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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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But in order to ascertain to what given intuitions objects, external me, really correspond, in other words, what intuitions belong to the external sense and not to imagination, I must have recourse, in every particular case, to those rules according to which experience in general (even internal experience) is distinguished from imagination, and which are always based on the proposition that there really is an external experience.

 But empirical cognition is experience; consequently no a priori cognition is possible for us, except of objects of possible experience.* As you vary this experience, he varies his reasoning. For this purpose, we must avail ourselves of such principles as add something to the original conception--something not identical with, nor contained in it, and by means of synthetical judgements a priori, leave far behind us the limits of experience; for example, in the proposition, "the world must have a beginning," and such like. For such certainty cannot be found in an a posteriori proposition; and the conceptions a priori of space and time are, according to this opinion, mere creations of the imagination, having their source really in experience, inasmuch as, out of relations abstracted from experience, imagination has made up something which contains, indeed, general statements of these relations, yet of which no application can be made without the restrictions attached thereto by nature. 
  • We shall therefore follow up the pure conceptions even to their germs and beginnings in the human understanding, in which they lie, until they are developed on occasions presented by experience, and, freed by the same understanding from the empirical conditions attaching to them, are set forth in their unalloyed purity.
 While a warm imagination is allowed to enter into philosophy, and hypotheses embraced merely for being specious and agreeable, we can never have any steady principles, nor any sentiments, which will suit with common practice and experience. For by this new method we are enabled perfectly to explain the possibility of a priori cognition, and, what is more, to demonstrate satisfactorily the laws which lie a priori at the foundation of nature, as the sum of the objects of experience--neither of which was possible according to the procedure hitherto followed. But though this be confirmed by undoubted experience, we must understand it with its proper limitations, and must regard the double relation, as requisite only to make one passion produce another.