The categories of the understanding
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Space and time were the mind’s forms for sensing. But sensing alone gives only a private slideshow. To think a slideshow as a world of objects, the mind needs a second toolkit — twelve concepts you never learned, because you were using them to learn everything else.
Last lesson, the category of cause turned “for me, so far” into “the sun warms the stone.” Kant now generalises: cause is one of a complete, systematic set of pure concepts of the understanding — the categories. He lays them out in Prolegomena to Any Future Metaphysics §21. Category here is a term of art: a pure concept of the understanding, one contributed a priori by the mind, not drawn from any object.
Keep the two-storey architecture in view. Sensibility supplies the a priori forms of intuition — space and time — in which anything can be given to us. The understanding supplies the a priori forms of judgment — the categories — under which anything given can be thought as an object. Sensing without concepts is blind; concepts without sensing are empty. Knowledge needs both floors.
Where do the categories come from? Kant’s claim is that they are derived from the logical forms of judgment. Whenever we judge at all — affirm, deny, relate subject to predicate — we use a fixed set of logical forms. To each such form corresponds a pure concept that lets us think an object in that form. The table of judgments yields the table of categories. (In the Critique this is the “metaphysical deduction”; the Prolegomena presents the result.)
There are twelve categories, in four groups of three. QUANTITY: unity, plurality, totality. QUALITY: reality, negation, limitation. RELATION: substance–accident, cause–effect, community (reciprocal action). MODALITY: possibility, existence, necessity. These twelve are the complete set of pure concepts under which any perception can be thought as belonging to an object.
Now the payoff. The categories are the necessary conditions under which perceptions can be thought as an object at all. Every judgment of experience subsumes what is given in intuition under one or more of them. So an object — and therefore a nature, a connected order of objects — is possible for us only because the understanding brings these concepts to what is given. Take the categories away and you are left with disconnected perception, never a world.
In Kant's two-storey architecture, how do the categories relate to space and time?
From what does Kant claim the twelve categories are derived, and what is their function?
So the parallel with Part I is complete. Mathematics was possible because space and time are our forms of intuition; a nature — a lawful order of objects — is possible because the categories are our forms of thought. But this raises the boldest question of all. If the understanding brings these concepts to nature, then in what sense are its laws nature’s own? Kant’s astonishing answer is the climax of the unit, and the lesson after next.