Page:Mind (New Series) Volume 9.djvu/314

 300 G. E. MOORE : This generality of necessary truths is what I take Kant to have established in part of his diverse proofs that they are a priori. But whereas he expressly maintains that if you see a truth to be absolutely necessary you may infer it to be a priori, my contention is that you can but show it to be a priori, and that you then add no new or true fact about it, but only a new name, when you also dub it necessary. The theory, briefly stated, is this : That a priori means logically prior, and that any truth which is logically prior to some other true proposition is so far necessary ; but, that as you get more and more true propositions to which a given truth is logically prior, so you approach that region within which the given truth will be said to be absolutely necessary or a priori. There will, then, be only a difference of degree between necessary truths and many others, namely, a differ- ence in the number of propositions to which they bear a certain logical relation ; but there will be a difference of kind between this logical relation and any other of the notions by means of which it has been sought to give a definition to necessity. If there be any truths which have this logical relation to all other propositions, then, indeed, the application of these would be not merely wide but absolutely universal ; such, it would seem, is the Law of Contradiction and, perhaps, some others : and these, perhaps, might be said to differ in kind from all others in this respect also. But into this question, which is exceedingly difficult, I do not propose to enter. It is sufficient for my purpose that there are some truths, commonly called necessary, certain axion.s of geometry, for instance, which have not this absolutely universal application, but which have a very wide one : and that this, at least, may be said of all necessary truths. The logical relation, by means of which I propose to define necessity, is one to which constant appeal is made in philo- sophical arguments ; but the appeal is almost as frequently misused. It is said that one proposition is presupposed, or implied, or involved in another; and this argument is considered to be final. And so indeed it is, if only the pro- position in question is really presupposed or implied or in- volved. It would seem, therefore, desirable that we should be clear about what this relation, which may be designated generally as logical priority, really is : and such clearness is essential to my definition of necessity. I propose, therefore, to try to point it out, but, without attempting to assign its exact limits, or to give an exhaustive enumeration of the various kinds of logical relation, which may all be justly