5 Feb 2009

Kant, Critique of Pure Reason, The Transcendental Aesthetic, §2

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

§2 "Metaphysical Exposition of This Concept"

One of our mind's properties is that it can sense things outside it. This is our outer sense. We represent all exterior objects as being in space. When objects have been spatialized, we may determine their shapes, magnitudes, and relations to one another.

Before we saw that an intuition is an immediate relation between a cognition and its object. When the mind has an intuition of itself or of its inner state, then it exercises its inner sense. However, the inner sense does not intuit our souls as objects. Nonetheless, inner intuitions are determinate forms, and they are the only means we have for intuiting our inner states. And because inner sense does not deal with external things, it represents its determinations in relations of time instead.
Time can no more be intuited externally than space can be intuited as something in us. (174c)
Kant now wonders what time and space actually are, and if they are real entities. He also asks if either
a) space and time are determinations of things or relations between them, and in this case, if they are determinations or relations that apply to things even when we are not intuiting them, or
b) space and time are only found attached to our intuitions, and thus as well to our mind's subjective constitution, and in this case time and space only come about when our minds predicate them to things.

Kant first begins to analyze space.

We give an exposition of a concept when we provide a distinct and perhaps complete representation of what belongs to the concept. We give a metaphysical exposition when our representation expresses what is a priori about the concept. (174d)

Our senses are related to things outside us. Thus these other things occupy a different place than we do. Moreover, the things outside us occupy different places from each other. The only way we could represent exterior objects then is if we presuppose space's "pre-presentation" if you will, or as the translators render: "the representation of space must already be their ground." (175a)
Thus we do not obtain representations of space by experiencing the relations between outer appearances. Rather, "outer experience is itself first possible only through this representation." (175a)

Hence "space is a necessary representation, a priori, that is the ground of all outer intuitions." (175ab) We can imagine there there are no objects in the space around us. But we cannot represent the outer world without space. Hence space never depends on these exterior appearances. Rather, space is "the condition of the possibility of appearances." And it is an "a priori representation that necessarily grounds outer appearances." (175b)

We might consider many spaces around us. But really these are part of one all-encompassing space. In fact, we can only think these smaller spaces through the concept of the single all-encompassing space. Thus space is not a general concept of things' relations. Rather, it is a pure intuition that makes things' spatial relations possible. So as a pure form of intuition, there is only one unique space, and the manifold is in it. Hence all spatial intuitions are grounded in this a priori intuition of space. Now, we might think that from the definitions of 'line' and 'triangle' we can deduce the following proposition: "two sides of a triangle together are always greater than the third side." However, this fact we really derive from our pure intuition of space. And we derive it a priori with absolute certainty. (175c)

A concept may be represented an infinite number of ways. We do not consider these representations to be within the concept. Although, we do think that they fall under it. Now, space is given to us as an infinite magnitude. Still, every part of that infinity of space is simultaneous with the rest. Thus the whole of space contains within it an infinite set of representations. They do not fall under it, because they are simultaneous together in the totality of space. Hence "the original representation of space is an a priori intuition, not a concept." (175d)

From the text of the Meiklejohn translation:
SS 2. Metaphysical Exposition of this Conception.
BY means of the external sense (a property of the mind), we represent to ourselves objects as without us, and these all in space. Herein alone are their shape, dimensions, and relations to each other determined or determinable. The internal sense, by means of which the mind contemplates itself or its internal state, gives, indeed, no intuition of the soul as an object; yet there is nevertheless a determinate form, under which alone the contemplation of our internal state is possible, so that all which relates to the inward determinations of the mind is represented in relations of time. Of time we cannot have any external intuition, any more than we can have an internal intuition of space. What then are time and space? Are they real existences? Or, are they merely relations or determinations of things, such, however, as would equally belong to these things in themselves, though they should never become objects of intuition; or, are they such as belong only to the form of intuition, and consequently to the subjective constitution of the mind, without which these predicates of time and space could not be attached to any object? In order to become informed on these points, we shall first give an exposition of the conception of space. By exposition, I mean the clear, though not detailed, representation of that which belongs to a conception; and an exposition is metaphysical when it contains that which represents the conception as given a priori.
1. Space is not a conception which has been derived from outward experiences. For, in order that certain sensations may relate to something without me (that is, to something which occupies a different part of space from that in which I am); in like manner, in order that I may represent them not merely as without, of, and near to each other, but also in separate places, the representation of space must already
exist as a foundation. Consequently, the representation of space cannot be borrowed from the relations of external phenomena through experience; but, on the contrary, this external experience is itself only possible through the said antecedent representation.
2. Space then is a necessary representation a priori, which serves for the foundation of all external intuitions. We never can imagine or make a representation to ourselves of the non -- existence of space, though we may easily enough think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of phenomena, and by no means as a determination dependent on them, and is a representation a priori, which necessarily supplies the basis for external phenomena.
3. Space is no discursive, or as we say, general conception of the relations of things, but a pure intuition. For, in the first place, we can only represent to ourselves one space, and, when we talk of divers spaces, we mean only parts of one and the same space. Moreover, these parts cannot antecede this one all -- embracing space, as the component parts from which the aggregate can be made up, but can be cogitated only as existing in it. Space is essentially one, and multiplicity in it, consequently the general notion of spaces, of this or that space, depends solely upon limitations. Hence it follows that an a priori intuition (which is not empirical) lies at the root of all our conceptions of space. Thus, moreover, the principles of geometry -- for example, that "in a triangle, two sides together are greater than the third," are never deduced from general conceptions of line and triangle, but from intuition, and this a priori, with apodeictic certainty.4. Space is represented as an infinite given quantity. Now every conception must indeed be considered as a representation which is contained in an infinite multitude of different possible representations, which, therefore, comprises these under itself; but no conception, as such, can be so conceived, as if it contained within itself an infinite multitude of representations. Nevertheless, space is so conceived of, for all parts of space are equally capable of being produced to infinity. Consequently, the original representation of space is an intuition a priori, and not a conception.

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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