INTRODUCTION. 15 



by Eobert Eecorde in his Whetstone of Wit, to avoid the 

 tedious repetition of the words "is equal to;" and he 

 chose a, pair of parallel lines, because no two things can be 

 more equal. 1 The meaning of the sign has however been 

 gradually extended beyond that of equality of quantities ; 

 mathematicians have themselves used it to indicate 

 equivalence of operations. The force of analogy has been 

 so great that writers in most other branches of science 

 have employed the same sign. The philologist uses it to 

 indicate the equivalence of meaning of words : chemists 

 adopt it to signify identity in kind and equality in weight 

 of the elements which form two different compounds. 

 Not a few logicians, for instance Lambert, Drobitsch, 

 George Bentham, 2 Boole, 8 have employed it as the copula 

 of propositions. De Morgan declined to use it for this 

 purpose, but still further extended its meaning so as to 

 include the equivalence of a proposition with the premises 

 from which it can be inferred ; 4 and Herbert Spencer has 

 applied it in a like manner. 5 



Many persons may think that the choice of a symbol is 

 a matter of slight importance or of mere convenience ; but 

 I hold that the common use of this sign = in so many 

 different meanings is really founded upon a generalisation 

 of the widest character and of the greatest importance 

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

 explain. The employment of the same sign in different 

 cases would be unphilosophical unless there were some real 

 analogy between its diverse meanings. If such analogy 

 exists, it is not only allowable, but highly desirable and 

 even imperative, to use the symbol of equivalence with a 

 generality of meaning corresponding to the generality of 

 the principles involved. Accordingly De Morgan's refusal 

 to use the symbol in logical propositions 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. 



1 Hallam's Literature of Europe, First Ed., vol. ii. p. \\\- 

 z Outline of a New System of Logic, London, 1827, pp. 133, &c. 

 3 An Investigation of the Laws of Thought, pp. 27, &c. 

 * Formal Logic, pp. 82, 106. In his later work, The Syllabus of a 

 New System of Logic, he discontinued the use of the sign. 

 5 Principles of Psychology t Second Ed., vol. ii. pp. 54, 55, 



