CONCEPTUAL AND FORMAL RIGOR OF MATHEATICAL PROOF
Vitaliy Valentinovich Tselishchev, Aleksandr Valerievich Khlebalin
Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Sciences, 8 Nikolaeva str., Novosibirsk, 630090, Russia
Keywords: languages of formalization, content of mathematical proof, rigor and clarity of proof
Abstract
The article discusses the relationship between clarity and rigor as characteristics of a mathematical argument and the achievement of proof by means of formalization. It is shown that the project of providing the connection between these characteristics, which is proclaimed by D. Hilbert, by means of formalization turns out to be unfeasible at the current stage because of the lack of formalization tools that preserve the content of mathematical reasoning. The requirements for the formalization tools which are necessary to implement Hilbert’s strategy are set out. In addition, a strategy is proposed for studying the dynamic relationship between formalization and the content of a mathematical theory, as well as their contribution to understanding the mathematical proof, which enables to overcome the apparent gap between meaningful and formalized mathematical theories with regard to the characteristics of clarity and rigor.
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