Ueki, Ichiro (2021) The infinite and contradiction: A history of mathematical physics by dialectical approach. [Preprint]

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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 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 the contradiction 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 theory of field; and subsequently the contradictions 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."
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Item Type:  Preprint  

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Keywords:  the infinite, contradiction, mathematical physics, dialectical approach, reverse mathematics  
Subjects:  General Issues > History of Science Case Studies Specific Sciences > Mathematics Specific Sciences > Physics 

Depositing User:  Mr. Ichiro Ueki  
Date Deposited:  18 Jan 2021 16:12  
Last Modified:  18 Jan 2021 16:12  
Item ID:  18611  
DOI or Unique Handle:  ueki  
Subjects:  General Issues > History of Science Case Studies Specific Sciences > Mathematics Specific Sciences > Physics 

Date:  18 January 2021  
URI:  https://philsciarchive.pitt.edu/id/eprint/18611 
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