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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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Sometimes this distance has a greater influence than even contrary experiments would have; and a man may receive a more lively conviction from a probable reasoning, which is close and immediate, than from a long chain of consequences, though just and conclusive in each part.

 Now if we find that, when we regard things from this double point of view, the result is in harmony with the principle of pure reason, but that, when we regard them from a single point of view, reason is involved in self-contradiction, then the experiment will establish the correctness of this distinction.] Secondly, we may conclude from the same principle, that the sense of justice is not founded on reason, or on the discovery of certain connexions and relations of ideas, which are eternal, immutable, and universally obligatory. All the conceptions produced, and all the questions raised, by pure reason, do not lie in the sphere of experience, but in that of reason itself, and hence they must be solved, and shown to be either valid or inadmissible, by that faculty. Above them all, there is the ideal teacher, who employs them as instruments for the advancement of the essential aims of human reason. But it is this that reason seeks for and requires. Of all the a priori sciences of reason, therefore, mathematics alone can be learned.