Quote: a physical continuum is not transitive (e.g., A=B, B=C, A<C); its contradictions lead to the mathematical continuum

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continuum in mathematics


It has, for instance, been observed [by Fechner] that a weight A of 10 grammes and a weight B of 11 grammes produced identical sensations, that the weight B could no longer be distinguished from a weight C of 12 grammes, but that the weight A was readily distinguished for the weight C. Thus the rough results of the experiments may be expressed by the following relations: A=B, B=C, A<C, which may be regarded as the formula of the physical continuum. But here is an intolerable disagreement with the law of contradiction, ... [which] has compelled us to invent the mathematical continuum.   Google-1   Google-2

Published before 1923

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Topic: continuum in mathematics (7 items)

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