thus starts with concrete facts, with the data 

 of observation and experiment, and aims at discovering general 

 truths and formulating general laws, about those tacts, its progress 

 is from the complex to the simple, from the particular to the 

 general. This is the analytic method (ava\v(o) ; it finds its place 

 mainly in the experimental sciences. 



We have already distinguished the reasoning by which we 

 thus ascend to higher and wider laws, as regressive, in opposition 

 to the progressive reasoning which is characteristic of the deductive 

 sciences (187). Professor Welton * thus illustrates the distinction : 

 &quot; Instead of starting from an axiom of the widest generality, in 

 physical science it more frequently happens that the highest and 

 most general principles are the last to be discovered. Certain 

 general propositions are first discovered (e.g. the laws of Kepler) 

 under which the individual facts are syllogistically subsumed. 

 The highest principles are discovered later (e.g. the Newtonian law 

 of Gravitation) from which those general propositions are neces- 



1 Logic, i., p. 392. 



