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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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Thus though we clearly perceive the dependence and interruption of our perceptions, we stop short in our career, and never upon that account reject the notion of an independent and continued existence.

 The supporters of this theory find no difficulty in admitting the reality of the phenomena of the internal sense in time; nay, they go the length of maintaining that this internal experience is of itself a sufficient proof of the real existence of its object as a thing in itself. If we do not set out from experience, or do not proceed according to the laws of the empirical connection of phenomena, our pretensions to discover the existence of a thing which we do not immediately perceive are vain. Objects have no discoverable connexion together; nor is it from any other principle but custom operating upon the imagination, that we can draw any inference from the appearance of one to the existence of another. But as experience is a cognition of objects by means of perceptions, it follows that the relation of the existence of the existence of the manifold must be represented in experience not as it is put together in time, but as it is objectively in time. 
Now, as I do not possess another intuition of self which gives the determining in me (of the spontaneity of which I am conscious), prior to the act of determination, in the same manner as time gives the determinable, it is clear that I am unable to determine my own existence as that of a spontaneous being, but I am only able to represent to myself the spontaneity of my thought, that is, of my determination, and my existence remains ever determinable in a purely sensuous manner, that is to say, like the existence of a phenomenon.
 Detection and Explanation of the Dialectical Illusion in all Transcendental Arguments for the Existence of a Necessary Being. I should have a reasonable hope of putting an end for ever to this sophistical mode of argumentation, by a strict definition of the conception of existence, did not my own experience teach me that the illusion arising from our confounding a logical with a real predicate (a predicate which aids in the determination of a thing) resists almost all the endeavours of explanation and illustration.