Page:Russell - The Problems of Philosophy, 1912.djvu/166

162 much more satisfactory manner than was possible before. Let us revert to the proposition "two and two are four." It is fairly obvious, in view of what has been said, that this proposition states a relation between the universal "two" and the universal "four." This suggests a proposition which we shall now endeavour to establish; namely, All a priori knowledge deals exclusively with the relations of universals. This proposition is of great importance, and goes a long way towards solving our previous difficulties concerning a priori knowledge.

The only case in which it might seem, at first sight, as if our proposition were untrue, is the case in which an a priori proposition states that all of one class of particulars belong to some other class, or (what comes to the same thing) that all particulars having some one property also have some other. In this case it might seem as though we were dealing with the particulars that have the property rather than with the property. The proposition "two and two are four" is really