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: Sat, 15 Mar 2025 20:19:10 -0500 Organization: A noiseless patient Spider Lines: 120 Message-ID: References: <3b57384a57c71e1880fe3f1df975003c1d743c07@i2pn2.org>

<9a2fbcc7a803bc91d320117f8c8e03e03799e9b3@i2pn2.org> <95ca0b344ae29f6911a73c655ddbe1c7214f8519@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 02:19:11 +0100 (CET) Injection-Info: dont-email.me; posting-host="33de22785a11a76beb5897cc3eba332a"; logging-data="726815"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+6psAQUBbx51cO/TA55ltS" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:YoftPsyxAVUXHUiPlAaRGCOngMk= Content-Language: en-US In-Reply-To: X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250315-4, 3/15/2025), Outbound message Bytes: 6011 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: 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. 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 -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer