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be there. Therefore the representation of space cannot be borrowed through experience from relations of external phenomena, but, on the contrary, 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. [24] It is impossible to imagine that there should be no space, though one might very well imagine that there should be space without objects to fill it. Spaceis therefore regarded as a condition of the possibility of phenomena, notas a determinationproduced by them; it is a representation a priori which necessarily precedes all external phenomena. [3. On this necessity of an apriori representation of space rests the apodictic certainty of all geometrical 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 faras hitherto observed, no space hasyet been found having more than three dimensions.] 4. Space is not a discursive or so-called general [25] [20] concept of the relations of things in general, but a pure intuition. For, first of all, we can imagine one space only and if we speak of many spaces, we mean parts only of one and the same space. Nor can these parts be considered as antecedent to the one and all-embracing space and, as it were, its component parts out of which an aggregate is formed, but they can be thought of as existing within it only. Space is essentially one; its multiplicity, and therefore the general concept of spaces in general, arises entirely from limitations. Hence it follows that, with respect to space, an intuition a priori, which is not empirical, must form the foundation of all conceptions of space. In the samemanner all geometrical principles, e.g. 'that in every triangle two sides togetherare greater than the third,' are never to be derived from the general concepts of side and triangle, but from an intuition, and that a priori, with apodictic certainty. [5. Space is represented as an infinite quantity. Now a general concept ofspace, which is found in a foot as wellas in an ell, could tell us nothing in respect to the quantity of the space. If there were not infinity in the progression of intuition, no concept of relations of space could ever contain a principle of infinity.1] Conclusions from the Foregoing Concepts [26]? a. Space does not represent any quality of objects by themselves, or objects in their relation to one another; i.e. space does not represent any determination which is inherent in the objects themselves, and would remain, [21] even if all subjective conditions of intuition were removed. For no determinations of objects, whether belonging to them absolutely or in relation to others, can enter into our intuition before the actual existence of the objects themselves, that is to say, they can never be intuitions a priori. b. Space is nothing but the form of all phenomena of the external senses; it is the subjective condition of our sensibility, without which no .