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Extract from THE CRITIQUE OF PURE REASON

In both, the mode of proof is quite in accordance with the common procedure of human reason, which often falls into discord with itself, from considering an object from two different points of view.
Herr von Mairan regarded the controversy between two celebrated astronomers, which arose from a similar difficulty as to the choice of a proper standpoint, as a phenomenon of sufficient importance to warrant a separate treatise on the subject.
The one concluded; the moon revolves on its own axis, because it constantly presents the same side to the earth; the other declared that the moon does not revolve on its own axis, for the same reason.
Both conclusions were perfectly correct, according to the point of view from which the motions of the moon were considered.
SECTION III. Of the Interest of Reason in these Self-contradictions.
We have thus completely before us the dialectical procedure of the cosmological ideas.
No possible experience can present us with an object adequate to them in extent.
Nay, more, reason itself cannot cogitate them as according with the general laws of experience.
And yet they are not arbitrary fictions of thought.
On the contrary, reason, in its uninterrupted progress in the empirical synthesis, is necessarily conducted to them, when it endeavours to free from all conditions and to comprehend in its unconditioned totality that which can only be determined conditionally in accordance with the laws of experience.
These dialectical propositions are so many attempts to solve four natural and unavoidable problems of reason.
There are neither more, nor can there be less, than this number, because there are no other series of synthetical hypotheses, limiting a priori the empirical synthesis.
The brilliant claims of reason striving to extend its dominion beyond the limits of experience, have been represented above only in dry formulae, which contain merely the grounds of its pretensions.
They have, besides, in conformity with the character of a transcendental philosophy, been freed from every empirical element; although the full splendour of the promises they hold out, and the anticipations they excite, manifests itself only when in connection with empirical cognitions.
In the application of them, however, and in the advancing enlargement of the employment of reason, while struggling to rise from the region of experience and to soar to those sublime ideas, philosophy discovers a value and a dignity, which, if it could but make good its assertions, would raise it far above all other departments of human knowledge--professing, as it does, to present a sure foundation for our highest hopes and the ultimate aims of all the exertions of reason.
The questions; whether the world has a beginning and a limit to its extension in space; whether there exists anywhere, or perhaps, in my own thinking Self, an indivisible and indestructible unity--or whether nothing but what is divisible and transitory exists; whether I am a free agent, or, like other beings, am bound in the chains of nature and fate; whether, finally, there is a supreme cause of the world, or all our thought and speculation must end with nature and the order of external things--are questions for the solution of which the mathematician would willingly exchange his whole science; for in it there is no satisfaction for the highest aspirations and most ardent desires of humanity.
Nay, it may even be said that the true value of mathematics- that pride of human reason--consists in this; that she guides reason to the knowledge of nature--in her greater as well as in her less manifestations--in her beautiful order and regularity--guides her, moreover, to an insight into the wonderful unity of the moving forces in the operations of nature, far beyond the expectations of a philosophy building only on experience; and that she thus encourages philosophy to extend the province of reason beyond all experience, and at the same time provides it with the most excellent materials for supporting its investigations, in so far as their nature admits, by adequate and accordant intuitions.
Unfortunately for speculation--but perhaps fortunately for the practical interests of humanity--reason, in the midst of her highest anticipations, finds herself hemmed in by a press of opposite and contradictory conclusions, from which neither her honour nor her safety will permit her to draw back.
Nor can she regard these conflicting trains of reasoning with indifference as mere passages at arms, still less can she command peace; for in the subject of the conflict she has a deep interest.
There is no other course left open to her than to reflect with herself upon the origin of this disunion in reason--whether it may not arise from a mere misunderstanding.
After such an inquiry, arrogant claims would have to be given up on both sides; but the sovereignty of reason over understanding and sense would be based upon a sure foundation.