Omitting the consideration of _a posteriori_ knowledge for the present, let us investigate the _a priori_ in order to learn something of the constitution of the intelligence which knows—always a proper subject for philosophy. Since, moreover, the _a priori analytical_ (“A horse is an animal”) adds nothing to our knowledge, we may confine ourselves, as Kant does, to _a priori synthetical_ knowledge. The axioms of mathematics are of this character. They are universal and necessary in their application, and we know this without making a single practical experiment. “Only one straight line can be drawn between two points,” or the proposition: “The sum of the three angles of a triangle is equal to two right angles,”—these are true in all possible experiences, and hence transcend any actual experience. Take any _a posteriori_ judgment, e. g. “All bodies are heavy,” and we see at once that it implies the restriction, “So far as we have experienced,” or else is a mere analytical judgment. The _universal and necessary_ is sometimes called the _apodeictical_. The conception of the _apodeictical_ lies at the basis of all true philosophical thinking. He who does not distinguish between _apodeictic_ and _contingent_ judgments must pause here until he can do so. IV. SPACE AND TIME. In order to give a more exhaustive application to our technique, let us seek the universal conditions of experience. The mathematical truths that we quoted relate to Space, and similar ones relate to Time. No experience would be possible without presupposing Time and Space as its logical condition. Indeed, we should never conceive our sensations to have an origin outside of ourselves and in distinct objects, unless we had the conception of Space _a priori_ by which to render it possible. Instead, therefore, of our being able to generalize particular experiences, and collect therefrom the idea of Space and Time in general, we must have added the idea of Space and Time to our sensation before it could possibly become an experience at all. This becomes more clear when we recur to the _apodeictic_ nature of Space and Time. Time and Space are thought as _infinites_, i. e. they can only be limited by themselves, and hence are universally continuous. But no such conception as _infinite_ can be derived analytically from an object of experience, for it does not contain it. All objects of experience must be _within_ Time and Space, and not _vice versa_. All that is limited in extent and duration presupposes Time and Space as its logical condition, and this we know, not from the senses but from the constitution of Reason itself. “The third side of a triangle is less than the sum of the two other sides.” This we never measured, and yet we are certain that we cannot be mistaken about it. It is so in all triangles, present, past, future, actual, or possible. If this was an inference _a posteriori_, we could