Again, as Kant rightly sees, the vindication of the presuppositions of natural science, to be complete, requires the discovery upon a definite principle of _all_ these presuppositions. The clue to this discovery he finds in the view that, just as the perceptions of space and time originate 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."