inate in the sensibility, so the _a priori_ conceptions
and laws which underlie natural science originate in the
understanding; for, on this view, the discovery of all the conceptions
and laws which originate in the understanding will be at the same time
the discovery of all the presuppositions of natural science.

Kant therefore in the _Analytic_ has a twofold problem to solve.
He has firstly to discover the conceptions and laws which belong to
the understanding as such, and secondly to vindicate their application
to individual things. Moreover, although it is obvious that the
conceptions and the laws of the understanding must be closely
related,[5] he reserves them for separate treatment.

[5] E. g. the conception of 'cause and effect', and the law
that 'all changes take place according to the law of the
connexion between cause and effect'.

The _Analytic_ is accordingly subdivided into the _Analytic of
Conceptions_ and the _Analytic of Principles_. The _Analytic of
Conceptions_, again, is divided into the _Metaphysical Deduction of
the Categories_, the aim of which is to discover the conceptions
of the understanding, and the _Transcendental Deduction of the
Categories_, the aim of which is to vindicate their validity,
i. e. their applicability to individual things.

It should further be noticed that, according to Kant, it is the
connexion of the _a priori_ conceptions and laws underlying natural
science with the _understanding_ which constitutes the main difficulty
of the vindication of their validity, and renders necessary an answer
of a different kind to that which would have been possible, if the
validity of mathematical judgements had been in question.

"We have been able above, with little trouble, to make comprehensible
how the conceptions of space and time, although _a priori_ knowledge,
must necessarily relate to objects and render possible a synthetic
knowledge of them independently of all experience. For since an object
can appear to us, i. e. be an object of empirical perception, only by
means of such pure forms of sensibility, space and time are pure
perceptions, which contain _a priori_ the condition of the possibility
of objects as phenomena, and the synthesis in space and time has
objective validity."

"On the other hand, the categories of the understanding do not
represent the conditions under which objects are given in perception;
consequently, objects can certainly appear to us wi