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From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Proving my 2004 claim that some decider/input pairs are incorrect
 questions
Date: Tue, 12 Mar 2024 11:12:08 -0500
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On 3/12/2024 10:47 AM, Richard Damon wrote:
> On 3/12/24 7:45 AM, olcott wrote:
>> This is my 2004 work that proposes that the halting problem has
>> an unsatisfiable specification thus asks an ill-formed question.
>> Two PhD computer science professors agree with this analysis.
>>
>> E C R Hehner. *Objective and Subjective Specifications*
>> WST Workshop on Termination, Oxford.  2018 July 18.
>> See https://www.cs.toronto.edu/~hehner/OSS.pdf
>>
>> Bill Stoddart. *The Halting Paradox*
>> 20 December 2017
>> https://arxiv.org/abs/1906.05340
>> arXiv:1906.05340 [cs.LO]
>>
>> Alan Turing's Halting Problem is incorrectly formed (PART-TWO)  sci.logic
>> On 6/20/2004 11:31 AM, Peter Olcott wrote:
>>  > PREMISES:
>>  > (1) The Halting Problem was specified in such a way that a solution
>>  > was defined to be impossible.
>>  >
>>  > (2) The set of questions that are defined to not have any possible
>>  > correct answer(s) forms a proper subset of all possible questions.
>>  > …
>>  > CONCLUSION:
>>  > Therefore the Halting Problem is an ill-formed question.
>>  >
>> USENET Message-ID:
>> <kZiBc.103407$Gx4.18142@bgtnsc04-news.ops.worldnet.att.net>
>>
>> *Direct Link to original message*
>> http://al.howardknight.net/?STYPE=msgid&MSGI=%3CkZiBc.103407%24Gx4.18142%40bgtnsc04-news.ops.worldnet.att.net%3E+
>>
>> An incorrect YES/NO (thus polar) question is defined as any
>> YES/NO question where both YES and NO are the wrong answer.
>> Correctly answering incorrect questions is logically impossible.
>>
>> 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
>> https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
>>
>> Because for every implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ that can
>> possibly exist both YES and NO are the wrong answer to
>> this question: Does Ĥ ⟨Ĥ⟩ halts on its input?
>>
>> This exactly meets the definition of an incorrect YES/NO
>> question for this decider/input pair: Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>
>> It is generally the case that the inability to do the
>> logically impossible places no actual limit on anything
>> or anyone otherwise CAD systems that cannot correctly
>> draw square circles would be another limit to computation.
>>
>> The common fake rebuttal to this claim is to use the
>> strawman deception to switch to some other decider/input
>> pair besides Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to deceptively try to show that
>> the question is not incorrect on the basis of some other
>> different question.
>>
>>
>>
> 
> Intentional LIE and fabrication.
> 
> It has been explained why this is wrong, and your ignoring that says you 
> KNOW you are lying.
> 

*I am telling the truth*
*I am telling the truth*
*I am telling the truth*

∀ H ∈ Turing_Machine_Deciders
∃ TMD ∈ Turing_Machine_Descriptions  |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)

In all of the H/TMD cases above where
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
H is being asked a question where both YES and NO
are the wrong answer.

It is not that H is gagged and cannot answer, it is
that both YES and NO are the wrong answer.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer