A priori, as applied to knowledge, signifies that which belongs to the nature of the mind itself. Knowledge which is before experience, or not dependent on it, is a priori.
A posteriori or empirical knowledge is derived from experience.
A criterion to be applied in order to test the application of these categories to any knowledge in question, is to be found in universality and necessity. If the truth expressed has universal and necessary validity it must be a priori, for it could not have been derived from experience. Of empirical knowledge we can only say: “It is true so far as experience has extended.” Of a priori knowledge, on the contrary, we affirm: “It is universally and necessarily true and no experience of its opposite can possibly occur; from the very nature of things it must be so.”
II.—ANALYTICAL AND SYNTHETICAL.
A judgment which, in the predicate, adds nothing new to the subject, is said to be analytical, as e. g. “Horse is an animal;”—the concept “animal” is already contained in that of “horse.”
Synthetical judgments, on the contrary, add in the predicate something new to the conception of the subject, as e. g. “This rose is red,” or “The shortest distance between two points is a straight line;”—in the first judgment we have “red” added to the general concept “rose;” while in the second example we have straightness, which is quality, added to shortest, which is quantity.
III.—APODEICTICAL.
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 only say: “It has been found to be so in all cases that have been measured and reported to us.”