Path: ...!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: Sun, 16 Mar 2025 18:50:05 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <5b7f8e24bbd9817f74e1f50ee3c3c6def714314b@i2pn2.org> 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 22:50:06 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="492667"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US In-Reply-To: Bytes: 9178 Lines: 199 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. >> > 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. Apparently you don't understand what it means to "reconstruct" something. Or the difference between the "Langauge" and the "Metalanguage" ========== REMAINDER OF ARTICLE TRUNCATED ==========