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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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If they are principles of the understanding, it is vain to expect that we should attain by their means to ideas of pure reason; for these principles are valid only in regard to objects of possible experience.

 Thus, then, appears the vanity of the hope of establishing a cognition which is to extend its rule beyond the limits of experience--a cognition which is one of the highest interests of humanity; and thus is proved the futility of the attempt of speculative philosophy in this region of thought. This is sufficiently evident from experience. For the substitution of the logical possibility of the conception--the condition of which is that it be not self-contradictory, for the transcendental possibility of things--the condition of which is that there be an object corresponding to the conception, is a trick which can only deceive the inexperienced.* Plato perceived very clearly that our faculty of cognition has the feeling of a much higher vocation than that of merely spelling out phenomena according to synthetical unity, for the purpose of being able to read them as experience, and that our reason naturally raises itself to cognitions far too elevated to admit of the possibility of an object given by experience corresponding to them- cognitions which are nevertheless real, and are not mere phantoms of the brain. Moreover, the poverty of the usual arguments which go to prove the existence of a vast sphere of possibility, of which all that is real (every object of experience) is but a small part, is very remarkable. For I can say only of a thing in itself that it exists without relation to the senses and experience. It follows that I am not entitled to make any assertion at all respecting the whole object of experience--the world of sense; I must limit my declarations to the rule according to which experience or empirical knowledge is to be attained. 
In other words, reason does not assure us of the objective validity of the conception; it merely gives us the idea of something, on which the supreme and necessary unity of all experience is based.
 In our experiences it is easy to observe that it is only the continuous influences in all parts of space that can conduct our senses from one object to another; that the light which plays between our eyes and the heavenly bodies produces a mediating community between them and us, and thereby evidences their coexistence with us; that we cannot empirically change our position (perceive this change), unless the existence of matter throughout the whole of space rendered possible the perception of the positions we occupy; and that this perception can prove the contemporaneous existence of these places only through their reciprocal influence, and thereby also the coexistence of even the most remote objects--although in this case the proof is only mediate.