WikiJournal Preprints/The infinite and contradiction: a history of mathematical physics by dialectical approach

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Author: Ichiro Ueki[a][i]  

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  1. ↑ The History of Mathematics Society of Japan, University of Tokyo
  1. ↑ ueki1@snow.ocn.ne.jp

Abstract

The following hypothesis is proposed: “In mathematics, the contradiction involved in the development of human knowledge is included in the form of the infinite.” To prove this hypothesis, the author tries to find what sorts of the infinite in mathematics were used to represent the contradictions involved in some revolutions in mathematical physics, and concludes “the contradiction involved in mathematical description of motion was represented with the infinite within recursive (computable) set level by early Newtonian mechanics; and then the contradiction to describe discontinuous phenomena with continuous functions and contradictions about “ether” were represented with the infinite higher than the recursive set level, namely of arithmetical set level in second order arithmetic (ordinary mathematics), by mechanics of continuous bodies and field theory; and subsequently the contradiction appeared in macroscopic physics applied to microscopic phenomena were represented with the further higher infinite in third or higher order arithmetic (set-theoretic mathematics), by quantum mechanics”.


Preprint text held at http://philsci-archive.pitt.edu/id/eprint/18611

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