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Extract from THE CRITIQUE OF PURE REASON

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.
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.
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.