Immanuel Kant, answered from the texts and cited to the page.
The categories of the pure understanding are the fundamental concepts through which the Verstand (understanding) thinks any object whatsoever — not concepts drawn from experience, but the very conditions under which experience becomes possible at all. They are, in a precise sense, the forms of thought itself. The table I established in the Critique of Pure Reason arranges them under four headings: Quantity (Unity, Plurality, Totality), Quality (Reality, Negation, Limitation), Relation (Substance-and-Accident, Cause-and-Effect, Community), and Modality (Possibility, Existence, Necessity, along with their opposites).1
What matters is that this is no arbitrary collection. Aristotle before me attempted the same search, and found ten categories, later supplementing them with five more — yet his catalogue remained defective, mixing in pure forms of sensibility such as quando and ubi, and even an empirical concept (motus), which can by no means belong to a register of the pure understanding.2
The fault was not diligence but method: he gathered his concepts rhapsodically, as they occurred to him, with no guiding principle to determine why precisely these concepts and no others should constitute the list.3 My derivation proceeds otherwise. The categories arise systematically from a single common principle — the faculty of judgement itself, that is, the power of thought as such — so that one can see not merely that there are twelve categories, but why there are exactly twelve, neither more nor less.4
Yet here is what Aristotle entirely missed, and what gives my system its philosophical significance rather than making it merely another catalogue of names: the categories, taken by themselves, without any grounding in sensuous intuition, represent no object at all.5 They are, strictly speaking, nothing but logical functions of the understanding; they serve to determine empirical judgements, rendering them universally valid and making experience in general possible — but only when a sensuous intuition is given as their basis.6
Without that basis, without the Anschauung (intuition) that sensibility supplies, the categories are empty functions, and the understanding that wields them reaches nothing. This is why the schemata — the temporal determinations that mediate between the pure category and the conditions of sensibility — are indispensable: stripped of their schemata, the categories are merely functions for the production of concepts, deriving their significance, their reality as cognitive tools, from sensibility alone.7
The consequence for metaphysics is severe. Every prior metaphysician who applied concepts such as substance, cause, or necessity to objects beyond all possible experience — to the soul, to the world as a whole, to God — was using the categories without any intuition to give them content. The result was not knowledge but the exhausting of the human understanding in obscure and vain speculations, rendering it unfit for genuine science.8
What I established is the precise boundary: the categories constitute a priori cognition of the understanding only insofar as they relate to possible experience, and nature — as an object of experience — is precisely the domain where the understanding legislates through them, insisting that the sensuous world must be an existence of things determined according to universal laws.9
TABLE OF THE CATEGORIES: 1 Of Quantity: Unity, Plurality, Totality; 2 Of Quality: Reality, Negation, Limitation; 3 Of Relation: Of Inherence and Subsistence, Of Causality and Dependence, Of Community; 4 Of Modality: Possibility—Impossibility, Existence—Non-existence, Necessity—Contingence.Critique of Pure Reason, p. 48
Destitute, however, of any guiding principle, he picked them up just as they occurred to him, and at first hunted out ten, which he called categories (predicaments). Afterwards he believed that he had discovered five others, which were added under the name of post predicaments. But his catalogue still remained defective. Besides, there are to be found among them some of the modes of pure sensibility (quando, ubi, situs, also prius, simul), and likewise an empirical conception (motus)—which can by no means belong to this genealogical register of the pure understanding.Critique of Pure Reason, p. 48
Aristotle collected ten pure elementary concepts under the name of Categories. To these, which are also called predicaments, he found himself obliged afterwards to add five post-predicaments, some of which however (prius, simul, and motus) are contained in the former; but this random collection must be considered (and commended) as a mere hint for future inquirers, not as a regularly developed idea.Prolegomena to Any Future Metaphysics, p. 11
This division is made systematically from a common principle, namely the faculty of judgement (which is just the same as the power of thought), and has not arisen rhapsodically from a search at haphazard after pure conceptions, respecting the full number of which we never could be certain, inasmuch as we employ induction alone in our search.Critique of Pure Reason, p. 48
it became obvious that they are themselves nothing but logical functions, and as such do not produce the least concept of an object, but require some sensuous intuition as a basis.Prolegomena to Any Future Metaphysics, p. 11
They therefore only serve to determine empirical judgments, which are otherwise undetermined and indifferent as regards all functions of judging, relatively to these functions, thereby procuring them universal validity, and by means of them making judgments of experience in general possible.Prolegomena to Any Future Metaphysics, p. 11
the categories, without schemata are merely functions of the understanding for the production of conceptions, but do not represent any object. This significance they derive from sensibility, which at the same time realizes the understanding and restricts it.Critique of Pure Reason, p. 62
Had the ancients ever conceived such a notion, doubtless the whole study of the pure rational knowledge, which under the name of metaphysics has for centuries spoiled many a sound mind, would have reached us in quite another shape, and would have enlightened the human understanding, instead of actually exhausting it in obscure and vain speculations, thereby rendering it unfit for true science.Prolegomena to Any Future Metaphysics, p. 11
we are not now concerned with the nature of things in themselves, which is independent of the conditions both of our sensibility and our understanding, but with nature, as an object of possible experience, and in this case the understanding, whilst it makes experience possible, thereby insists that the sensuous world is either not an object of experience at all, or must be nature [viz., an existence of things, determined according to universal laws].Prolegomena to Any Future Metaphysics, p. 11