Path: nntp.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory,sci.logic,comp.ai.philosophy Subject: Re: The error of the standard proof of the halting problem Date: Tue, 22 Jul 2025 11:22:10 -0500 Organization: A noiseless patient Spider Lines: 82 Message-ID: <105odri$hate$9@dont-email.me> References: <105ht1n$36s20$1@dont-email.me> <105kvub$2q17h$1@dont-email.me> <105lg9k$3v8t8$6@dont-email.me> <105n3d3$bgdn$1@dont-email.me> <6MKfQ.127469$uM3d.111752@fx39.iad> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 22 Jul 2025 18:22:11 +0200 (CEST) Injection-Info: dont-email.me; posting-host="a14401adad5651a253e4d054a1d0c031"; logging-data="568238"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/6Clp/2S26tJUkXYVgbPI+" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:NQ74nk4fdnh5lIF/Eb0RdB6sb3c= Content-Language: en-US In-Reply-To: <6MKfQ.127469$uM3d.111752@fx39.iad> X-Antivirus: Norton (VPS 250722-2, 7/22/2025), Outbound message X-Antivirus-Status: Clean On 7/22/2025 6:39 AM, Richard Damon wrote: > On 7/22/25 12:17 AM, olcott wrote: >> On 7/21/2025 9:20 PM, Richard Damon wrote: >>> On 7/21/25 9:45 AM, olcott wrote: >>>> On 7/21/2025 4:06 AM, Mikko wrote: >>>>> On 2025-07-20 11:48:37 +0000, Mr Flibble said: >>>>> >>>>>> On Sun, 20 Jul 2025 07:13:43 -0400, Richard Damon wrote: >>>>>> >>>>>>> On 7/20/25 12:58 AM, olcott wrote: >>>>>>>> Title: A Structural Analysis of the Standard Halting Problem Proof >>>>>>>> >>>>>>>> Author: PL Olcott >>>>>>>> >>>>>>>> Abstract: >>>>>>>> This paper presents a formal critique of the standard proof of the >>>>>>>> undecidability of the Halting Problem. While we do not dispute the >>>>>>>> conclusion that the Halting Problem is undecidable, we argue >>>>>>>> that the >>>>>>>> conventional proof fails to establish this conclusion due to a >>>>>>>> fundamental misapplication of Turing machine semantics. >>>>>>>> Specifically, >>>>>>>> we show that the contradiction used in the proof arises from >>>>>>>> conflating >>>>>>>> the behavior of encoded simulations with direct execution, and from >>>>>>>> making assumptions about a decider's domain that do not hold >>>>>>>> under a >>>>>>>> rigorous model of computation. >>>>>>>> >>>>>>> Your problem is you don't understand the meaning of the words you >>>>>>> are >>>>>>> using. >>>>>> >>>>>> This is an ad hominem attack, not argumentation. >>>>> >>>>> It is also honest and truthful, which is not as common as it should. >>>>> >>>> >>>> It is also honest and truthful that people >>>> that deny verified facts are either liars >>>> or lack sufficient technical competence. >>>> >>> >>> Right, so YOU are the liar. >>> >>> It is a verified fact that the PROGRAM DDD halts since your HHH(DDD) >>> returns 0. >>> >> >> It is a self-evident truth that the halting problem proof >> has always been incorrect when it requires a halt decider >> to report on the behavior of the direct execution of any >> Turing machine because no Turing machine decider can ever >> take another directly executed Turing machine as its input. > > If it seems "self-evident" to you, that just shows how warped you ideas > are of what the field means. > In this field it is common knowledge that no Turing machine decider ever takes another directly executed Turing machine as its input. This means that Linz is wrong that machine M should report on the behavior of its own direct execution as his words state below. WM is the machine description of M q0 WM ⊢* Ĥq0 WM WM ⊢* Ĥ∞, if M applied to WM halts, and q0 WM ⊢* Ĥq0 Wm WM ⊢* Ĥ y1 qn y2, if M applied to WM does not halt. TM's can only compute the mapping from inputs and M is not an input. https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer