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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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Mathematical science affords us a brilliant example, how far, independently of all experience, we may carry our a priori knowledge.

 The idea of systematic unity is available as a regulative principle in the connection of phenomena according to general natural laws; and, how far soever we have to travel upon the path of experience to discover some fact or event, this idea requires us to believe that we have approached all the more nearly to the completion of its use in the sphere of nature, although that completion can never be attained. The idea of transcendental freedom, on the contrary, requires that reason--in relation to its causal power of commencing a series of phenomena--should be independent of all sensuous determining causes; and thus it seems to be in opposition to the law of nature and to all possible experience. For as the philosophical system is found by experience to take hold of many minds, and in particular of all those, who reflect ever so little on this subject, it must derive all its authority from the vulgar system; since it has no original authority of its own. For supposing that in all past experience we have found two objects to have been always conjoined together, it is evident, that upon the appearance of one of these objects in an impression, we must from custom make an easy transition to the idea of that object, which usually attends it; and by means of the present impression and easy transition must conceive that idea in a stronger and more lively manner, than we do any loose floating image of the fancy. However natural that conversion may seem, we cannot be sure it is practicable, before we have had experience of it. For it has then left the ground of experience, in which alone are to be found the criteria of truth, and has ventured into the region of the incomprehensible and unsearchable, on the heights of which it loses its power and collectedness, because it has completely severed its connection with experience. But it is plain that this continuity of forms is a mere idea, to which no adequate object can be discovered in experience. After men have found by experience, that their selfishness and confined generosity, acting at their liberty, totally incapacitate them for society; and at the same time have observed, that society is necessary to the satisfaction of those very passions, they are naturally induced to lay themselves under the restraint of such rules, as may render their commerce more safe and commodious. 
  • But as this latter conclusion is contrary to evident experience, and as it is possible we may have a like experience in the operations of the mind, and may perceive a constant conjunction of thought and motion; you reason too hastily, when from the mere consideration of the ideas, you conclude that it is impossible motion can ever produce thought, or a different position of parts give rise to a different passion or reflection.