CHAP. XI.] OF SECONDARY PROPOSITIONS. 167 



dary propositions, the universe of discourse may be limited to a 

 single day or to the passing moment, or it may comprise the 

 whole duration of time. It may, in the most literal sense, be 

 " eternal." Indeed, unless there is some limitation expressed or 

 implied in the nature of the discourse, the proper interpretation 

 of the symbol 1 in secondary propositions is " eternity ;" even as 

 its proper interpretation in the primary system is the actually 

 existent universe. 



9. Instead of appropriating the symbols x 9 y, z, to the repre- 

 sentation of the truths of propositions, we might with equal pro- 

 priety apply them to represent the occurrence of events. In fact, 

 the occurrence of an event both implies, and is implied by, the 

 truth of a proposition, viz., of the proposition which asserts the 

 occurrence of the event. The one signification of the symbol x 

 necessarily involves the other. It will greatly conduce to con- 

 venience to be able to- employ our symbols in either of these 

 really equivalent interpretations which the circumstances of a 

 problem may suggest to us as most desirable ; and of this liberty 

 I shall avail myself whenever occasion requires. In problems of 

 pure Logic I shall consider the symbols #, y, &c. as representing 

 elementary propositions, among which relation is expressed in 

 the premises. In the mathematical theory of probabilities, which, 

 as before intimated (I. 12), rests upon a basis of Logic, and 

 which it is designed to treat in a subsequent portion of this work, 

 I shall employ the same symbols to denote the simple events, 

 whose implied or required frequency of occurrence it counts 

 among its elements. 



PROPOSITION III. 



1 0. To deduce general Rules for the expression of Secondary 

 Propositions. 



In the various inquiries arising out of this Proposition, fulness 

 of demonstration will be the less necessary, because of the exact 

 analogy which they bear with similar inquiries already completed 

 with reference to primary propositions. We shall first consider 

 the expression of terms ; secondly, that of the propositions by 

 which they are connected. 



