FORMAL TOOLS IN MATHEMATICS AND THE CONCEPT OF UNDERSTANDING
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: формализованный язык, естественный язык, понимание, семантика, передоказательства теорем, formalized language, natural language, understanding, semantics, reproving of theorems
Abstract
The article considers a popular trend in the philosophy of mathematics, according to which the semantic and cognitive features of mathematical knowledge can be adequately explained by analyzing mathematical practice, particularly natural language, within which mathematical thinking initially occurs. On the example of the analysis of T. Hofweber’s concept, which contrasts the semantic and syntactic characteristics of natural languages and formalized ones and claims an exclusively representative role to the latter, we show that this approach is limited by the elementary sections of arithmetic, as well as that underestimation of the role of formalized language in the development of mathematical knowledge is groundless.
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