Hence, it is only by means of the form of sensuous intuition that we can intuit things apriori, but in this way we intuit the objects only as they appear to our senses, not as they may be in themselves; an assumption absolutely necessary if synthetic propositions aprioriare to be admitted as possible, or in the event of their being actually met with, if their possibility is to be conceived and defined beforehand.
Now, such intuitions are space and time, and these lie at the basis of all the cognitions and judgments of pure mathematics, exhibiting themselves at once as apodictic and necessary. For mathematics must present all its conceptions primarily in intuition, and pure mathematics in pure intuition, i.e., it must construct them. For without this it is impos- sible to make a single step, so long, that is to say, as a pure intuition is wanting, in which alone the matter of synthetic judgments apriori can be given; because it cannot proceed analytically, that is, by the dissection of conceptions, but is obliged to proceed synthetically. The pure intuition of space constitutes the basis of geometry—even arithmetic brings about its numerical conceptions by the successive addition of units in time; but above all, pure mechanics can evolve its conception of motion solely with the aid of the presentation of time. Both presentations, however, are mere intuitions; for when all that is empirical, namely, that belongs to feeling, is left out of the empirical intuitions of bodies and their changes (motion), space and time still remain over, and are therefore pure intuitions, lying aprioriat the foundation of the former. For this reason, they can never be left out, but being pure intuitions apriori, prove that they are the bare forms of our sensibility, which must precede all empirical intuition, i.e., the perception of real objects, and in accor- dance with which objects can be known apriori, though only as they appear to us.