5 Feb 2009

Kant, Critique of Pure Reason, The Transcendental Aesthetic, §3

The Critique of Pure Reason
I. Transcendental Doctrine of Elements
Part 1: The Transcendental Aesthetic
Section 1: On Space

§3 "Transcendental Exposition of the Concept of Space"

We noted previously that a concept's metaphysical exposition exhibits what is a priori in it. Kant now says that a transcendental exposition explains a concept as a principle which allows us to gain insight into the possibility of other a priori cognitions. There are two requirements for giving a transcendental exposition:
1) the other a priori cognitions actually flow from the concept we are explaining, and
2) we must presuppose this way of explaining the concept in order for these other a priori cognitions to flow from it.

For example, we have (synthetic) a priori geometrical spatial-cognitions. They must flow from some representation of space which makes these cognitions possible. Now, in geometry we derive propositions that go beyond what we know merely about space. But we cannot draw from a concept propositions that go beyond it. So geometrical space cannot be a concept. Thus it must be an intuition. (176b) Yet, consider the proposition that space has only three dimensions. This is necessarily true, and hence apodictically certain. But empirical or experiential (a posteriori) judgments are never apodictic. Hence the geometrical intuition of space must "be encountered in us a priori, i.e., prior to all perception of an object." (176bc)

So, this geometrical intuition regards space. And space is something that is found only outwardly. Thus the geometrical intuition of space is an outer intuition that
1) lives in the mind
2) precedes the spatial objects, and
3) determines exterior objects a priori.
Now, we intuit spatial objects. By doing so, our outer intuition of space is "affected" by our intuitions of these outer objects. For this to be so, our outer spatial intuitions must be seated somewhere. But because they are a priori, they could only be seated in the subject. And it is by means of the subject's "formal constitution" that our intuition of space may be housed and affected by intuitions of outer objects. Thus also it is only by means of the subject that the outer objects obtain immediate representation, that is, intuition.

So we have just explained our concept of space as the principle that accounts for the possibility of geometry as a synthetic a priori cognition. Hence we have given a transcendental exposition.

From the text of the Meiklejohn translation:
SS 3. Transcendental Exposition of the Conception of Space.
By a transcendental exposition, I mean the explanation of a conception, as a principle, whence can be discerned the possibility of other synthetical a priori cognitions. For this purpose, it is requisite, firstly, that such cognitions do really flow from the given conception; and, secondly, that the said cognitions are only possible under the presupposition of a given mode of explaining this conception.
Geometry is a science which determines the properties of space synthetically, and yet a priori. What, then, must be our representation of space, in order that such a cognition of it may be possible? It must be originally intuition, for from a mere conception, no propositions can be deduced which go out beyond the conception,* and yet this happens in geometry. (Introd. V.) But this intuition must be found in the mind a priori, that is, before any perception of objects, consequently must be pure, not empirical, intuition. For geometrical principles are always apodeictic, that is, united with the consciousness of their necessity, as: "Space has only three dimensions." But propositions of this kind cannot be empirical judgements, nor conclusions from them. (Introd. II.) Now, how can an external intuition anterior to objects themselves, and in which our conception of objects can be determined a priori, exist in the human mind? Obviously not otherwise than in so far as it has its seat in the subject only, as the formal capacity of the subject's being affected by objects, and thereby of obtaining immediate representation, that is, intuition; consequently, only as the form of the external sense in general.

* That is, the analysis of a conception only gives you what is contained in it, and does not add to your knowledge of the object of which you have a conception, but merely evolves it. -- Tr.
Thus it is only by means of our explanation that the possibility of geometry, as a synthetical science a priori, becomes comprehensible. Every mode of explanation which does not show us this possibility, although in appearance it may be similar to ours, can with the utmost certainty be distinguished from it by these marks.

Summary based on:
Kant. Critique of Pure Reason. Eds. & Transls. Paul Guyer and Allen Wood. Cambridge: Cambridge University Press, 1998.

Full text taken from:
Kant. Critique of Pure Reason. Transl. J.M.D Meiklejohn.
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