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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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Neither can we assert that reason has previously inferred this unity from the contingent nature of phenomena.

 That is to say, a proof in the sphere of transcendental cognition does not show that the given conception (that of an event, for example) leads directly to another conception (that of a cause)--for this would be a saltus which nothing can justify; but it shows that experience itself, and consequently the object of experience, is impossible without the connection indicated by these conceptions. Men are not able radically to cure, either in themselves or others, that narrowness of soul, which makes them prefer the present to the remote. 
After long labour he may be able to guard against the error, but he can never be thoroughly rid of the illusion which continually mocks and misleads him.
 But we cannot stop at these doubts, much less regard the conviction of our ignorance, not only as a cure for the conceit natural to dogmatism, but as the settlement of the disputes in which reason is involved with itself. And not only so, but the causes of the firm conception exhaust the whole subject, and nothing is left to produce any other effect. On the same principle is founded that common custom of making wives bear the name of their husbands, rather than husbands that of their wives; as also the ceremony of giving the precedency to those, whom we honour and respect. The discussion of this argument we postpone for the present. 
When we gradually follow an object in its successive changes, the smooth progress of the thought makes us ascribe an identity to the succession; because it is by a similar act of the mind we consider an unchangeable object.
 The former--discursive proofs--ought to be termed acroamatic proofs, rather than demonstrations, as only words are employed in them, while demonstrations proper, as the term itself indicates, always require a reference to the intuition of the object.