Two false dogmas related with Godel's second incompleteness theorem. I
A. V. Bessonov1,2
1Institute of philosophy and law SB RAS, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
Keywords: Godel's incompleteness theorems, inadequacy of a provability predicate, unprovability predicate
Abstract
It is shown that Godel's proof of the second incompleteness theorem for formal arithmetic depends on a chosen provability predicate. We use an unprovability predicate to construct counterexamples to the second theorem and prove that in the generall case the conclusion of the second theorem is not true.
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