Open AccessRules, understanding and language games in mathematics
Author(s) -
Vitaly V. Tselishchev
Publication year - 2021
Publication title -
filosofskie problemy informacionnyh tehnologij i kiberprostranstva
Language(s) - English
Resource type - Journals
ISSN - 2305-3763
DOI - 10.17726/philit.2021.1.2
Subject(s) - ambiguity , conventionalism , referent , meaning (existential) , context (archaeology) , language game , epistemology , representation (politics) , ordinary language philosophy , mathematical practice , philosophy of mathematics , mathematics , linguistics , philosophy , politics , paleontology , philosophy of sport , political science , law , biology
The article is devoted to the applicability of Wittgenstein’s following the rule in the context of his philosophy of mathematics to real mathematical practice. It is noted that in «Philosophical Investigations» and «Remarks on the Foundations of Mathematics» Wittgenstein resorted to the analysis of rather elementary mathematical concepts, accompanied also by the inherent ambiguity and ambiguity of his presentation. In particular, against this background, his radical conventionalism, the substitution of logical necessity with the «form of life» of the community, as well as the inadequacy of the representation of arithmetic rules by a language game are criticized. It is shown that the reconstruction of the Wittgenstein concept of understanding based on the Fregian division of meaning and referent goes beyond the conceptual framework of Wittgenstein language games.