2. How is pure natural science possible？
3. How is metaphysics in general possible？
4. How is metaphysics as a science possible？ It may be seen that the solution of these problems， though chiefly designed to exhibit the essential matter of the Critique， has yet something peculiar， which for itself alone deserves attention. This is the search for the sources of given sciences in reason itself， so that its faculty of knowing something a priori may by its own deeds be investigated and measured. By this procedure these sciences gain， if not with regard to their contents， yet as to their proper use， and while they throw light on the higher question concerning their common origin， they give， at the same time， an occasion better to explain their own nature.
第一章First Part Of The Transcendental Problem： How Is Pure Mathematics Possible？
Here is a great and established branch of knowledge， encompassing even now a wonderfully large domain and promising an unlimited extension in the future. Yet it carries with it thoroughly apodictical certainty， i.e.， absolute necessity， which therefore rests upon no empirical grounds. Consequently it is a pure product of reason， and moreover is thoroughly synthetical.
[Here the question arises：] "How then is it possible for human reason to produce a cognition of this nature entirely a priori ？" Does not this faculty [which produces mathematics]， as it neither is nor can be based upon experience， presuppose some ground of cognition a priori， which lies deeply hidden， b，.--， which might reveal itself by these its effects， if their first beginnings were but diligently ferreted out？ Sect. 7. But we find that all mathematical cognition has this peculiarity： it must first exhibit its concept in a visual form [ Anschauung ] and indeed a priori， therefore in a visual form which is not empirical， but pure. Without this mathematics cannot take a single step； hence its judgments are always visual， viz.， "Intuitive"； whereas philosophy must be satisfied with discursive judgments from mere concepts， and though it may illustrate its doctrines through a visual figure， can never derive them from it. This observation on the nature of mathematics gives us a clue to the first and highest condition of its possibility， which is， that some non-sensuous visualization [called pure intuition， or reine Anschauung ] must form its basis， in which all its concepts can be exhibited or constructed， in concrete and yet a priori . If we can find out this pure intuition and its possibility， we may thence easily explain how synthetical propositions a priori are possible in pure mathematics， and consequently how this science itself is possible. Empirical intuition [viz.， sense-perception] enables us without difficulty to enlarge the concept which we frame of an object of intuition [or sense-perception]， by new predicates， which intuition [i.e.， sense-perception] itself presents synthetically in experience.
Pure intuition [viz.， the visualization of forms in our imagination， from which every thing sensual， i.e.， every thought of material qualities， is excluded] does so likewise， only with this difference， that in the latter case the synthetical judgment is a priori certain and apodictical， in the former， only a posteriori and empirically certain； because this latter contains only that which occurs in contingent empirical intuition， but the former， that which must necessarily be discovered in pure intuition.
He.-e intuition， being an intuition a priori， is before all experience， viz.， before any perception of particular objects， inseparably conjoined with its concept. Sect. 8. But with this step our perplexity seems rather to increase than to lessen. For the question now is， "How is it possible to intuit [in a visual form] anything a priori " An intuition [viz.， a visual sense perception] is such a representation as immediately depends upon the presence of the object. Hence it seems impossible to intuit from the outset a priori， because intuition would in that event take place without either a former or a present object to refer to， and by consequence could not be intuition. Concepts indeed are such， that we can easily form some of them a priori， viz.， such as contain nothing but the thought of an object in general； and we need not find ourselves in an immediate relation to the object. Take， for instance， the concepts of Quantity， of Cause， etc. But even these require， in order to make them understood， a certain concrete use-that is， an application to some sense- experience [ Anschauung ]， by which an object of them is given us. But how can the intuition of the object [its visualization] precede the object itself？ Sect. 9. If our intuition [i.e.， our sense-experience] were perforce of such a nature as to represent things as they are in themselves， there would not be any intuition a priori， but intuition would be always empirical.
