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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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The science of mathematics presents the most brilliant example of the extension of the sphere of pure reason without the aid of experience. Such principles mathematical science possesses, but their application to experience, consequently their objective validity, nay the possibility of such a priori synthetical cognitions (the deduction thereof) rests entirely upon the pure understanding. What we have found once to follow from any object, we conclude will for ever follow from it; and if this maxim be not always built upon as certain, it is not for want of a sufficient number of experiments, but because we frequently meet with instances to the contrary; which leads us to the second species of probability, where there is a contrariety in our experience and observation. Of these it is impossible to present an intelligible conception; they are a kind of monogram, drawn according to no determinate rule, and forming rather a vague picture--the production of many diverse experiences--than a determinate image. APHRODISIAQUE for man and women This attempt succeeds as well as we could desire, and promises to metaphysics, in its first part--that is, where it is occupied with conceptions a priori, of which the corresponding objects may be given in experience--the certain course of science.