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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --Mendelson--
Date: Thu, 25 Apr 2024 11:26:07 +0300
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On 2024-04-24 16:01:46 +0000, olcott said:

> On 4/24/2024 4:49 AM, Mikko wrote:
>> On 2024-04-23 14:54:09 +0000, olcott said:
>> 
>>> 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:
>>>>>> 
>>>>>>> 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.
>>>> 
>>>> It is not a good idea to lie where the truth can be seen.
>>>> 
>>> 
>>> It is not a good idea to say gibberish nonsense and
>>> expect it to be understood.
>>>  >>> a reference to the term "undecidability"
>>>  >>> is not a reference to the concept 'undecidability'.
>> 
>> That is how a sentence must be quoted. The proof that the quoted
>> sentence can be understood is that Richard Damon undesstood it.
>> 
>>>>> 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 usually means one cannot make up one's mind.
>>> In math it means an epistemological antinomy expression
>>> is not a proposition thus a type mismatch error for every
>>> bivalent system of logic.
>> 
>> No, it doesn't. There is no reference to an epistemological
>> anitnomy in "undecidable".
>> 
> 
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)

That is not a part of the definition of "undecidable".

-- 
Mikko