Once Again on Misinterpretations of Gödel’s Second Incompleteness Theorem
نویسندگان
چکیده
منابع مشابه
On Gödel’s Second Incompleteness Theorem
Gödel’s Second Incompleteness Theorem states that no sufficiently strong consistent mathematical theory can prove its own consistency. In [1] this is proved for every axiomatic theory extending the Peano Arithmetic. For axiomatic set theory a simpler proof was given in [2] using the fact that in set theory, consistency of a set of axioms is equivalent to the existence of a model. In this note w...
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In several recent articles, we have shown how such totality conditions are related to both generalizations and boundary-case exceptions for the Second Incompleteness Theorem. For instance, our article [2] showed how essentially all axiom systems recognizing addition and multiplication as “total” functions are unable to prove a theorem affirming their semantic tableaux consistency. In contrast, ...
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First of all, when I say "proved", what I will mean is "proved with the aid of the whole of math". Now then: two plus two is four, as you well know. And, of course, it can be proved that two plus two is four (proved, that is, with the aid of the whole of math, as I said, though in the case of two plus two, of course we do not need the whole of math to prove that it is four). And, as may not be ...
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ژورنال
عنوان ژورنال: Siberian Journal of Philosophy
سال: 2021
ISSN: 2541-7517
DOI: 10.25205/2541-7517-2020-18-3-132-143