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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: =?UTF-8?Q?Re=3A_ZFC_solution_to_incorrect_questions=3A_reject_them_?=
 =?UTF-8?Q?--G=C3=B6del--?=
Date: Fri, 15 Mar 2024 11:50:54 -0700
Organization: i2pn2 (i2pn.org)
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On 3/15/24 7:28 AM, olcott wrote:
> On 2024-03-13 14:25:10 +0000, olcott said:
> 
>> On 3/13/2024 5:03 AM, Mikko wrote:
>>> On 2024-03-12 20:38:34 +0000, olcott said:
>>>
>>>> On 3/12/2024 3:31 PM, immibis wrote:
>>>>> On 12/03/24 20:02, olcott wrote:
>>>>>> On 3/12/2024 1:31 PM, immibis wrote:
>>>>>>> On 12/03/24 19:12, olcott wrote:
>>>>>>>> ∀ H ∈ Turing_Machine_Deciders
>>>>>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>
>>>>>>>> There is some input TMD to every H such that
>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>
>>>>>>> And it can be a different TMD to each H.
>>>>>>>
>>>>>>>> When we disallow decider/input pairs that are incorrect
>>>>>>>> questions where both YES and NO are the wrong answer
>>>>>>>
>>>>>>> Once we understand that either YES or NO is the right answer, the 
>>>>>>> whole rebuttal is tossed out as invalid and incorrect.
>>>>>>>
>>>>>>
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not 
>>>>>> halt
>>>>>> BOTH YES AND NO ARE THE WRONG ANSWER FOR EVERY Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>
>>>>>
>>>>> Once we understand that either YES or NO is the right answer, the 
>>>>> whole rebuttal is tossed out as invalid and incorrect.
>>>>>
>>>>>>>> Does the barber that shaves everyone that does not shave
>>>>>>>> themselves shave himself? is rejected as an incorrect question.
>>>>>>>
>>>>>>> The barber does not exist.
>>>>>>
>>>>>> Russell's paradox did not allow this answer within Naive set theory.
>>>>>
>>>>> Naive set theory says that for every predicate P, the set {x | 
>>>>> P(x)} exists. This axiom was a mistake. This axiom is not in ZFC.
>>>>>
>>>>> In Turing machines, for every non-empty finite set of alphabet 
>>>>> symbols Γ, every b∈Γ, every Σ⊆Γ, every non-empty finite set of 
>>>>> states Q, every q0∈Q, every F⊆Q, and every δ:(Q∖F)×Γ↛Q×Γ×{L,R}, 
>>>>> ⟨Q,Γ,b,Σ,δ,q0,F⟩ is a Turing machine. Do you think this is a 
>>>>> mistake? Would you remove this axiom from your version of Turing 
>>>>> machines?
>>>>>
>>>>> (Following the definition used on Wikipedia: 
>>>>> https://en.wikipedia.org/wiki/Turing_machine#Formal_definition)
>>>>>
>>>>>>> The following is true statement:
>>>>>>>
>>>>>>> ∀ Barber ∈ People. ¬(∀ Person ∈ People. Shaves(Barber, Person) ⇔ 
>>>>>>> ¬Shaves(Person, Person))
>>>>>>>
>>>>>>> The following is a true statement:
>>>>>>>
>>>>>>> ¬∃ Barber ∈ People. (∀ Person ∈ People. Shaves(Barber, Person) ⇔ 
>>>>>>> ¬Shaves(Person, Person))
>>>>>>>
>>>>>>
>>>>>> That might be correct I did not check it over and over
>>>>>> again and again to make sure.
>>>>>>
>>>>>> The same reasoning seems to rebut Gödel Incompleteness:
>>>>>> ...We are therefore confronted with a proposition which
>>>>>> asserts its own unprovability. 15 ... (Gödel 1931:43-44)
>>>>>> ¬∃G ∈ F | G := ~(F ⊢ G)
>>>>>>
>>>>>> Any G in F that asserts its own unprovability in F is
>>>>>> asserting that there is no sequence of inference steps
>>>>>> in F that prove that they themselves do not exist in F.
