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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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For in this case we are compelled to seek for some other existence upon which the former depends.

 Taking then penetration in this sense, for the annihilation of one body upon its approach to another, I ask any one, if he sees a necessity, that a coloured or tangible point should be annihilated upon the approach of another coloured or tangible point? On the contrary, does he not evidently perceive, that from the union of these points there results an object, which is compounded and divisible, and may be distinguished into two parts, of which each preserves its existence distinct and separate, notwithstanding its contiguity to the other? Let him aid his fancy by conceiving these points to be of different colours, the better to prevent their coalition and confusion. Hence I am compelled to say; "The aggregate of parts in a given phenomenon is in itself neither finite nor infinite; and these parts are given only in the regressive synthesis of decomposition--a synthesis which is never given in absolute completeness, either as finite, or as infinite." The same is the case with the series of subordinated causes, or of the conditioned up to the unconditioned and necessary existence, which can never be regarded as in itself, ind in its totality, either as finite or as infinite; because, as a series of subordinate representations, it subsists only in the dynamical regress and cannot be regarded as existing previously to this regress, or as a self-subsistent series of things. According to these, beyond one state or epoch of the world there is always to be found one more ancient; in every part always other parts themselves divisible; preceding every event another, the origin of which must itself be sought still higher; and everything in existence is conditioned, and still not dependent on an unconditioned and primal existence. The three modi of time are permanence, succession, and coexistence. 
Our Critique would be an investigation utterly superfluous, if there existed a possibility of proving a priori, that all thinking beings are in themselves simple substances, as such, therefore, possess the inseparable attribute of personality, and are conscious of their existence apart from and unconnected with matter.
 But if we proceed analytically--the "I think" as a proposition containing in itself an existence as given, consequently modality being the principle--and dissect this proposition, in order to ascertain its content, and discover whether and how this Ego determines its existence in time and space without the aid of anything external; the propositions of rationalistic psychology would not begin with the conception of a thinking being, but with a reality, and the properties of a thinking being in general would be deduced from the mode in which this reality is cogitated, after everything empirical had been abstracted; as is shown in the following table: But this experience merely aids reason in making one step--to the existence of a necessary being.