56 THE PRINCIPLES OF SCIENCE. 



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 mention 

 that if x = y then also y = x. He would not consider 

 these to be two equations at all, but one same 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 ; each is simultaneously equal 

 and identical to the other. These remarks will hold true 

 equally of logical and mathematical identity; so that I 

 shall consider the two forms 



A = B and B = A 



to express exactly the same identity differently written. 

 All need for rules of conversion disappears, and there 

 will be no single proposition in the system which may 

 not be written with either term foremost. Thus A = AB 

 is the same as AB = A, AB = AC as AC = AB, and so on. 



The same remarks are partially true of differences or 

 inequalities, which are also reciprocal to the extent that 

 one thing cannot differ from a second without the second 

 differing from the first. Mars differs in colour from 



8 Chesterfield's Letters, 8vo, 1744 ; vol. i. p. 302. 



