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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 the principle of individuation is nothing but the INVARIABLENESS and UNINTERRUPTEDNESS of any object, thro a supposd variation of time, by which the mind can trace it in the different periods of its existence, without any break of the view, and without being obligd to form the idea of multiplicity or number.

 It is evident I can never account for this phenomenon, conformable to my experience in other instances, without spreading out in my mind the whole sea and continent between us, and supposing the effects and continued existence of posts and ferries, according to my Memory and observation. To make this evident, let us [Part II, SECT. 6.] remember, that as every idea is derived from a preceding perception, it is impossible our idea of a perception, and that of an object or external existence can ever represent what are specifically different from each other. But if we do not thus make them objective forms of all things, there is no other way left than to make them subjective forms of our mode of intuition--external and internal; which is called sensuous, because it is not primitive, that is, is not such as gives in itself the existence of the object of the intuition (a mode of intuition which, so far as we can judge, can belong only to the Creator), but is dependent on the existence of the object, is possible, therefore, only on condition that the representative faculty of the subject is affected by the object. Our perceptions are our only objects: Resembling perceptions are the same, however broken or uninterrupted in their appearance: This appealing interruption is contrary to the identity: The interruption consequently extends not beyond the appearance, and the perception or object really continues to exist, even when absent from us: Our sensible perception s have, therefore, a continued and uninterrupted existence. When therefore we see other creatures, in millions of instances, perform like actions, and direct them to the ends, all our principles of reason and probability carry us with an invincible force to believe the existence of a like cause. And, indeed, how should it be possible, merely by the aid of the unity of consciousness--which we cognize only for the reason that it is indispensable to the possibility of experience--to pass the bounds of experience (our existence in this life); and to extend our cognition to the nature of all thinking beings by means of the empirical--but in relation to every sort of intuition, perfectly undetermined--proposition, "I think"? Examine it in all lights, and see if you can find that matter of fact, or real existence, which you call vice. 
The simple but empirically determined consciousness of my own existence proves the existence of external objects in space.
 The simple but empirically determined consciousness of my own existence proves the existence of external objects in space.