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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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It is an established maxim in metaphysics, That whatever the mind clearly conceives, includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible.

 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. For we find neither in transcendental nor in natural theology, however far reason may lead us in these, any ground to warrant us in assuming the existence of one only Being, which stands at the head of all natural causes, and on which these are entirely dependent. But, let it be granted that we could discover, not in experience, but in certain firmly-established a priori laws of the use of pure reason-- laws relating to our existence, authority to consider ourselves as legislating a priori in relation to our own existence and as determining this existence; we should, on this supposition, find ourselves possessed of a spontaneity, by which our actual existence would be determinable, without the aid of the conditions of empirical intuition. 

We must now shew, that as the union betwixt motives and actions has the same constancy, as that in any natural operations, so its influence on the understanding is also the same, in determining us to infer the existence of one from that of another.

 But the science of mathematics has nothing to do with such questions, nor with the question of existence in any fashion; it is concerned merely with the properties of objects in themselves, only in so far as these are connected with the conception of the objects.