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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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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. Upon the solution of this problem, or upon sufficient proof of the impossibility of synthetical knowledge a priori, depends the existence or downfall of the science of metaphysics. If, again, I infer from the form of the universe, from the way in which all things are connected and act and react upon each other, the existence of a cause entirely distinct from the universe--this would again be a judgement of purely speculative reason; because the object in this case--the cause--can never be an object of possible experience. But as we do not attribute to continued existence to both these perceptions, and as they are both of the same nature, we clearly perceive, that all our perceptions are dependent on our organs, and the disposition of our nerves and animal spirits. But our proof shows that external experience is properly immediate,* that only by virtue of it--not, indeed, the consciousness of our own existence, but certainly the determination of our existence in time, that is, internal experience--is possible.