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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Undecidability based on epistemological antinomies V2
 --Mendelson--
Date: Sun, 21 Apr 2024 09:34:44 -0500
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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:
>>>
>>>> On 4/18/2024 8:58 PM, Richard Damon wrote:
>>>
>>>>> Godel's proof you are quoting from had NOTHING to do with 
>>>>> undecidability,
>>>>
>>>> *Mendelson (and everyone that knows these things) disagrees*
>>>>
>>>> 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
>>>
>>> On questions whether Gödel said something or not the sumpreme authority
>>> is not Mendelson but Gödel.
>>>
>>
>> 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; Genius
hits a target no one else can see." Arthur Schopenhauer