Sujet : Re: Undecidability based on epistemological antinomies V2 --Mendelson--
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.logic comp.theoryDate : 21. Apr 2024, 19:05:22
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <v03h0i$1q6tg$1@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 4/21/24 10:34 AM, olcott wrote:
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))
Except incompleteness and undecidablity are attributes of different sorts of things.
Yes, they are related, as Incompleteness of a Theory K, is a statement that in K there exists a theory that is accepted as a valid statement in K (and thus, for well defined Theory K that statement has a truth value) but that statement is not provable or refutable in the Theory K, which in the later terminology says that statement is undecidable.
Note the different, The SYSTEM (K) is incomplete, but it is the STATEMENT that is undecidable.
Godel focues on the SYSTEM, and shows that he can construct the unprovable but true statement. He doesn't focus on the statement itself, as no one is particularlly interested in that particular statement, so it being unprovable, by itself, doesn't mean much, except that, by existing, he shows that the full system must be incomplete, and thus there may well exist MANY such statements that are true but unprovable. THAT is an important fact.
Note, this is different then the Halting Problem, where even if Turing Computation was shown to be "incomplete" in that there existed some mappings that were not computable, being able to compute the Halting Mapping would have extreme value, so the focus isn't on the "system" as a whole, but that one particular problem, the computing of the Halting Function given a description of the machine.
Thus, "Uncomputable" and "Incompleteness" while highly related and intertwined are NOT "the same".
Your confusing the two just shows your fundamental lack of understanding of what you are talking about.
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 |