Every noun or term denotes an object, and usually implies the possession by that object of certain qualities or circumstances common to all the objects denoted. There are certain terms, however, which imply the absence of qualities or circumstances attaching to other objects. It will be convenient to employ a special mode of indicating these *negative terms*, as they are called. If the general name A denotes an object or class of objects possessing certain defined qualities, then the term Not A will denote any object which does not possess the whole of those qualities; in short, Not A is the sign for anything which differs from A in regard to any one or more of the assigned qualities. If A denote “transparent object,” Not A will denote “not transparent object.” Brevity and facility of expression are of no slight importance in a system of notation, and it will therefore be desirable to substitute for the negative term Not A a briefer symbol. De Morgan represented negative terms by small Roman letters, or sometimes by small italic letters;[30] as the latter seem to be highly convenient, I shall use *a*, *b*, *c*, ... *p*, *q*, &c., as the negative terms corresponding to A, B, C, ... P, Q, &c. Thus if A means “fluid,” *a* will mean “not fluid.” [30] *Formal Logic*, p. 38. *Expression of Identity and Difference.* To denote the relation of sameness or identity I unhesitatingly adopt the sign =, so long used by mathematicians to denote equality. This symbol was originally appropriated by Robert Recorde 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.[31] 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,[32] Boole,[33] 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;[34] and Herbert Spencer has applied it in a like manner.[35] [31] Hallam’s *Literature of Europe*, First Ed., vol. ii. p. 444. [32] *Outline of a New System of Logic*, London, 1827, pp. 133, &c. [33] *An Investigation of the Laws of Thought*, pp. 27, &c. [34] *Formal Logic*, pp. 82, 106. In his later work, *The Syllabus of a New System of Logic*, he discontinued the use of the sign. [35] *Principles of Psychology*, Second Ed., vol. ii. pp. 54, 55.