Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!i2pn.org!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: Sun, 16 Mar 2025 07:33:25 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <826c8dc93d6f1449302cf3a2992a0d8d42b317df@i2pn2.org> 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 11:33:26 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="423216"; 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 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. > > 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 to get to a goal, something that seems to be beyond you. You are just too stupid to understand the thoughts he is thinking because you "logic" isn't correct, and too simple.