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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott <polcott2@gmail.com> Newsgroups: comp.theory,sci.logic Subject: Proving my 2004 claim that some decider/input pairs are incorrect questions Date: Tue, 12 Mar 2024 09:45:51 -0500 Organization: A noiseless patient Spider Lines: 63 Message-ID: <usppqv$b9av$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 12 Mar 2024 14:45:52 -0000 (UTC) Injection-Info: dont-email.me; posting-host="2de151991156ec4f63802e311fdc7732"; logging-data="370015"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19afYL8duV0jrgY4cUs5b8C" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:1ZsHa+ckLCE564RoXXWRshenEak= Content-Language: en-US Bytes: 3500 This is my 2004 work that proposes that the halting problem has an unsatisfiable specification thus asks an ill-formed question. Two PhD computer science professors agree with this analysis. E C R Hehner. *Objective and Subjective Specifications* WST Workshop on Termination, Oxford. 2018 July 18. See https://www.cs.toronto.edu/~hehner/OSS.pdf Bill Stoddart. *The Halting Paradox* 20 December 2017 https://arxiv.org/abs/1906.05340 arXiv:1906.05340 [cs.LO] Alan Turing's Halting Problem is incorrectly formed (PART-TWO) sci.logic On 6/20/2004 11:31 AM, Peter Olcott wrote: > PREMISES: > (1) The Halting Problem was specified in such a way that a solution > was defined to be impossible. > > (2) The set of questions that are defined to not have any possible > correct answer(s) forms a proper subset of all possible questions. > … > CONCLUSION: > Therefore the Halting Problem is an ill-formed question. > USENET Message-ID: <kZiBc.103407$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. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer