Sujet : Re: Undecidability based on epistemological antinomies V2 --Mendelson--
De : polcott333 (at) *nospam* gmail.com (olcott)
Groupes : sci.logic comp.theoryDate : 21. Apr 2024, 16:34:44
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v03866$bitp$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10
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On 4/21/2024 2:50 AM, Mikko wrote:
On 2024-04-20 16:37:27 +0000, olcott said:
On 4/20/2024 2:41 AM, Mikko wrote:
On 2024-04-19 02:25:48 +0000, olcott said:
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On 4/18/2024 8:58 PM, Richard Damon wrote:
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Godel's proof you are quoting from had NOTHING to do with undecidability,
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*Mendelson (and everyone that knows these things) disagrees*
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https://sistemas.fciencias.unam.mx/~lokylog/images/Notas/la_aldea_de_la_logica/Libros_notas_varios/L_02_MENDELSON,%20E%20-%20Introduction%20to%20Mathematical%20Logic,%206th%20Ed%20-%20CRC%20Press%20(2015).pdf
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On questions whether Gödel said something or not the sumpreme authority
is not Mendelson but Gödel.
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When some authors affirm that undecidability and incompleteness
are the exact same thing then whenever Gödel uses the term
incompleteness then he is also referring to the term undecidability.
That does not follow. Besides, a reference to the term "undecidability"
is not a reference to the concept 'undecidability'.
In other words you deny the identity principle thus X=X is false.
An undecidable sentence of a theory K is a closed wf ℬ of K such that
neither ℬ nor ¬ℬ is a theorem of K, that is, such that not-⊢K ℬ and
not-⊢K ¬ℬ. (Mendelson: 2015:208)
Incomplete(F) ≡ ∃x ∈ L ((L ⊬ x) ∧ (L ⊬ ¬x))
-- Copyright 2024 Olcott "Talent hits a target no one else can hit; Geniushits a target no one else can see." Arthur Schopenhauer
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