Path: 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: Sat, 15 Mar 2025 22:34:15 -0500 Organization: A noiseless patient Spider Lines: 196 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 04:34:16 +0100 (CET) Injection-Info: dont-email.me; posting-host="33de22785a11a76beb5897cc3eba332a"; logging-data="940032"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX188yBEif0wGs7hnj2J/aDWN" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:XF83fytEa5v6P6MD3Iyy8jRcB8w= X-Antivirus: Norton (VPS 250315-4, 3/15/2025), Outbound message X-Antivirus-Status: Clean In-Reply-To: Content-Language: en-US On 3/15/2025 10:05 PM, dbush wrote: > On 3/15/2025 10:52 PM, olcott wrote: >> On 3/15/2025 9:41 PM, dbush wrote: >>> On 3/15/2025 10:27 PM, olcott wrote: >>>> On 3/15/2025 9:18 PM, dbush wrote: >>>>> 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 ========== REMAINDER OF ARTICLE TRUNCATED ==========