Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: The key undecidable instance that I know about --- Truth-bearers ONLY Date: Sun, 16 Mar 2025 09:32:34 -0500 Organization: A noiseless patient Spider Lines: 169 Message-ID: References: <3b57384a57c71e1880fe3f1df975003c1d743c07@i2pn2.org>

<9a2fbcc7a803bc91d320117f8c8e03e03799e9b3@i2pn2.org> <95ca0b344ae29f6911a73c655ddbe1c7214f8519@i2pn2.org>

<826c8dc93d6f1449302cf3a2992a0d8d42b317df@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 16 Mar 2025 15:32:36 +0100 (CET) Injection-Info: dont-email.me; posting-host="07a083537033e8637263f61b76c22e15"; logging-data="2045751"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18zbJnGdsljulZ6LrpLhVYP" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:16rKPjOjD1KHG0gatj0mn+nDiqQ= In-Reply-To: <826c8dc93d6f1449302cf3a2992a0d8d42b317df@i2pn2.org> Content-Language: en-US X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250316-2, 3/16/2025), Outbound message Bytes: 8075 On 3/16/2025 6:33 AM, Richard Damon wrote: > On 3/15/25 10:37 PM, olcott wrote: >> On 3/15/2025 9:12 PM, Richard Damon wrote: >>> On 3/15/25 9:19 PM, olcott wrote: >>>> On 3/15/2025 3:44 PM, Richard Damon wrote: >>>>> On 3/15/25 1:15 PM, olcott wrote: >>>>>> On 3/11/2025 5:50 AM, Mikko wrote: >>>>>>> On 2025-03-11 03:23:51 +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 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 >>>>>>>> >>>>>>>> It may seem that way if you fail to understand >>>>>>>> Clocksin & Mellish explanation of >>>>>>>> >>>>>>>> Most Prolog systems will allow you to >>>>>>>> satisfy goals like: >>>>>>>> equal(X, X). >>>>>>>> ?- equal(foo(Y), Y). >>>>>>>> >>>>>>>> that is, they will allow you to match a >>>>>>>> term against an uninstantiated subterm of itself. >>>>>>>> >>>>>>>> ON PAGE 3 >>>>>>>> https://www.researchgate.net/ >>>>>>>> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence >>>>>>> >>>>>>> That you can quote some text but don't say anything about it >>>>>>> supports the >>>>>>> hypthesis that you don't understand the text you quoted. >>>>>>> >>>>>> >>>>>> I said that unify_with_occurs_check() detects >>>>>> cycles in the directed graph of the evaluation >>>>>> sequence of an expression that does explain >>>>>> everything even if it seems like I said >>>>>> blah, blah, blah to everyone not knowing the >>>>>> meaning of these words: "cycle", directed graph" >>>>>> "evaluation sequence". >>>>>> >>>>> >>>>> Except for the fact that you aren't giving it the actual x that >>>>> Tarski creates (or the G for Godel) as expressed in the language, >>>>> in part because it uses logic that can't be expressed in Prolog. >>>>> >>>> >>>> >>>> Tarski's Liar Paradox from page 248 >>>> It would then be possible to reconstruct the antinomy of the liar >>>> in the metalanguage, by forming in the language itself a sentence >>>> x such that the sentence of the metalanguage which is correlated >>>> with x asserts that x is not a true sentence. >>>> https://liarparadox.org/Tarski_247_248.pdf >>> >>> >>> >>>> >>>> Formalized as: >>> >>> NO!! >>> >>> That is what it reduces to in the metalangugae, but not what it is in >>> the language, which is where it counts. >>> >>>> x ∉ True if and only if p >>>> where the symbol 'p' represents the whole sentence x >>>> https://liarparadox.org/Tarski_275_276.pdf >>>> >>>> Not all all. It is merely that Tarski's somewhat clumsy >>>> syntax does not encode the Liar Paradox where its >>>> pathological self-reference can be directly seen. >>> >>> No, Tarski's syntax >>> >>>> >>>> He does not formalize most important part: >>>> "where the symbol 'p' represents the whole sentence x" >>>> >>>> If he did formalize that most important part it would >>>> be this: x ∉ True if and only if x >>>> >>> >>> >>> Nope, you are just not understanding that 'x' is a fairly complecated >>> sentence in the language, for which in the metalanguge, it can be >>> reduced to the symbol p. >>> >> >> When Tarski formalized the Liar Paradox >> HE DID IT INCORRECTLY. > > We wasn't "Formalizing" the Liar Paradox. > reconstruct the antinomy of the liar in the metalanguage, by forming in the language itself a sentence x such that the sentence of the metalanguage which is correlated with x asserts that x is not a true sentence. >> >> LP := ~True(LP) "This sentence is not true" >> Tarski GOT THIS WRONG. >> > > Nope, you don't understand what he is doing, because he is using thought ========== REMAINDER OF ARTICLE TRUNCATED ==========