46 THE PRINCIPLES OF SCIENCE. [CHAP. 



but not by it. Difference is incapable of becoming the 

 ground of inference ; it is only the implied agreement with 

 other differing objects which admits of deductive reason- 

 ing; and it will always be found advantageous to employ 

 propositions in the form which exhibits clearly the implied 

 agreements. 



Conversion of Propositions. 



The old books of logic contain many rules concerning 

 the conversion of propositions, that is, the transposition of 

 the subject and predicate in such a way as to obtain a new 

 proposition which will be true when the original proposi- 

 tion is true. The reduction of every proposition to the form 

 of an identity renders all such rules and processes neediest. 

 Identity is essentially reciprocal. If the colour of the 

 Atlantic Ocean is the same as that of the Pacific Ocean, 

 that of the Pacific must be the same as that of the Atlantic. 

 Sodium chloride being identical with common salt, common 

 salt must be identical with sodium chloride. If the number 

 of windows in Salisbury Cathedral equals the number of 

 days in the year, the number of days in the year must 

 equal the number of the windows. Lord Chesterfield was 

 not wrong when he said, " I will give anybody their choice 

 of these two truths, which amount to the same thing ; He 

 who loves himself best is the honestest man; or, The 

 honestest man loves himself best." Scotus Erigena exactly 

 expresses this reciprocal character of identity in saying, 

 " There are not two studies, one of philosophy and the 

 other of religion ; true philosophy is true religion, and true 

 religion is true philosophy." 



A mathematician would not think it worth while to 

 mention that if x = y then also y = x. He would not con- 

 sider these to be two equations at all, but one equation 

 accidentally written in two different manners. In written 

 symbols one of two names must come first, and the other 

 second, and a like succession must perhaps be observed in 

 our thoughts: but in the relation of identity there is no 

 need for succession in order (see p. 33) , each is simul- 

 taneously equal and identical to the other. These remarks 

 will hold true both of logical and mathematical identity ; 

 s? that I shall consider the two forms 



