1. Space is not an empirical concept which has been derived from external experience. For in order that certain sensations should be referred to something outside myself... the representation of space must already be there. ...this external experience becomes possible only by means of the representation of space.
2. Space is a necessary representation a priori, forming the very foundation of all external intuitions. It is impossible to imagine that there should be no space... Space is therefore regarded as a condition of the possibility of phenomena, not as a determination produced by them; it is a representation a priori which necessarily precedes all external phenomena.
3. On this necessity of an a priori representation of space rests on the apodictic certainty of all geometric principles, and the possibility of their construction a priori. For if the intuition of space were a concept gained a posteriori, borrowed from general external experience, the first principles of mathematical definition would be nothing but perceptions. They would be exposed to all the accidents of perception, and there being but one straight line between two points would not be a necessity, but only something taught in each case by experience. Whatever is derived from experience possesses a relative generality only, based on induction. We should therefore not be able to say more than that, so far as hitherto observed, no space has yet been found having more than three dimensions.
4. Space is not a discursive or so-called general concept of the relations of things, but a pure intuition. ...
5. Space is represented as an infinite quantity. ...If there were not infinity in the progression of intuition, no concept of relations of space could ever contain a concept of infinity.
Immanuel Kant, Critique of Pure Reason (1781) Tr. (1922) F. Max Müller, pp. 18-19.
