AXIOMATIC METHOD IN CONTEMPORARY SCIENCE AND TECHNOLOGY: PRAGMATIC ASPECTS

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Transliteration of original Title: 
Aksiomaticheskiy metod v sovremennoy nauke i tekhnike: pragmaticheskie aspekty
Author(s): 
Serge Kovalyov
Institute of Control Sciences V. A. Trapeznikov, Russian Academy of Sciences
Andrei Rodin
Institute of Philosophy, Russian Academy of Sciences
Issue number: 
No. 1 (Vol. 47)
Pages: 
153-169
Abstract: 

In 1900 David Hilbert announced his famous list of then-opened mathematical problems; the problem number 6 in this list is axiomatization of physical theories. Since then a lot of systematic efforts have been invested into solving this problem. However the results of these efforts turned to be less successful than the early enthusiasts of axiomatic method expected. The existing axiomatizations of physical and biological theories provide a valuable logical analysis of these theories but they do not constitute anything like their standard presentation, which can be used for transmission, evaluation, and justification of physical and biological knowledge. This state of the art in the axiomatization of physics is strong evidence that the standard notion of axiomatic theory stemming from Hilbert and Tarski is not appropriate for the task. However in the recent years in mathematics there emerged a new axiomatic approach best represented by the Homotopy Type theory (HoTT). We argue that the constructive axiomatic architecture used in HoTT has better chances to be successfully applied in physics as well as in computer science and engineering.

Keywords: 
axiomatic method, axiomatization of physics, constructive axiomatic architecture, homotopy type theory
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