>>>>>
>>>>> The barber does not exist and the proposition does not exist.
>>>>>
>>>>
>>>> When we do this exact same thing that ZFC did for self-referential
>>>> sets then Gödel's self-referential expressions that assert their
>>>> own unprovability in F also cease to exist.
>>>
> Path: 
> i2pn2.org!i2pn.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
> From: olcott <polcott2@gmail.com>
> Newsgroups: sci.logic
> Subject: 
> =?UTF-8?Q?Re=3A_ZFC_solution_to_incorrect_questions=3A_reject_them_?=
> =?UTF-8?Q?--G=C3=B6del--?=
> Date: Fri, 15 Mar 2024 09:28:49 -0500
> Organization: A noiseless patient Spider
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> Xref: i2pn2.org sci.logic:68595
> 
> On 3/15/2024 6:07 AM, Mikko wrote:
>> On 2024-03-13 14:25:10 +0000, olcott said:
>>
>>> On 3/13/2024 5:03 AM, Mikko wrote:
>>>> On 2024-03-12 20:38:34 +0000, olcott said:
>>>>
>>>>> On 3/12/2024 3:31 PM, immibis wrote:
>>>>>> On 12/03/24 20:02, olcott wrote:
>>>>>>> On 3/12/2024 1:31 PM, immibis wrote:
>>>>>>>> On 12/03/24 19:12, olcott wrote:
>>>>>>>>> ∀ H ∈ Turing_Machine_Deciders
>>>>>>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>>
>>>>>>>>> There is some input TMD to every H such that
>>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>
>>>>>>>> And it can be a different TMD to each H.
>>>>>>>>
>>>>>>>>> When we disallow decider/input pairs that are incorrect
>>>>>>>>> questions where both YES and NO are the wrong answer
>>>>>>>>
>>>>>>>> Once we understand that either YES or NO is the right answer, 
>>>>>>>> the whole rebuttal is tossed out as invalid and incorrect.
>>>>>>>>
>>>>>>>
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not 
>>>>>>> halt
>>>>>>> BOTH YES AND NO ARE THE WRONG ANSWER FOR EVERY Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>
>>>>>>
>>>>>> Once we understand that either YES or NO is the right answer, the 
>>>>>> whole rebuttal is tossed out as invalid and incorrect.
>>>>>>
>>>>>>>>> Does the barber that shaves everyone that does not shave
>>>>>>>>> themselves shave himself? is rejected as an incorrect question.
>>>>>>>>
>>>>>>>> The barber does not exist.
>>>>>>>
>>>>>>> Russell's paradox did not allow this answer within Naive set theory.
>>>>>>
>>>>>> Naive set theory says that for every predicate P, the set {x | 
>>>>>> P(x)} exists. This axiom was a mistake. This axiom is not in ZFC.
>>>>>>
>>>>>> In Turing machines, for every non-empty finite set of alphabet 
>>>>>> symbols Γ, every b∈Γ, every Σ⊆Γ, every non-empty finite set of 
>>>>>> states Q, every q0∈Q, every F⊆Q, and every δ:(Q∖F)×Γ↛Q×Γ×{L,R}, 
>>>>>> ⟨Q,Γ,b,Σ,δ,q0,F⟩ is a Turing machine. Do you think this is a 
>>>>>> mistake? Would you remove this axiom from your version of Turing 
>>>>>> machines?
>>>>>>
>>>>>> (Following the definition used on Wikipedia: 
>>>>>> https://en.wikipedia.org/wiki/Turing_machine#Formal_definition)
>>>>>>
>>>>>>>> The following is true statement:
>>>>>>>>
>>>>>>>> ∀ Barber ∈ People. ¬(∀ Person ∈ People. Shaves(Barber, Person) ⇔ 
>>>>>>>> ¬Shaves(Person, Person))
========== REMAINDER OF ARTICLE TRUNCATED ==========