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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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From which continued perception, it ascribes a continued existence and identity to the object.

 But I ask; Is there any more difficulty in supposing the time and place to be fixed without a cause, than to suppose the existence to be determined in that manner? The first question that occurs on this subject is always, whether the object shall exist or not: The next, when and where it shall begin to exist. Hence we are entitled to apply the term substance to a phenomenon, only because we suppose its existence in all time, a notion which the word permanence does not fully express, as it seems rather to be referable to future time. But as a little reflection destroys this conclusion, that our perceptions have a continued existence, by shewing that they have a dependent one, it would naturally be expected, that we must altogether reject the opinion, that there is such a thing in nature as a continued existence, which is preserved even when it no longer appears to the senses. With this purpose, we reason from an actual existence--an experience in general, to an absolutely necessary condition of that existence. But when we compare experiments, and reason a little upon them, we quickly perceive, that the doctrine of the independent existence of our sensible perceptions is contrary to the plainest experience. A business, which is your ticket to freedom from others telling you what to do. Philosophers have always talked of an absolutely necessary being, and have nevertheless declined to take the trouble of conceiving whether--and how--a being of this nature is even cogitable, not to mention that its existence is actually demonstrable. This consciousness of my existence in time is, therefore, identical with the consciousness of a relation to something external to me, and it is, therefore, experience, not fiction, sense, not imagination, which inseparably connects the external with my internal sense. 

But since the moral precept is, at the same time, my maxim (as reason requires that it should be), I am irresistibly constrained to believe in the existence of God and in a future life; and I am sure that nothing can make me waver in this belief, since I should thereby overthrow my moral maxims, the renunciation of which would render me hateful in my own eyes.