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

On 4/20/24 12:37 PM, olcott wrote:

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.

Nope. And the key is that they are NOT "the exact same thing" but are interrelated and one proves the other.

 It is common knowledge the undecidability derives incompleteness
or undecidability is incompleteness. I already posted a bunch of
links that show this.

Right, the theories intertwine and either can prove the other.
That doesn't make them "the same thing".

 On 4/18/2024 8:58 PM, Richard Damon wrote:
 > INCOMPLETENESS is EXACTLY about the inability to prove statements that
 > are true.
 Here is where Mendelson agrees with that:
 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.
 On 4/18/2024 8:58 PM, Richard Damon wrote:
 > INCOMPLETENESS is EXACTLY about the inability to prove statements that
 > are true.
 *Here is where Mendelson agrees with that*
 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)