CHAP. XI.] OF SECONDARY PROPOSITIONS. 171 



eluded in the time #, but which does not fill up the measure of 

 that time, vx will represent a part of the time x. If, lastly, v is 

 determined to represent a time, of which no part is common with 

 any part of the time x, vx will assume the value 0, and will be 

 equivalent to " no time," or " never." 



Now it is to be observed that the proposition, " If Y is true, 

 -XT is true," contains no assertion of the truth of either of the 

 propositions X and Y. It may equally consist with the suppo- 

 sition that the truth of the proposition Y is a condition indis- 

 pensable to the truth of the proposition X, in which case we 

 shall have v = I ; or with the supposition that although Y ex- 

 presses a condition which, when realized, assures us of the truth 

 of X, yet X may be true without implying the fulfilment of that 

 condition, in which case v denotes a time, some part of which is 

 contained in the whole time x ; or, lastly, with the supposition 

 that the proposition'T is not true at all, in which case v repre- 

 sents some time, no part of which is common with any part of 

 the time x. All these cases are involved in the general suppo- 

 sition that v is a symbol of time indefinite. 



5th. To express a proposition in which the conditional and the 

 disjunctive characters both exist. 



The general form of a conditional proposition is, " If Y is 

 true, X is true," and its expression is, by the last section, y = vx. 

 We may properly, in analogy with the usage which has been es- 

 tablished in primary propositions, designate Y and X as the 

 terms of the conditional proposition into which they enter ; and 

 we may further adopt the language of the ordinary Logic, which 

 designates the term Y, to which the particle if is attached, the 

 " antecedent" of the proposition, and the term X the " conse- 

 quent." 



Now instead of the terms, as in the above case, being simple 

 propositions, let each or either of them be a disjunctive propo- 

 sition involving different terms connected by the particles either , 

 or, as in the following illustrative examples, in which X, Y, Z, 

 &c. denote simple propositions. 



1st. If either X is true or Y is true, then ^is true. 



2nd. If X is true, then either Y is true or Z true. 



