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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 sensuous objects, this is attained by their connection according to empirical laws with some one of my perceptions; but there is no means of cognizing the existence of objects of pure thought, because it must be cognized completely a priorI. But all our knowledge of existence (be it immediately by perception, or by inferences connecting some object with a perception) belongs entirely to the sphere of experience--which is in perfect unity with itself; and although an existence out of this sphere cannot be absolutely declared to be impossible, it is a hypothesis the truth of which we have no means of ascertaining.

 But here the interruptions in the appearance of these perceptions are so long and frequent, that it is impossible to overlook them; and as the appearance of a perception in the mind and its existence seem at first sight entirely the same, it may be doubted, whether we can ever assent to so palpable a contradiction, and suppose a perception to exist without being present to the mind. 
Now in experience our perceptions come together contingently, so that no character of necessity in their connection appears, or can appear from the perceptions themselves, because apprehension is only a placing together of the manifold of empirical intuition, and no representation of a necessity in the connected existence of the phenomena which apprehension brings together, is to be discovered therein.
 They are nothing more than principles of the determination of the existence of phenomena in time, according to the three modi of this determination; to wit, the relation to time itself as a quantity (the quantity of existence, that is, duration), the relation in time as a series or succession, finally, the relation in time as the complex of all existence (simultaneity). I should have a reasonable hope of putting an end for ever to this sophistical mode of argumentation, by a strict definition of the conception of existence, did not my own experience teach me that the illusion arising from our confounding a logical with a real predicate (a predicate which aids in the determination of a thing) resists almost all the endeavours of explanation and illustration. In that case their imagination easily anticipates the satisfaction, and conveys the same joy, as if they were persuaded of its real and actual existence. Now, if these laws necessarily presuppose the existence of some being, as the condition of the possibility of their obligatory power, this being must be postulated, because the conditioned, from which we reason to this determinate condition, is itself cognized a priori as absolutely necessary. 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. I am interested in your partnership in business dealing Thus it appears, that the definitions of mathematics destroy the pretended demonstrations; and that if we have the idea of indivisible points, lines and surfaces conformable to the definition, their existence is certainly possible: but if we have no such idea, it is impossible we can ever conceive the termination of any figure; without which conception there can be no geometrical demonstration.