10 THE PRINCIPLES OF SCIENCE. 



Identity and Difference, and occupy himself in developing 

 the variety of forms of reasoning in which their truth may 

 be manifested. 



Again, I need hardly dwell upon the question whether 

 logic treats of language, notions, or things. As reasonably 

 might we debate whether a mathematician treats of 

 symbols, quantities, or things. A mathematician certainly 

 does treat of symbols, but only as the instruments 

 whereby to facilitate his reasoning concerning quantities ; 

 and as the axioms and rules of mathematical science must 

 be verified in concrete objects in order that the calcu- 

 lations founded upon them may have any validity or 

 utility, it follows that the ultimate objects of mathe- 

 matical science are the things themselves. In like man- 

 ner I conceive that the logician treats of language so far 

 as it is essential for the embodiment and exhibition of 

 thought. Even if reasoning can take place in the inner 

 consciousness of man without the use of any signs, at 

 any rate it cannot become the subject of discussion until 

 by some system of material signs it is manifested to other 

 persons. The logician then uses words and symbols as 

 instruments of reasoning, and leaves the nature and pe- 

 culiarities of existing language to the grammarian. But 

 signs again must correspond to the thoughts and things 

 expressed, in order that they shall serve their intended 

 purpose. We may therefore say that logic treats ulti- 

 mately of thoughts and things, and immediately of the 

 signs which stand for them. Signs, thoughts and ex- 

 terior objects may be regarded as parallel and analogous 

 series of phenomena, and to treat one series is equivalent 

 to treating either of the other series h . 



h See also 'Elementary Lessons in Logic/ Second Ed., p. 10. 



