INTRODUCTION. 19 



of the widest character and of the greatest importance - 

 one indeed which it is a principal object of this work to 

 endeavour to explain. The employment of the same sign 

 in different cases would be wholly unphilosophical unless 

 there were some real analogy between its diverse meanings. 

 If such analogy exist, it is not only allowable, but highly 

 desirable and even imperative, to use the symbol of equi- 

 valency with a generality of meaning corresponding to the 

 generality of the principles involved. Accordingly Prof, 

 de Morgan's refusal to use the symbol in logical proposi- 

 tions indicated his opinion that there was a want of analogy 

 between logical propositions and mathematical equations. 

 I use the sign because I hold the contrary opinion. 



I conceive that the sign = always denotes some form 

 or degree of sameness or equivalency, and the particular 

 form is usually indicated by the nature of the terms joined 

 by it. Thus '6720 pounds = 3 tons' is evidently an 

 equation of quantities. The formula x = -f ex-; 

 presses the equivalency of operations. ' Exogens Dico- 

 tyledons ' is a logical identity expressing a profound 

 truth concerning the character of vegetables. 



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

 copula, because the little verb is, hitherto used both in 

 logic and ordinary discourse, is thoroughly ambiguous. 

 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 re- 

 quires 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 



c 2 



