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Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: sci.logic Subject: Re: The key undecidable instance that I know about --- Truth-bearers ONLY Date: Thu, 20 Mar 2025 11:59:41 +0200 Organization: - Lines: 109 Message-ID: <vrgoud$30230$1@dont-email.me> References: <vqkib1$r5np$1@dont-email.me> <3b57384a57c71e1880fe3f1df975003c1d743c07@i2pn2.org> <vqksgr$sf7f$2@dont-email.me> <c2a4c70287c029f462d5579a8602746386f546fc@i2pn2.org> <vql4mq$uv13$1@dont-email.me> <9a2fbcc7a803bc91d320117f8c8e03e03799e9b3@i2pn2.org> <vqlmtf$11p4p$2@dont-email.me> <95ca0b344ae29f6911a73c655ddbe1c7214f8519@i2pn2.org> <vqo4ke$1l6i0$1@dont-email.me> <c5b83ef1ae7f77e3ff1fe97dcb557af5380c2ddd@i2pn2.org> <vqo7or$1l6i0$3@dont-email.me> <vqo8bf$1lehl$1@dont-email.me> <vr4c6h$3u6l5$1@dont-email.me> <vr8oq5$3qi1v$1@dont-email.me> <vr97q9$6vsn$2@dont-email.me> <vrbvfv$2lq1i$1@dont-email.me> <vrd803$3oqkg$1@dont-email.me> <vreph9$16e25$1@dont-email.me> <vrfjkd$1s64t$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 20 Mar 2025 10:59:41 +0100 (CET) Injection-Info: dont-email.me; posting-host="07eb843a3e8d1b9262ebd76c548f87cc"; logging-data="3147872"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18WB2zfKYp/ceum6meuW9WH" User-Agent: Unison/2.2 Cancel-Lock: sha1:AO1Pw3HnfN4Se6bUWop2wbYEXTU= On 2025-03-19 23:22:53 +0000, olcott said: > On 3/19/2025 10:57 AM, Mikko wrote: >> On 2025-03-19 01:52:01 +0000, olcott said: >> >>> On 3/18/2025 9:20 AM, Mikko wrote: >>>> On 2025-03-17 13:24:24 +0000, olcott said: >>>> >>>>> On 3/17/2025 4:08 AM, Mikko wrote: >>>>>> On 2025-03-15 17:08:33 +0000, olcott said: >>>>>> >>>>>>> On 3/10/2025 9:49 PM, dbush wrote: >>>>>>>> On 3/10/2025 10:39 PM, olcott wrote: >>>>>>>>> On 3/10/2025 9:21 PM, Richard Damon wrote: >>>>>>>>>> On 3/10/25 9:45 PM, olcott wrote: >>>>>>>>>>> On 3/10/2025 5:45 PM, Richard Damon wrote: >>>>>>>>>>>> On 3/9/25 11:39 PM, olcott wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> LP := ~True(LP) DOES SPECIFY INFINITE RECURSION. >>>>>>>>>>>> >>>>>>>>>>>> WHich is irrelevent, as that isn't the statement in view, only what >>>>>>>>>>>> could be shown to be a meaning of the actual statement. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> The Liar Paradox PROPERLY FORMALIZED <is> Infinitely recursive >>>>>>>>>>> thus semantically incorrect. >>>>>>>>>> >>>>>>>>>> But is irrelevent to your arguement. >>>>>>>>>> >>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> "It would then be possible to reconstruct the antinomy of the liar >>>>>>>>>>> in the metalanguage, by forming in the language itself a sentence" >>>>>>>>>> >>>>>>>>>> Right, the "Liar" is in the METALANGUAGE, not the LANGUAGE where the >>>>>>>>>> predicate is defined. >>>>>>>>>> >>>>>>>>>> You are just showing you don't understand the concept of Metalanguage. >>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Thus anchoring his whole proof in the Liar Paradox even if >>>>>>>>>>> you do not understand the term "metalanguage" well enough >>>>>>>>>>> to know this. >>>>>>>>>> >>>>>>>>>> Yes, there is a connection to the liar's paradox, and that is that he >>>>>>>>>> shows that the presumed existance of a Truth Predicate forces the logic >>>>>>>>>> system to have to resolve the liar's paradox. >>>>>>>>>> >>>>>>>>> >>>>>>>>> bool True(X) >>>>>>>>> { >>>>>>>>> if (~unify_with_occurs_check(X)) >>>>>>>>> return false; >>>>>>>>> else if (~Truth_Bearer(X)) >>>>>>>>> return false; >>>>>>>>> else >>>>>>>>> return IsTrue(X); >>>>>>>>> } >>>>>>>>> >>>>>>>>> LP := ~True(LP) >>>>>>>>> True(LP) resolves to false. >>>>>>>> >>>>>>>> ~True(LP) resolves to true >>>>>>>> LP := ~True(LP) resolves to true >>>>>>>> >>>>>>>> Therefore the assumption that a correct True() predicate exists is >>>>>>>> proven false. >>>>>>> >>>>>>> When you stupidly ignore Prolog and MTT that >>>>>>> both prove there is a cycle in the directed graph >>>>>>> of their evaluation sequence. If you have no idea >>>>>>> what "cycle", "directed graph" and "evaluation sequence" >>>>>>> means then this mistake is easy to make. >>>>>> >>>>>> Prolog does not prove anything other than what you ask. I don't think >>>>>> you can ask Prolog whether there is a cycle in LP after LP = not(true(LP)). >>>>> >>>>> ?- LP = not(true(LP)). >>>>> LP = not(true(LP)). >>>> >>>> Meaning that LP = not(true(LP)) is accepted as a valid query and evalated >>>> as true with the implication that LP is the same as not(true(LP)). >>>> >>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>> false. >>>> >>>> Meaning that unify_with_occurs_check(LP, not(true(LP))) is accepted as a >>>> valid query and evaluated as false. >>> >>> I have been saying "cycles" all along and it has always been cycles. >> >> Not all along, just occasionally. What you did say that Prolog proves >> that there is a cycle in the directed graph of their evaluation sequence. >> I said that Prolog does not prove that. Then you posted some examples of >> prolog not proving that and didn't mention "cycles" any more. >> >>> https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2 >> >> That link confirms what I said above. It also said that one of the arguments >> already has a cycle then that cycle does not prevent unification and does >> not cause infinite execution. > > Clearly you have no idea what a cycle in a directed graph means. It is a sin to present a false claim about another person. -- Mikko