Sujet : Re: Undecidability based on epistemological antinomies V2 --Tarski Proof--
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.logic comp.theoryDate : 21. Apr 2024, 18:52:46
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <v03g8u$1q6th$1@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 4/21/24 11:26 AM, olcott wrote:
On 4/20/2024 10:39 AM, Richard Damon wrote:
On 4/20/24 11:20 AM, olcott wrote:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
>
When we create a three-valued logic system that has these
three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
>
Such three valued logic has the problem that a tautology of the
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic.
>
>
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It
is basically invalid input.
>
>
In other words, you admit that you are being inconsistant about what you are saying, because your whole logic system is just inconsistant.
>
Not at all.
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)
The notion of incompleteness and undecidability requires non truth
bearers to be construed as truth bearers.
Nope, and you stating that just proves your stupidity.
A Theory K will define its "language" and what statements it accepts within it. Normally that "language" excludes non-truth-bearers. This seems to be something outside your understanding, as you don't seem to understand anything about the nature of actual FORMAL logic systems, but seem to be stuck
Yes, non-truth bearing statements will be undecidable,
A proposition is a central concept in the philosophy of language,
semantics, logic, and related fields, often characterized as the primary
bearer of truth or falsity. https://en.wikipedia.org/wiki/Proposition
When we quit construing expressions that cannot possibly be true or
false as propositions then incompleteness and undecidability cease to
exist.
Nope. There exist statements that are True, in that they have an (infinite) sequence of connections from the truth makers of the system to the statement, but are not provable, as there is no FINITE sequence of connections that do so.
Godel's G is an example of this, stating that there does not exist a number that matches a specific property. Since the property is computable for all numbers, we know that G must be a truth bearer, as either such a number exists, or it doesn't exist.
This fact can be established in F, as either it is false, because we CAN find such a number, and the checking of the number with the relationship provides a definite proof that G is false, or no such number exists, and this is established by the INFINITE chain of checking every number, and seeing that none satisfies it.
We happen to be able to reduce that infinite chain to be finite in a partitulare meta-theory of F that understands a hidden meaning in the relationship, and allows us to PROVE that no such number exists.
This PROVES that G is a true statement. While the proof is in Meta-F, the proof also establishes that G is true in F.
On 4/18/2024 8:58 PM, Richard Damon wrote:
> INCOMPLETENESS is EXACTLY about the inability to prove statements that
> are true.
Truth_Bearer(F, x) ≡ ∃x ∈ F ((F ⊢ x) ∨ (F ⊢ ¬x))
Nope, not PROVES, but ESTABLISHES.
Truth_Bearer(F, x) ≡ ∃x ∈ F ((F ⊨ x) ∨ (F ⊨ ¬x))
Truth Bearing allows for the INFINTE sequence to establish the fact, even if that can not be a proof of it.
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43-44)
Yep, you can build another proof just like the one presented based on any epistemological antinomy. Note, the proof USES the antinomy, but does not "derive" from it, in that its validity and soundness are not based on the truth of the antinomy.
You don't seem to understand the syntactic transformation that was done on the statement at the beginning, that created a NEW PROPOSITION, that turns out to be a Truth Bearer.
"X says that X is not True in F", is an epistemological antinomy.
"X says that X is not Provable in F" is not, as the logical valuation of X being True but not Provable is a possible valid combination of states.
Gödel is essentially saying that expressions that are not propositions
prove that a formal system of propositions has undecidable propositions.
Nope.
Since you don't understand what Godel did, you are just showing you stupidity by making your claim.
That you persist is making the claim after being shown to be wrong, make you just a stupid pathological liar, and proves you just don't understand what Truth actually is.
You don't seem to understand that predicates, DEFINED to be able to work on ALL memebers of the input domain, must IN FACT, work on all members of that domain.
>
For a Halt Decider, that means the decider needs to be able to answer about ANY machine given to it as an input, even a machine that uses a copy of the decider and acts contrary to its answer.
>
If you are going to work on a different problem, you need to be honest about that and not LIE and say you are working on the Halting Problem.
>
And, if you are going to talk about a "Truth Predicate", which is defined to be able to take ANY "statement" and say if it is True or not, with "nonsense" statements (be they self-contradictory statements, or just nonsense) being just not-true.
>
ANY statement means any statement, so if we define this predicate as True(F, x) to be true if x is a statement that is true in the field F, then we need to be able to give this predicate the statemet:
>
In F de define s as NOT True(F, s)
>
>
If you claim that your logic is ACTUALLY "two-valued" then if True(F,s) returns false, because s is a statement without a truth value, then we have the problem that the definition of s now says that s has the value of NOT false, which is True.
>
So, the True predicate was WRONG, as True of a statement that IS true, must be true.
>
If True(F,s) is true, then we have that s is not defined as NOT true, which is false, so the True predicate is again WRONG.
>
The predicate isn't ALLOWED to say "I reject this input" as that isn't a truth value (since you claimed you are actually useing a two-valued logic) and this predicate is defined to ALWAYS return a truth value.
>
So, it seems you have a two-valued logic system with three logical values.
>
Which is just A LIE!
>
You are just proving you are too stupid to understand what you are talking about as you don't understand the meaning of the words you are using, as you just studied the system by Zero order principles.
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 |