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: Mon, 17 Mar 2025 08:18:42 -0500 Organization: A noiseless patient Spider Lines: 126 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: Mon, 17 Mar 2025 14:18:43 +0100 (CET) Injection-Info: dont-email.me; posting-host="5a2e111456ff0aca17d02f184acd802e"; logging-data="229271"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19HhP1F1QQbCRSQLGTDqv4V" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:gK5/q5N/QuyrCz2KJLrGD3xefsc= Content-Language: en-US In-Reply-To: X-Antivirus: Norton (VPS 250317-2, 3/17/2025), Outbound message X-Antivirus-Status: Clean Bytes: 6406 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* 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) -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer