| 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. |
| 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. |