16 THE PRINCIPLES OF SCIENCE. [CHAP. 



I conceive that the sign = as commonly employed, always 

 denotes some form or degree of sameness, and the particular 

 form is usually indicated by the nature of the terms joined 

 by it. Thus " 6,720 pounds = 3 tons " is evidently an 

 equation of quantities. The formula X = + ex- 

 presses the equivalence of operations. " Exogens = Dico- 

 tyledons " is a logical identity expressing a profound truth 

 concerning the character and origin of a most important 

 group of plants. 



We have great need in logic of a distinct sign for the 

 copula, because the little verb is (or are), hitherto used 

 both in logic and ordinary discourse, is thoroughly am- 

 biguous. It sometimes denotes identity, as in " St. Paul's 

 is the chef-d'oeuvre of Sir Christopher Wren ; " but it 

 more commonly indicates inclusion of class within class, 

 or partial identity, as in " Bishops are members of the 

 House of Lords." This latter relation involves identity, 

 but requires careful discrimination from simple identity, as 

 will be shown further on. 



When with this sign of equality we join two nouns or 

 logical terms, as in 



Hydrogen = The least dense element, 

 we signify that the object or group of objects denoted by 

 one term is identical with that denoted by the other, in 

 everything except the names. The general formula 



A = B 



must be taken to mean that A and B are symbols for the 

 same object or group of objects. This identity may some- 

 times arise from the mere imposition of names, but it may 

 also arise from the deepest laws of the constitution of 

 nature ; as when we say 



Gravitating matter = Matter possessing inertia, 

 Exogenous plants = Dicotyledonous plants, 

 Plagihedral quartz crystals = Quartz crystals causing 



the plane of polarisation of light to rotate. 

 We shall need carefully to distinguish between relations 

 of terms which can be modified at our own will and those 

 which are fixed as expressing the laws of nature ; but at 

 present we are considering only the mode of expression 

 which may be the same in either case. 



Sometimes, but much less frequently, we require a 

 symbol to indicate difference or the absence of complete 



