The argument follows the strict, rigorous, synthetic method. From the already demonstrated _a priori_ character of space, Kant deduces the apodictic certainty of all geometrical principles. But though the paragraph thus expounds a consequence that follows from the _a priori_ character of space, not an argument in support of it, something in the nature of an argument is none the less implied. The fact that this view of the representation of space alone renders mathematical science possible can be taken as confirming this interpretation of its nature. Such an argument, though circular, is none the less cogent. Consideration of Kant’s further statements, that were space known in a merely empirical manner we could not be sure that in all cases only one straight line is possible between two points, or that space will always be found to have three dimensions, must meantime be deferred.[455] In the new transcendental exposition Kant adopts the analytic method of the _Prolegomena_, and accordingly presents his argument in independence of the results already established. He starts from the assumption of the admitted validity of geometry, as being a body of synthetic _a priori_ knowledge. Yet this, as we have already noted, does not invalidate the argument; in both the first and the last paragraphs it is implied that the _a priori_ and intuitive characteristics of space have already been proved. From the synthetic character of geometrical propositions Kant argues[456] that space must be an intuition. Through pure concepts no synthetic knowledge is possible. Then from the apodictic character of geometry he infers that space exists in us as pure and _a priori_;[457] no experience can ever reveal necessity. But geometry also exists as an applied science; and to account for our power of anticipating experience, we must view space as existing only in the perceiving subject as the form of its sensibility. If it precedes objects as the necessary subjective condition of their apprehension, we can to that extent predetermine the conditions of their existence.