Oyonale - Créations 3D et expériences graphiques
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Cliquer sur les phrases pour les voir dans leur contexte. Les textes de Immanuel Kant et David Hume sont disponibles auprès du Projet Gutenberg.
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It deals with mere conceptions--not, like mathematics, with conceptions applied to intuition--and in it, reason is the pupil of itself alone. The reason why I impute any defect to geometry, is, because its original and fundamental principles are derived merely from appearances; and it may perhaps be imagined, that this defect must always attend it, and keep it from ever reaching a greater exactness in the comparison of objects or ideas, than what our eye or imagination alone is able to attain. But, though all our knowledge begins with experience, it by no means follows that all arises out of experience. This not only happens, where they remark this resemblance betwixt themselves and others, but also by the natural course of the disposition, and by a certain sympathy, which always arises betwixt similar characters. On the contrary, whatever strikes in with the natural propensities, and either externally forwards their satisfaction, or internally concurs with their movements, is sure to give a sensible pleasure. I made fun of the whole thing, spouting my knowledge of the population and percentages involved. The school were so sensible of the force of this argument, that some of them maintained, that nature has mixed among those particles of matter, which are divisible in infinitum, a number of mathematical points, in order to give a termination to bodies; and others eluded the force of this reasoning by a heap of unintelligible cavils and distinctions. I first ask mathematicians, what they mean when they say one line or surface is EQUAL to, or GREATER or LESS than another? Let any of them give an answer, to whatever sect he belongs, and whether he maintains the composition of extension by indivisible points, or by quantities divisible in infinitum.