Open AccessConception of understanding in mathematical proof
Author(s) -
Vitaly V. Tselishchev,
Aleksandr V. Khlebalin
Publication year - 2021
Publication title -
omskij naučnyj vestnik. seriâ "obŝestvo. istoriâ. sovremennostʹ"
Language(s) - English
Resource type - Journals
eISSN - 2541-7983
pISSN - 2542-0488
DOI - 10.25206/2542-0488-2021-6-4-82-86
Subject(s) - mathematical proof , argument (complex analysis) , epistemology , interpretation (philosophy) , natural (archaeology) , calculus (dental) , structural proof theory , mathematical theory , computer science , mathematics , proof theory , philosophy , history , medicine , biochemistry , chemistry , geometry , physics , archaeology , dentistry , quantum mechanics , programming language
The article analyzes the role of the concept of understanding in mathematical proof. Understanding seems to be a natural and necessary characteristic of proof, interpreted as an argument in favor of the established result. It is shown that in general two traditions in the treatment of mathematical proofs can be distinguished, going back to Descartes and Leibniz. It arguments for conceptual treatment of category of understanding which is not connected with individual mental acts are resulted. The prospect of achieving conceptual understanding in the computational interpretation of mathematical proof is problematized.