TWO FALSE DOGMAS RELATED WITH GODEL'S SECOND INCOMPLETENESS THEOREM. II
A. V. Bessonov1,2
1Novosibirsk State University, ul. Pirogova, 2, Novosibirsk, 630090 Russia
2Institute of Philosophy and Low SB RAS, ul. Nikolaeva, 8, Novosibirsk, 630090 Russia
Keywords: программа Гильберта, вторая теорема Гёделя о неполноте, формализация доказуемости, неадекватность предиката доказуемости, предикат недоказуемости, Hilbert’s program, GГ¶del's second incompleteness theorem, formalization of provability, inadequacy of a provability predicate, unprovability predicate
Abstract
We look at argumentation against realizability of Hilbert's program based on Gödel's second incompleteness theorem. It is proved that such argumentation is incorrect from the outset, since it necessarily leads to absurd conclusions. This implies that the second theorem can not be thought of as a decisive argument against feasibility of Hilbert’s finitistic program.
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