XII. 



Description of a Notation for the Logic of B< latins, renting frovt an A^/fi 



of the Conceptions of Boole's Calculus of Logic 



BY C. S. PEIRCE. 



Communicated January 2C>, 1870 



Relative terms usually receive some slight treatment in works upon logic, but th 

 only considerable investigation into the formal laws which govern them ii contained 

 in a valuable paper by Mr. De Morgan in the tenth volume of the Cambridge Philo- 

 sophical Transactions. He there uses a convenient algebraic notation, which is formed 



by adding to the well-known spiculce of that writer the signs used in the following 

 examples. 



X . . LY signifies that X is some one of the objects of thought which stand to Y 

 in the relation L, or is one of the L's of Y. 



X . LMY signifies that X is not an L of an M of Y. 

 X . . (L,M)Y signifies that X is either an L or an M of Y. 

 LM' an L of every M. LM an L of none but M's. 

 L[— ! JY something to which Y is L 1 (small L) non-L. 



This system still leaves something to be desired. Moreover, Uoole's logical algebra 

 has such singular beauty, so far as it goes, that it is interestin to inquire whether 

 it cannot be extended over the whole realm of formal logic, instead of being re- 

 stricted to that simplest and least useful part of the subject, the logic of absolute 

 terms, which, when he wrote, was the only formal logic known. The object of thin 

 paper is to show that an affirmative answer can be given to this question. I think 

 there can be no doubt that a calculus, or art of drawing inferences, based upon the 

 notation I am to describe, would be perfectly possible and even practically useful 

 in some difficult cases, and particularly in the inves ligation of logic. I regret that 

 I am not in a situation to be able to perform this labor, but the account here given 

 of the notation itself will afford the ground of a judgment concerning its probable 

 utility. 



In extending the use of old symbols to new subjects, we must of course be 





uided by certain principles of analogy, which, when formulated, become new and 



vol. ix. 44 





