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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 it is evident that, by this idea of a supreme author of all, which I place as the foundation of all inquiries into nature, I do not mean to assert the existence of such a being, or that I have any knowledge of its existence; and, consequently, I do not really deduce anything from the existence of this being, but merely from its idea, that is to say, from the nature of things in this world, in accordance with this idea.

 The perplexity arising from this contradiction produces a propension to unite these broken appearances by the fiction of a continued existence, which is the third part of that hypothesis I proposed to explain. The schema of reality is existence in a determined time. If the veins are popping out of your neck and you feel like your doing the bench press, you NEED to cleanse your colon. For reason is thus confined within her own peculiar province--the arrangement of ends or aims, which is at the same time the arrangement of nature; and, as a practical faculty, without limiting itself to the latter, it is justified in extending the former, and with it our own existence, beyond the boundaries of experience and life. But this relation is far from being perfect; since some of the chances lie on the side of existence, and others on that of non-existence; which are objects altogether incompatible. The dynamical ideas, which we are about to discuss in this and the following section, possess the peculiarity of relating to an object, not considered as a quantity, but as an existence; and thus, in the discussion of the present question, we may make abstraction of the quantity of the series of conditions, and consider merely the dynamical relation of the condition to the conditioned. 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. 
Thus it appears upon the whole, that every kind of opinion or judgment, which amounts not to knowledge, is derived entirely from the force and vivacity of the perception, and that these qualities constitute in the mind, what we call the BELIEF Of the existence of any object.
 Philosophers are so far from rejecting the opinion of a continued existence upon rejecting that of the independence and continuance of our sensible perceptions, that though all sects agree in the latter sentiment, the former, which is, in a manner, its necessary consequence, has been peculiar to a few extravagant sceptics; who after all maintained that opinion in words only, and were never able to bring themselves sincerely to believe it.