[Footnote 1:  “All bodies are extended” is an analytic judgment; “all bodies possess weight,” a synthetic judgment.  The former explicates the concept of the subject by bringing into notice an idea already contained in it and belonging to the definition as a part thereof; it is based on the law of contradiction:  an unextended body is a self-contradictory concept.  The latter, on the contrary, goes beyond the concept of the subject and adds a predicate which had not been thought therein.  It is experience which teaches us that weight is joined to matter, a fact which cannot be derived from the concept of matter.  Almost all mathematical principles are synthetic, and here, as will be shown, it is not experience but “pure intuition” which permits us to go beyond the concept and add a new mark to it.]

[Footnote 2:  The Scholastics applied the term a priori to knowledge from causes (from that which precedes), and a posteriori to knowledge from effects.  Kant, following Leibnitz and Lambert, uses the terms to designate the antithesis, knowledge from reason and knowledge from experience.  An a priori judgment is a judgment obtained without the aid of experience.  When the principle from which it is derived is also independent of experience it is absolutely a priori, otherwise it is relatively a priori.]

Two sciences discuss the how, and a third the if of such judgments, which, at the same time, are ampliative and absolutely universal and necessary.  The first two sciences are pure mathematics and pure natural science, of which the former is protected against doubt concerning its legitimacy by its evident character, and the latter, by the constant possibility of verification in experience; each, moreover, can point to the continuous course of its development.  All this is absent in the third science, metaphysics, as science of the suprasensible, and to its great disadvantage.  Experiential verification is in the nature of things denied to a presumptive knowledge of that which is beyond experience; it lacks evidence to such an extent that there is scarcely a principle to be found to which all metaphysicians assent, much less a metaphysical text-book to compare with Euclid; there is so little continuous advance that it is rather true that the later comers are likely to overthrow all that their predecessors have taught.  In metaphysics, therefore, which, it must be confessed, is actual as a natural tendency, the question is not, as in the other two sciences, concerning the grounds of its legitimacy, but concerning this legitimacy itself.  Mathematics and pure physics form synthetic judgments a priori, and metaphysics does the same.  But the principles of the two former are unchallenged, while those of the third are not.  In the former case the subject for investigation is, Whence this authority? in the latter case, Is she thus authorized?