80 OF INTERPRETATION. [CHAP. VI. 



CHAPTER VI. 



OF THE GENERAL INTERPRETATION OF LOGICAL EQUATIONS, AND 

 THE RESULTING ANALYSIS OF PROPOSITIONS. ALSO, OF THE 

 CONDITION OF INTERPRETABILITY OF LOGICAL FUNCTIONS. 



1 . TT has been observed that the complete expansion of any 

 -*- function by the general rule demonstrated in the last 

 chapter, involves two distinct sets of elements, viz., the consti- 

 tuents of the expansion, and their coefficients. I propose in 

 the present chapter to inquire, first, into the interpretation of 

 constituents, and afterwards into the mode in which that inter- 

 pretation is modified by the coefficients with which they are 

 connected. 



The terms " logical equation," " logical function," &c., will 

 be employed generally to denote any equation or function in- 

 volving the symbols a, ?/, &c., which may present itself either 

 in the expression of a system of premises, or in the train of sym- 

 bolical results which intervenes between the premises and the 

 conclusion. If that function or equation is in a form not imme- 

 diately interpretable in Logic, the symbols #, y, &c., must be re- 

 garded as quantitative symbols of the species described in previous 

 chapters (II. 15), (V. 6), as satisfying the law, 



x (1 - x] = 0. 



By the problem, then, of the interpretation of any such logical 

 function or equation, is meant the reduction of it to a form in 

 which, when logical values are assigned to the symbols #, y, &c., 

 it shall become interpretable, together with the resulting inter- 

 pretation. These conventional definitions are in accordance with 

 the general principles for the conducting of the method of this 

 treatise, laid down in the previous chapter. 



