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

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)