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Click on the phrases to see them in context. The original texts by Immanuel Kant and David Hume are available from the Gutenberg Projet.

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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.

 Nay, more, reason itself cannot cogitate them as according with the general laws of experience. 
The desired proof must therefore demonstrate that we have experience of external things, and not mere fancies.
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