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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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In the case of probability the contrary chances are so far related, that they determine concerning the existence or non-existence of the same object.

 But as I require for this purpose something that is permanent, such as is not given in internal intuition; the mode of my existence, whether as substance or as accident, cannot be determined by means of this simple self-consciousness. But this is impossible, for the internal empirical intuition is sensuous, and presents us with nothing but phenomenal data, which do not assist the object of pure consciousness in its attempt to cognize itself as a separate existence, but are useful only as contributions to experience. 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. But with what right can we do this if we make them forms of objects as things in themselves, and such, moreover, as would continue to exist as a priori conditions of the existence of things, even though the things themselves were annihilated? It does this by applying the order of time to phenomena, and their existence. 
It follows from this that you must accept the absolutely necessary as out of and beyond the world, inasmuch as it is useful only as a principle of the highest possible unity in experience, and you cannot discover any such necessary existence in the would, the second rule requiring you to regard all empirical causes of unity as themselves deduced.
 We are on this account incompetent to extend the sphere of our objects of thought beyond the conditions of our sensibility, and to assume the existence of objects of pure thought, that is, of noumena, inasmuch as these have no true positive signification. But, as there has thus been proved the existence of a faculty which can of itself originate a series in time--although we are unable to explain how it can exist--we feel ourselves authorized to admit, even in the midst of the natural course of events, a beginning, as regards causality, of different successions of phenomena, and at the same time to attribute to all substances a faculty of free action.