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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 synthesis or conjunction of the manifold in these conceptions relates, we have said, only to the unity of apperception, and is for this reason the ground of the possibility of a priori cognition, in so far as this cognition is dependent on the understanding.

 I shall here take occasion to propose a second observation concerning our demonstrative reasonings, which is suggested by the same subject of the mathematics. This sceptical doubt, both with respect to reason and the senses, is a malady, which can never be radically cured, but must return upon us every moment, however we may chace it away, and sometimes may seem entirely free from it. It is a melancholy reflection that reason, in its highest exercise, falls into an antithetic; and that the supreme tribunal for the settlement of differences should not be at union with itself. For it is perfectly permissible to employ, in the presence of reason, the language of a firmly rooted faith, even after we have been obliged to renounce all pretensions to knowledge. 
The true reason why indirect proofs are employed in different sciences is this.