Hence the pure conceptions of the understanding have no meaning whatever, when they quit the objects of experience and refer to things in themselves (noumena). They serve, as it were, to spell out phenomena, that these may be able to be read as experience. The axioms arising from their relation to the world of sense, only serve our understanding for use in experience. Beyond this, are only arbitrary combinations, destitute of objective reality, and the possibility of which can neither be known apriori, nor their reference to objects be confirmed, or even made intelligible by an example, because all examples are borrowed from some possible experience, and consequently the objects of those conceptions are nothing but what may be met with in a possible experience.
This complete solution of Hume’s problem, although it turns out to be contrary to the opinion of its originator, preserves for the pure conceptions of the understanding their origin apriori, and for the universal laws of Nature their validity as laws of the understanding, but in such a manner that their use is limited to experience, because their possi- bility has its basis, solely, in the reference of the understanding to experience; not because they are derived from expe- rience, but because experience is derived from them, which completely reversed mode of connection never occurred to Hume.
The following result of all previous researches follows from the above investigations: “All synthetic axioms aprioriare nothing more than principles of possible experience,” and can never be referred to things in themselves, but only to phenomena as objects of experience. Hence pure mathematics no less than pure natural science can never refer to any- thing more than mere phenomena, and only present that which either makes experience in general possible, or which, inasmuch as it is derived from these principles, must always be able to be presented in some possible experience.
- What constraint does Kant put on the application of the categories?
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