Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: dbush Newsgroups: sci.logic Subject: Re: The key undecidable instance that I know about --- Truth-bearers ONLY Date: Sat, 15 Mar 2025 21:27:06 -0400 Organization: A noiseless patient Spider Lines: 142 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: Sun, 16 Mar 2025 02:27:05 +0100 (CET) Injection-Info: dont-email.me; posting-host="67c63d6f95dcce4899f1b1432e20e56d"; logging-data="758557"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1985nx3ik/m8lmKtNV99tfI" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:qGRpts+Mb3g/PGKYHd9aqSmDTDE= Content-Language: en-US In-Reply-To: Bytes: 6723 On 3/15/2025 9:03 PM, olcott wrote: > On 3/15/2025 2:25 PM, dbush wrote: >> On 3/15/2025 3:16 PM, olcott wrote: >>> On 3/15/2025 2:05 PM, dbush wrote: >>>> On 3/15/2025 2:55 PM, olcott wrote: >>>>> On 3/15/2025 12:39 PM, dbush wrote: >>>>>> On 3/15/2025 1:08 PM, olcott wrote: >>>>>>> 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 >>>>>>>> LP := ~True(LP) resolves to true >>>>>>>> >>>>>>>> Therefore the assumption that a correct True() predicate exists >>>>>>>> is proven false. >>>>>>> >>>>>>> When you stupidly ignore Prolog and MTT that >>>>>>> both prove there is a cycle in the directed graph >>>>>>> of their evaluation sequence. If you have no idea >>>>>>> what "cycle", "directed graph" and "evaluation sequence" >>>>>>> means then this mistake is easy to make. >>>>>>> >>>>>> >>>>>> That doesn't change the fact that >>>>> >>>>> You have just proven you are clueless about these things >>>>> by your next statement. >>>>> >>>>>> that ~True(LP) evaluates to true. >>>>>> >>>>> >>>>> When >>>>> LP := ~True(LP) True_Bearer(LP) == FALSE >>>> >>>> And by the above function, because True_Bearer(LP) == FALSE: >>>> >>> >>> Which means that LP cannot possibly be either TRUE or FALSE >>> and instead must be rejected as invalid input to a True(X) >>> predicate. >> >> False. The True() predicate must return "true" for true statements >> and false for *all other statements*. >> >> The fact that the True() you've defined *does* accept non-truth >> bearers and returns false for them shows you know this, but are being >> deliberately deceptive. >> >>> >>>> True(LP) == FALSE, then >>>> ~True(LP) == TRUE, so >>>> LP == TRUE >>>> >>>> Contradiction. Therefore the assumption that a correct True() >>>> predicate exists is proven false >>>> >>> >>> Likewise Truth_Bearer("ksdnf34589jknsdf34r87&%78^%78") == FALSE >>> >>> and on that basis we know that True(X) predicates cannot >>> exist because True(X) predicates must correctly determine >>> whether random gibberish is true or false. >>> >>> >> >> True(X) predicates must correctly determine >> whether random gibberish is true or *not true*. And because random >> gibberish is not true, True("ksdnf34589jknsdf34r87&%78^%78") must >> return false >> > > That is fine, and makes Tarski wrong. > Nope. Tarski uses a proof by contradiction. You know, that type of proof you still don't understand 50 years after learning it. He starts by assuming that a True() predicate exists in a system that can express the full properties of natural numbers. He then shows that it's possible to create in the system that can be shown in a meta system to effectively mean: LP := ~True(LP) Given that True(LP) == false, we then have ~True(LP) == true. And since ~True(LP) is the same as LP, that gives us LP == true. Contradiction. Therefore the assumption that a True() predicate exists is proven false.