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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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And as I wish to prove the existence of simple substances, only in relation to, and as the elements of, the composite, I might term the antithesis of the second Antinomy, transcendental Atomistic.

 No one can once doubt but existence and non-existence destroy each other, and are perfectly incompatible and contrary. That is to say, if the state, b, differs from the state, a, only in respect to quantity, the change is a coming into existence of b - a, which in the former state did not exist, and in relation to which that state is = O. 

The separation, therefore, of the idea of a cause from that of a beginning of existence, is plainly possible for the imagination; and consequently the actual separation of these objects is so far possible, that it implies no contradiction nor absurdity; and is therefore incapable of being refuted by any reasoning from mere ideas; without which it is impossible to demonstrate the necessity of a cause.

 For although we posit a thing corresponding to the idea--a something, an actual existence--we do not on that account aim at the extension of our cognition by means of transcendent conceptions. Now as the understanding possesses no other fundamental conceptions besides the categories, it takes for granted that an object considered as a thing in itself must be capable of being thought by means of these pure conceptions, and is thereby led to hold the perfectly undetermined conception of an intelligible existence, a something out of the sphere of our sensibility, for a determinate conception of an existence which we can cognize in some way or other by means of the understanding. 
However harmless idealism may be considered--although in reality it is not so--in regard to the essential ends of metaphysics, it must still remain a scandal to philosophy and to the general human reason to be obliged to assume, as an article of mere belief, the existence of things external to ourselves (from which, yet, we derive the whole material of cognition for the internal sense), and not to be able to oppose a satisfactory proof to any one who may call it in question.
 Our present purpose is to avail ourselves of this series of states or conditions as a guide to an existence which may be the highest condition of all changeable phenomena, that is, to a necessary being.  It may not be amiss, before we leave this subject, to explain the ideas of existence and of external existence; which have their difficulties, as well as the ideas of space and time.