Immanuel Kant, answered from the texts and cited to the page.
The question is well-posed, and the answer requires care, because the transcendental deduction is the most demanding piece of work in the entire Critique of Pure Reason — the argument on which the whole edifice of the critical philosophy stands or falls. Begin with the problem it addresses. Among the conceptions we employ, some are destined for pure use a priori, independent of all experience, and their claim to such use always requires a deduction, since proofs from experience are not sufficient to justify it.1
I distinguish this sharply from what I call the empirical deduction — which merely traces how a conception was in fact acquired through experience and reflection — because the empirical deduction concerns only the fact of our obtaining conceptions in such a manner, not the right by which we employ them.2 The transcendental deduction, by contrast, is an examination of the manner in which conceptions can apply a priori to objects at all; it is a question of quid juris — by what right? — rather than quid facti.3
Now, there are only two possible ways in which a representation and its object can stand in necessary relation to one another. Either the object makes the representation possible, in which case the relation is merely empirical and no a priori representation is achievable; or the representation is a priori determinative with respect to the object, so that we can cognize something as an object only through that representation.4
The categories of the understanding fall into the second case. They are not drawn from experience; they are the conditions under which anything whatsoever can be thought as an object. And if that is so, then all empirical cognition must necessarily conform to them — not because experience teaches us their necessity, but because experience is possible only by their means.5
Locke saw pure conceptions at work in experience and tried to derive them from experience, then inconsistently used them to reach beyond all experience. Hume saw more clearly that such conceptions would need an a priori origin, but, unable to explain how the understanding could itself be the author of the experience in which its objects are presented to it, he reduced the necessity of causal connection to habit — a subjective association mistaken for an objective bond — and then, with perfect consistency, declared it impossible to overstep the limits of experience by means of such conceptions.6
Neither could account for the fact that we actually possess scientific a priori cognitions, such as those of pure mathematics and general physics.7 The transcendental deduction closes this gap. Its whole aim is to show that the pure conceptions of the understanding — the categories — are a priori conditions of the possibility of all experience, and that for precisely this reason they apply necessarily and a priori to objects of experience.8
Geometry, it is true, proceeds without needing philosophy to certify the legitimacy of its fundamental conception of space, because geometrical cognition rests on a priori intuition and its objects are given in that intuition directly. But the pure conceptions of the understanding make affirmations concerning objects through pure thought alone, without any condition of sensibility, without any a priori intuition in which to anchor their synthesis antecedently to experience — and this is precisely why their deduction is not merely useful but absolutely necessary.9
I say to the reader: be quite convinced of this necessity before taking a single step in the field of pure reason, because otherwise one proceeds blindly, wanders in every direction, and returns to the same ignorance from which one started.10
Among the many conceptions, which make up the very variegated web of human cognition, some are destined for pure use à priori, independent of all experience; and their title to be so employed always requires a deduction, inasmuch as, to justify such use of them, proofs from experience are not sufficient.Critique of Pure Reason, p. 48
I distinguish it from the empirical deduction, which indicates the mode in which conception is obtained through experience and reflection thereon; consequently, does not concern itself with the right, but only with the fact of our obtaining conceptions in such and such a manner.Critique of Pure Reason, p. 48
There exist also, however, usurped conceptions, such as fortune, fate, which circulate with almost universal indulgence, and yet are occasionally challenged by the question, 'quid juris?' In such cases, we have great difficulty in discovering any deduction for these terms.Critique of Pure Reason, p. 48
There are only two possible ways in which synthetical representation and its objects can coincide with and relate necessarily to each other... Either the object alone makes the representation possible, or the representation alone makes the object possible. In the former case, the relation between them is only empirical, and an à priori representation is impossible.Critique of Pure Reason, p. 48
consequently, the objective validity of the categories, as à priori conceptions, will rest upon this, that experience (as far as regards the form of thought) is possible only by their means.Critique of Pure Reason, p. 48
David Hume perceived that, to render this possible, it was necessary that the conceptions should have an à priori origin. But as he could not explain how it was possible... he was forced to drive these conceptions from experience, that is, from a subjective necessity arising from repeated association of experiences erroneously considered to be objective—in one word, from habit.Critique of Pure Reason, p. 48
The empirical derivation, however, which both of these philosophers attributed to these conceptions, cannot possibly be reconciled with the fact that we do possess scientific à priori cognitions, namely, those of pure mathematics and general physics.Critique of Pure Reason, p. 48
The whole aim of the transcendental deduction of all à priori conceptions is to show that these conceptions are à priori conditions of the possibility of all experience.Critique of Pure Reason, p. 48
With the pure conceptions of understanding, on the contrary, commences the absolute necessity of seeking a transcendental deduction... inasmuch as they make affirmations concerning objects not by means of the predicates of intuition and sensibility, but of pure thought à priori, they apply to objects without any of the conditions of sensibility.Critique of Pure Reason, p. 48
The reader, then, must be quite convinced of the absolute necessity of a transcendental deduction, before taking a single step in the field of pure reason; because otherwise he goes to work blindly, and after he has wondered about in all directions, returns to the state of utter ignorance from which he started.Critique of Pure Reason, p. 48