IF-LOGIC IN THE MATHEMATICAL THEORIZING
Vitaliy Valentinovich Tselishchev1,2
1Novosibirsk National Research State University, 2, Pirogov st., Novosibirsk, 630090, Russia
2Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Science, 8, Nikolaev st., Novosibirsk, 630090, Russia
Keywords: IF-логика, логика первого порядка, равномерная непрерывность, квантор, теоретико-игровая семантика, IF-logic, first-order logic, uniform continuity, quantifier, game-theoretic semantics
Abstract
The article is deals with the comparison of expressive means of the standard first-order logic and IF-logic as the logic of mathematical discourse. The problem of the uniform continuity in Cauchy's theorem serves as an illustration of the analysis in both systems. It is shown that we can overcom limitations of the standard first-order logic in the IF-logic. Also, the fallacy of criticism of IF-logic as a vehicle for mathematical theorizing is shown.
|
