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 22:18:36 -0400 Organization: A noiseless patient Spider Lines: 153 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 03:18:36 +0100 (CET) Injection-Info: dont-email.me; posting-host="67c63d6f95dcce4899f1b1432e20e56d"; logging-data="844941"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18S8PXUokzSg1nM8ZmbZd9U" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:jShrwhFDeEECVOOty+ge/4QaXUg= In-Reply-To: Content-Language: en-US Bytes: 7261 On 3/15/2025 9:47 PM, olcott wrote: > On 3/15/2025 8:27 PM, dbush wrote: >> 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. > > True(LP) == FALSE And ~True(LP) == TRUE Therefore LP == TRUE Contradiction. Therefore the assumption that a True() predicate exists is proven false