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MEMOIRS OF THE AMERICAN ACADEMY. 



Application of the Algebraic Signs to Logic. 



While holding ourselves free to use the signs of algebra in any sense conformable 

 to the above absolute conditions, we shall find it convenient to restrict ourselves to 

 one particular interpretation except where another is indicated. I proceed to de- 

 scribe the special notation which is adopted in this paper. 



Use of the Letters. 



The letters of the alphabet will denote logical signs. Now logical terms are of 

 three grand classes. The first embraces those whose logical form involves only the 

 conception of quality, and which therefore represent a thing simply as "a — ." These 

 discriminate objects in the most rudimentary way, which does not involve any con- 

 sciousness of discrimination. They regard an object as it is in itself as such {quale)) 

 for example, as horse, tree, or man. These are absolute terms. The second class em- 

 braces terms whose logical form involves the conception of relation, and which require 

 the addition of another term to complete the denotation. These discriminate objects 

 with a distinct consciousness of discrimination. They regard an object as over against 

 another, that is as relative ; as father of, lover of, or servant of. These are simple rela- 

 live terms. The third class embraces terms whose logical form involves the conception 

 of bringing things into relation, and which require the addition of more than one 

 term to complete the denotation. They discriminate not only with consciousness of 



but with consciousness of 



6 



They regard an object as med 



or third between two others, that is as conjugative ; as giver of — to — , or buyer of 

 for — from — . These may be termed conjugative terms. The conjugative term in- 

 volves the conception of third, the relative that of second or other, the absolute term 

 simply considers an object. No fourth class of terms exists involving the conception 

 of fourth, because when that of third is introduced, since it involves the conception of 

 bringing objects into relation, all higher numbers are given at once, inasmuch as the 

 conception of bringing objects into relation is independent of the number of mem- 

 bers of the relationship. Whether this reason for the fact that there is no fourth 

 class of terms fundamentally different from the third is satisfactory or not, the fact 

 itself is made perfectly evident by the study of the logic of relatives. I shall denote 

 absolute terms by the Roman alphabet, a, b, e, d, etc.; relative terms by italics, a, 6, 

 c, d, etc. ; and conjugative terms by a kind of type called Madisonian, a, L, c, d, etc. 



I shall commonly denote individuals by capitals, and generals by small letters. ' 

 General symbols for numbers will be printed in black-letter, thus, a, t», C, to, etc. 

 The Greek letters will denote operations. 





