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Refuting Gödel's 1931 Incompleteness Theorem in one sentence
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peteolcott
May 16, 2019, 11:01:56 AM5/16/19
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If the notion of true is defined as provable from axioms and axioms
are defined to be finite strings having the semantic property of
Boolean true then any expression of language that is not provable
is not true.
English: C is not Provable entails that C is not a Theorem:
∀C (¬∃Γ(Γ ⊢ C) → (⊬C))
[Within the above definition of True]
English: C is not a Theorem entails that C is not True:
∀C (⊬C) → ¬True(C)
https://plato.stanford.edu/entries/goedel-incompleteness/
The first incompleteness theorem states that in any consistent
formal system F within which a certain amount of arithmetic
can be carried out, there are statements of the language of F
which can neither be proved nor disproved in F.
(Raatikainen, Panu: Fall 2018)
--
Copyright 2019 Pete Olcott
All rights reserved
--
Copyright 2019 Pete Olcott
All rights reserved
are defined to be finite strings having the semantic property of
Boolean true then any expression of language that is not provable
is not true.
English: C is not Provable entails that C is not a Theorem:
∀C (¬∃Γ(Γ ⊢ C) → (⊬C))
[Within the above definition of True]
English: C is not a Theorem entails that C is not True:
∀C (⊬C) → ¬True(C)
https://plato.stanford.edu/entries/goedel-incompleteness/
The first incompleteness theorem states that in any consistent
formal system F within which a certain amount of arithmetic
can be carried out, there are statements of the language of F
which can neither be proved nor disproved in F.
(Raatikainen, Panu: Fall 2018)
--
Copyright 2019 Pete Olcott
All rights reserved
--
Copyright 2019 Pete Olcott
All rights reserved
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