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Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott <polcott333@gmail.com> Newsgroups: comp.theory,comp.ai.philosophy,sci.logic Subject: Re: HP counter-example INPUT cannot possibly exist --- Peter Linz HP Proof Date: Sat, 21 Jun 2025 12:30:25 -0500 Organization: A noiseless patient Spider Lines: 83 Message-ID: <1036q7i$16lpk$1@dont-email.me> References: <YpG1Q.1572310$4AM6.1293015@fx17.ams4> <ab53329d43e0587e58fe949b7a8f1dce83bb580f@i2pn2.org> <1027uhs$r7bj$2@dont-email.me> <6f1855be769b3afc319d871c0d451f381803ba5e@i2pn2.org> <1029hvm$1ah2f$1@dont-email.me> <102bhn6$1t2a1$1@dont-email.me> <102c462$20jl4$10@dont-email.me> <102e2p4$2iugr$1@dont-email.me> <102er47$2ohps$3@dont-email.me> <102gv1s$3cscf$1@dont-email.me> <102hgcp$3gqbm$3@dont-email.me> <102m36e$qohc$1@dont-email.me> <102mm8v$uef9$8@dont-email.me> <102ok6o$1gto6$1@dont-email.me> <102uj28$369b2$1@dont-email.me> <1030gop$3p2jt$1@dont-email.me> <10342se$4ms9$1@dont-email.me> <1035qea$vbnq$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 21 Jun 2025 19:30:27 +0200 (CEST) Injection-Info: dont-email.me; posting-host="c33a34d5810729869e79acc5a916ae39"; logging-data="1267508"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/+TIyPMAq3yOVGn+Yjk0OQ" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:8zPVjfiCpUBu09VLbtPOES0YGuQ= Content-Language: en-US X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250621-6, 6/21/2025), Outbound message In-Reply-To: <1035qea$vbnq$1@dont-email.me> On 6/21/2025 3:27 AM, Mikko wrote: > On 2025-06-20 16:39:40 +0000, olcott said: > >> On 6/19/2025 3:12 AM, Mikko wrote: >>> >>> But this is not. A proof starts with assumptions that may be true of >>> false. Each statement that is not a definition, axiom, postulate, >>> hypthesis or other assumption follows from some previous statements >>> by an inference rule. The conclusion of a proof is the last statement >>> of the sequence. >> >> Some proofs begin with definitions instead of assumptions. > > Definitions often enable a clearer presentation of the assumptions > and of the proof. > Some proofs begin with "assumptions" that are defined to be true, thus are not really mere assumptions at all. <snip>>>> >>> Depending on the style of the proof one can ither prove that >>> the counter example exists or that if a halting decider exists >>> then the caunter example exists, too, and otherwise none is >>> needed. >> >> No this is counter-factual. >> It has never been possible for *AN ACTUAL INPUT* to do >> the opposite of whatever value that it decider decides. >> *For 90 years no one ever bothered to notice this* > > There is nothing impossible in Linz' construction of the > counter example. If you think there is you could tell us > the page, paragraph, and sentence in Linz' book that says > someting impossible. > https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf When M is applied to WM q0 WM ⊢* Ĥ q0 WM WM ⊢* Ĥ∞ if M applied to WM halts, and q0 WM ⊢* Ĥ q0 Wm WM ⊢* Ĥ y1 qn y2 if M applied to WM does not halt. *From the bottom of page 319 has been adapted to this* When Ĥ is applied to ⟨Ĥ⟩ Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞ if Ĥ applied to ⟨Ĥ⟩ halts Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn if Ĥ applied to ⟨Ĥ⟩ does not halt This does not have embedded_H reporting on the behavior specified by its input it has embedded_H reporting on its own behavior. When embedded_H is a simulating partial halt decider then its transition to Ĥ.qn does correctly report that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its own simulated final halt state of ⟨Ĥ.qn⟩. *It does this even though embedded_H itself halts. embedded_H* *is not allowed to report on its own behavior. It is only* *allowed to report on the behavior that its input specifies* When Ĥ is applied to ⟨Ĥ⟩ and embedded_H is a simulating partial halt decider (a) Ĥ copies its input ⟨Ĥ⟩ (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩ (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩ (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩ (g) goto (d) with one more level of simulation until embedded_H sees the repeating pattern and transitions to Ĥ.qn. ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its own simulated final halt state of ⟨Ĥ.qn⟩ thus can never do the opposite of whatever embedded_H decides. 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