Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!border-4.nntp.ord.giganews.com!border-1.nntp.ord.giganews.com!nntp.giganews.com!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.logic Subject: Re: The key undecidable instance that I know about --- Truth-bearers ONLY Date: Mon, 17 Mar 2025 07:26:40 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <71ee1fe6f1c2b4e16f9250107531b6a43112cb95@i2pn2.org> References:

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

<826c8dc93d6f1449302cf3a2992a0d8d42b317df@i2pn2.org> <5b7f8e24bbd9817f74e1f50ee3c3c6def714314b@i2pn2.org>

MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 17 Mar 2025 11:26:41 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="560995"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Lines: 223 On 3/17/25 12:36 AM, olcott wrote: > On 3/16/2025 9:52 PM, Richard Damon wrote: >> On 3/16/25 8:22 PM, olcott wrote: >>> On 3/16/2025 5:50 PM, Richard Damon wrote: >>>> On 3/16/25 10:32 AM, olcott wrote: >>>>> 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. >>>>>> ========== REMAINDER OF ARTICLE TRUNCATED ==========