Sujet : Re: Undecidability based on epistemological antinomies V2 --Mendelson--
De : polcott333 (at) *nospam* gmail.com (olcott)
Groupes : sci.logic comp.theoryDate : 23. Apr 2024, 16:54:09
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v08i2i$1m5hp$2@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12
User-Agent : Mozilla Thunderbird
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'.
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.
not-⊢K ℬ and not-⊢K ¬ℬ. (Mendelson: 2015:208)
K ⊬ ℬ and K ⊬ ¬ℬ. // switching notational conventions
Incomplete(F) ≡ ∃x ∈ L ((L ⊬ x) ∧ (L ⊬ ¬x))
So not the same.
When an expression cannot be proved or refuted is a formal system
this is exactly the same as an expression cannot be proved or refuted
in a formal system.
-- Copyright 2024 Olcott "Talent hits a target no one else can hit; Geniushits a target no one else can see." Arthur Schopenhauer
Date | Sujet | # | | Auteur |
18 Apr 24 | Undecidability based on epistemological antinomies V2 | 277 | | olcott |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 220 | | Richard Damon |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 219 | | olcott |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 218 | | Richard Damon |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 217 | | olcott |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 216 | | Richard Damon |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 27 | | olcott |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 5 | | Richard Damon |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 4 | | olcott |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 3 | | Richard Damon |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 2 | | olcott |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 1 | | Richard Damon |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 21 | | olcott |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Richard Damon |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 19 | | olcott |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Richard Damon |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Richard Damon |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 16 | | Mikko |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 4 | | olcott |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 3 | | Richard Damon |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 2 | | olcott |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Richard Damon |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 11 | | olcott |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 10 | | olcott |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Richard Damon |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 7 | | Ross Finlayson |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 6 | | olcott |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 5 | | Richard Damon |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 4 | | Ross Finlayson |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 3 | | olcott |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 2 | | Richard Damon |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Ross Finlayson |
27 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | olcott |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 2 | | olcott |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 1 | | Richard Damon |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 186 | | olcott |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 3 | | Richard Damon |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 2 | | olcott |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 1 | | Richard Damon |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 182 | | olcott |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 3 | | Richard Damon |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 2 | | olcott |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 1 | | Richard Damon |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 178 | | olcott |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 177 | | olcott |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 176 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 171 | | Richard Damon |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 170 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 10 | | Richard Damon |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 9 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 8 | | Richard Damon |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 7 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 6 | | Richard Damon |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 2 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 1 | | Richard Damon |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 2 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 1 | | Richard Damon |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 1 | | Ross Finlayson |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 159 | | olcott |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 1 | | Richard Damon |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 139 | | olcott |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 138 | | Richard Damon |
26 Apr 24 | D simulated by H never halts no matter what H does | 137 | | olcott |
26 Apr 24 | Re: D simulated by H never halts no matter what H does | 1 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 135 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 134 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 133 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 132 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 131 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 130 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 1 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does | 1 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 127 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 126 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 125 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 124 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 123 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 19 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 18 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 17 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 16 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 15 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 14 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 13 | | Richard Damon |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 12 | | olcott |
27 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 11 | | Richard Damon |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 10 | | olcott |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 9 | | Richard Damon |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 8 | | olcott |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 7 | | Richard Damon |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 6 | | olcott |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 5 | | Richard Damon |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 4 | | olcott |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 3 | | Richard Damon |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 2 | | olcott |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 1 | | Richard Damon |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 103 | | olcott |
28 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 1 | | Richard Damon |
29 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 101 | | olcott |
29 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 99 | | Mikko |
29 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 98 | | olcott |
30 Apr 24 | Re: D simulated by H never halts no matter what H does V3 | 1 | | Richard Damon |
28 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 18 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 4 | | olcott |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 54 | | olcott |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 2 | | olcott |