Re: Undecidability based on epistemological antinomies V2 --Mendelson--

On 4/22/2024 3:26 AM, Mikko wrote:

On 2024-04-21 14:34:44 +0000, olcott said:
 

On 4/21/2024 2:50 AM, Mikko wrote:

On 2024-04-20 16:37:27 +0000, olcott said:
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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.

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That does not follow. Besides, a reference to the term "undecidability"
is not a reference to the concept 'undecidability'.
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In other words you deny the identity principle thus X=X is false.

 It is not a good idea to lie where the truth can be seen.
 

 >>>"undecidability" is not a reference to the concept 'undecidability'.
That is the best that I could make about the above quote. There is no
standard practice of using different kind of quotes that I am aware of.

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)

 So that is what "undecideble" means in Mendelson: 2015. Elsewhere it may
mean something else.
 

It never means anything else.

Incomplete(F) ≡ ∃x ∈ L ((L ⊬  x) ∧ (L ⊬ ¬x))

 So not the same.
 

Not provable or refutable in a formal system is exactly
the same as not provable of refutable in a formal system.
I think that you are playing head games.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer