Page:Mind (New Series) Volume 9.djvu/309

 NECESSITY. 295 possess it, as that they have superior certainty, or are uni- versal and eternal. For any of these predicates can only be asserted of it on the ground of a synthetic truth. But if (2) we say that the necessity of analytic truths is not identical with their being analytic, then that they are necessary is a synthetic proposition. And only, while this synthetic proposi- tion is necessary, can any analytic proposition be so. Even, then, if there be some special necessity attaching to analytic propositions it is secondary to that which attaches to some kinds of synthesis. But there is much doubt whether any truths are analytic. Any proposition, it would seem, must contain at least two different terms and their relation ; and, this being so, the relation may always be denied of the two terms with- out a contradiction. It takes two propositions to make a contradiction : the law of contradiction itself excludes the possibility of any single proposition being both true and false, or self-contradictory. And hence the definition of an analytic proposition as a proposition, the contradictory of which is self-contradictory can apply to nothing. If, on the other hand, we take the definition that it is a proposition of which the predicate is contained in the subject, then either its meaning is that that predicate is united in some way with the other predicates, which along with it define the subject : in which case the analytic proposition is as synthetic as you please ; or else the predicate is simply identical with the subject. But in this latter case, where the supposed analytic proposition may be expressed in the form, A is A, we have certainly not two different terms, and therefore we have no proposition. Moreover, the law of contradiction itself, than which nothing is commonly supposed to be more plainly analytic, is certainly synthetic. For suppose some one to hold that Not every proposition is either true or false. You cannot deny that this is a proposition, unless you are also willing to allow that the law which it contradicts is not a proposition ; and he may perfectly well maintain that this is one of those propositions which is true, and the contradictory of which, your law, is false, although this is not the case with every proposition. Whereas, if you urge that it is included in the notion of a proposition that it should be either true or false, either your law becomes a pure tautology and nut a propo- sition, or else there is something else in the notion of a proposition beside the property that it is either true or false, and then you are asserting a synthetic connexion between this property and those others.