Sujet : Re: Undecidability based on epistemological antinomies V2 --H(D,D)--
De : polcott333 (at) *nospam* gmail.com (olcott)
Groupes : sci.logicDate : 26. Apr 2024, 18:21:21
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v0gka2$3pm6f$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
User-Agent : Mozilla Thunderbird
On 4/26/2024 4:16 AM, Mikko wrote:
On 2024-04-25 14:08:49 +0000, olcott said:
On 4/25/2024 3:11 AM, Mikko wrote:
However, whether there are any impossible inputs depends
on the meaning of the word "impossible". If "impossible input" means an
imput that cannot be an input then of course every input is possible.
>
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to be
impossible to construct an algorithm that always leads to a correct yes-
or-no answer. https://en.wikipedia.org/wiki/Undecidable_problem
In logic "undecidable" is more often used in the expressions like
"undecidable proposition" where it means that neither the proposition
nor its negation is provable. In the expression "undecidable problem"
the meaning of "undecidable" is different. In order to avoid confusion
it is better to use the expression "unsolvable problem".
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)
AKA Undecidable(K, ℬ) ≡ ∃ℬ ∈ K ((K ⊬ ℬ) ∧ (K ⊬ ¬ℬ))
impossible to construct an algorithm that always leads to a correct yes
or-no answer is isomorphic to cannot be proved or refuted from axioms.
True(L, x) ≡ ∃x ∈ L (L ⊢ x)
False(L, x) ≡ ∃x ∈ L (L ⊢ ¬x)
Truth_Bearer(L, x) ≡ ∃x ∈ L (True(L, x) ∨ False(L, ¬x))
Because Quine convinced most people that there is no such thing as
{true on the basis of meaning} most people simply disbelieve that
expressions of language can be proved true on the basis of axioms
that formalize the meanings of these expressions.
That is like saying we cannot know that 2 + 3 = 5 because people
simply do not "believe in" numbers or arithmetic.
Inputs not having an algorithm leading to a correct YES/NO
answer are called impossible inputs.
"Inputs not having an algorithm" does not make sense. If there is an
algorithm for a problem it is for all inputs.
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof... (Gödel 1931:43-44)
epistemological antinomies (AKA Self-contradictory expressions) cannot
be proved or refuted by formal systems or algorithms because they are
neither true nor false.
When a decision problem does not reject self-contradictory expressions
then they seem to prove that this problem is undecidable.
-- 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 | 323 | | olcott |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 262 | | Richard Damon |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 261 | | olcott |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 260 | | Richard Damon |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 259 | | olcott |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 258 | | Richard Damon |
19 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 56 | | 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 | 50 | | Mikko |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 49 | | 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-- | 47 | | Mikko |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 46 | | 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-- | 43 | | Mikko |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 10 | | olcott |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 5 | | 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 | | Mikko |
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 | | Mikko |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 4 | | Richard Damon |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 3 | | olcott |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Richard Damon |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Mikko |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 32 | | olcott |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 31 | | Mikko |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 30 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 29 | | Mikko |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 28 | | olcott |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 27 | | Mikko |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 26 | | 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-- | 17 | | Mikko |
27 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 16 | | olcott |
28 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 15 | | Mikko |
28 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 14 | | olcott |
29 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 13 | | Mikko |
29 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 12 | | olcott |
29 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 11 | | Mikko |
29 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 10 | | olcott |
30 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 9 | | Mikko |
30 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 8 | | olcott |
1 May 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 7 | | Mikko |
1 May 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 6 | | olcott |
2 May 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 5 | | Mikko |
2 May 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 4 | | olcott |
3 May 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 3 | | Mikko |
3 May 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 2 | | olcott |
4 May 24 | Re: Undecidability based on epistemological antinomies V2 --Mendelson-- | 1 | | Mikko |
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-- | 199 | | 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-- | 195 | | Mikko |
20 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 194 | | 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-- | 190 | | Mikko |
21 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 189 | | olcott |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 188 | | Mikko |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 187 | | olcott |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 186 | | Mikko |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 1 | | olcott |
22 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 184 | | olcott |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 183 | | Mikko |
23 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 182 | | olcott |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- | 181 | | Mikko |
24 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 180 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 149 | | Richard Damon |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 148 | | 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)-- | 137 | | Mikko |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 136 | | 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)-- | 134 | | Mikko |
26 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 26 | | olcott |
26 Apr 24 | D simulated by H never halts no matter what H does | 107 | | olcott |
25 Apr 24 | Re: Undecidability based on epistemological antinomies V2 --H(D,D)-- | 30 | | Mikko |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 54 | | olcott |
18 Apr 24 | Re: Undecidability based on epistemological antinomies V2 | 6 | | olcott |