as belonging to it, and even necessarily? what is here the unknown
= X, upon which the understanding rests when it believes it has found,
out of the conception A a foreign predicate B, which it nevertheless
considers to be connected with it? It cannot be experience, because
the principle adduced annexes the two representations, cause and
effect, to the representation existence, not only with universality,
which experience cannot give, but also with the expression of
necessity, therefore completely a priori and from pure conceptions.
Upon such synthetical, that is augmentative propositions, depends
the whole aim of our speculative knowledge a priori; for although
analytical judgements are indeed highly important and necessary,
they are so, only to arrive at that clearness of conceptions which
is requisite for a sure and extended synthesis, and this alone is a
real acquisition.



V. In all Theoretical Sciences of Reason, Synthetical Judgements
"a priori" are contained as Principles.

1. Mathematical judgements are always synthetical. Hitherto this
fact, though incontestably true and very important in its
consequences, seems to have escaped the analysts of the human mind,
nay, to be in complete opposition to all their conjectures. For as
it was found that mathematical conclusions all proceed according to
the principle of contradiction (which the nature of every apodeictic
certainty requires), people became persuaded that the fundamental
principles of the science also were recognized and admitted in the
same way. But the notion is fallacious; for although a synthetical
proposition can certainly be discerned by means of the principle of