Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: sci.logic Subject: Re: The key undecidable instance that I know about --- Truth-bearers ONLY Date: Thu, 20 Mar 2025 14:57:40 +0200 Organization: - Lines: 129 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: Thu, 20 Mar 2025 13:57:41 +0100 (CET) Injection-Info: dont-email.me; posting-host="60f4bef9f01dfedd0a7e4274e98fdf68"; logging-data="3446255"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/HIH5WAl677/T2GapMOxKW" User-Agent: Unison/2.2 Cancel-Lock: sha1:fD/6GbfAoqRYCeAny5Z5qLjdeNE= Bytes: 6447 On 2025-03-17 13:18:42 +0000, olcott said: > On 3/17/2025 4:04 AM, Mikko wrote: >> On 2025-03-16 14:38:16 +0000, olcott said: >> >>> On 3/16/2025 8:19 AM, Mikko wrote: >>>> On 2025-03-15 17:15:39 +0000, olcott said: >>>> >>>>> 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". >>>> >>>> The above is irrelevant to the fact that you didn't say anothing about >>>> the text you quoted. >>>> >>> >>> LP := ~True(LP) expanded to infinite recursion >>> ~True(~True(~True(~True(~True(~True(...)))))) >>> The same way that Clocksin and Mellish do on their example >>> that you dishonestly keep ignoring. >> >> They don't say so in the above quoted text. What they do say is essentially >> what I have said in another context but not relevant here. >> > > *It seems to me that you are dishonest abut that* Doesn't matter. Hopefully readers can see that you are dishonest but that is their problem, not yours or mine. > BEGIN:(Clocksin & Mellish 2003:254) > Finally, a note about how Prolog matching sometimes differs from the > unification used in Resolution. 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. In this example, foo(Y) is matched against Y, which > appears within it. As a result, Y will stand for foo(Y), which is > foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), > and soon. So Y ends up standing for some kind of infinite structure. > END:(Clocksin & Mellish 2003:254) The above quote is irrelevant to the question whether ~True(LP) resolves to true. -- Mikko