Path: ...!feeds.phibee-telecom.net!2.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: This is how I overturn the Tarski Undefinability theorem Date: Sat, 7 Sep 2024 08:06:52 -0500 Organization: A noiseless patient Spider Lines: 113 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 07 Sep 2024 15:06:53 +0200 (CEST) Injection-Info: dont-email.me; posting-host="fc36cd944b9fa7fa30157002795d809b"; logging-data="1449925"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+0B62KsaiIeYxbiLUQ259H" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:UCsxsb5MvVG4n1YEDSAfJDJFL8Q= In-Reply-To: Content-Language: en-US Bytes: 5819 On 9/7/2024 3:35 AM, Mikko wrote: > On 2024-09-06 12:22:04 +0000, olcott said: > >> On 9/6/2024 6:55 AM, Mikko wrote: >>> On 2024-09-03 12:44:00 +0000, olcott said: >>> >>>> On 9/3/2024 5:38 AM, Mikko wrote: >>>>> On 2024-09-02 13:01:23 +0000, olcott said: >>>>> >>>>>> On 9/2/2024 2:54 AM, Mikko wrote: >>>>>>> On 2024-09-01 13:47:00 +0000, olcott said: >>>>>>> >>>>>>>> On 9/1/2024 7:52 AM, Mikko wrote: >>>>>>>>> On 2024-08-31 18:48:18 +0000, olcott said: >>>>>>>>> >>>>>>>>>> *This is how I overturn the Tarski Undefinability theorem* >>>>>>>>>> An analytic expression of language is any expression of formal >>>>>>>>>> or natural language that can be proven true or false entirely >>>>>>>>>> on the basis of a connection to its semantic meaning in this >>>>>>>>>> same language. >>>>>>>>>> >>>>>>>>>> This connection must be through a sequence of truth preserving >>>>>>>>>> operations from expression x of language L to meaning M in L. >>>>>>>>>> A lack of such connection from x or ~x in L is construed as x >>>>>>>>>> is not a truth bearer in L. >>>>>>>>>> >>>>>>>>>> Tarski's Liar Paradox from page 248 >>>>>>>>>>     It would then be possible to reconstruct the antinomy of >>>>>>>>>> the liar >>>>>>>>>>     in the metalanguage, by forming in the language itself a >>>>>>>>>> sentence >>>>>>>>>>     x such that the sentence of the metalanguage which is >>>>>>>>>> correlated >>>>>>>>>>     with x asserts that x is not a true sentence. >>>>>>>>>>     https://liarparadox.org/Tarski_247_248.pdf >>>>>>>>>> >>>>>>>>>> Formalized as: >>>>>>>>>> x ∉ True if and only if p >>>>>>>>>> where the symbol 'p' represents the whole sentence x >>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf >>>>>>>>>> >>>>>>>>>> *Formalized as Prolog* >>>>>>>>>> ?- LP = not(true(LP)). >>>>>>>>>> LP = not(true(LP)). >>>>>>>>> >>>>>>>>> According to Prolog semantics "false" would also be a correct >>>>>>>>> response. >>>>>>>>> >>>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>> false. >>>>>>>>> >>>>>>>>> To the extend Prolog formalizes anything, that only formalizes >>>>>>>>> the condept of self-reference. I does not say anything about >>>>>>>>> int. >>>>>>>>> >>>>>>>>>> When formalized as Prolog unify_with_occurs_check() >>>>>>>>>> detects a cycle in the directed graph of the evaluation >>>>>>>>>> sequence proving the LP is not a truth bearer. >>>>>>>>> >>>>>>>>> Prolog does not say anything about truth-bearers. >>>>>>>>> >>>>>>>> >>>>>>>> It may seem that way if you have no idea what >>>>>>>> (a) a directed is >>>>>>>> (b) what cycles in a directed graph are >>>>>>>> (c) What an evaluation sequence is >>>>>>> >>>>>>> More relevanto would be what a "truth-maker" is. >>>>>>> Anyway, it seems that Prolog does not say anything about >>>>>>> truth-bearers because Prolog does not say anything about >>>>>>> truth-bearers. >>>>>>> >>>>>> >>>>>> When Prolog derives expression x from Facts and Rules >>>>>> by applying the truth preserving operations of Rules to >>>>>> Facts is the truthmaker for truth-bearer x. >>>>> >>>>> A Prolog impementation applies Prolog operations. >>>> >>>> Which are (like logic) for the most part truth preserving. >>>> If (A & B) then A >>> >>> Logic where the infoerence rules are for the most part truth prserving >>> is not useful. They all must be. >>> >>>>> For some cases >>>>> Prolog offers several operations letting the implementation to >>>>> choose which one to apply. >>>> >>>> I don't thing so. Once the Facts and Rules are specified >>>> Prolog chooses whatever Facts and Rules to prove x or not. >>>> It is back-chained inference. >>> >>> Standard Prolog is what the Prolog standard says. Conforming >>> implementations >>> may vary if the standard allows. If you think otherwise you are wrong. >>> There are also non-starndard Prlongs that vary even more. >>> >> >> The fundamental architectural overview of all Prolog implementations >> is the same True(x) means X is derived by applying Rules (AKA truth >> preserving operations) to Facts. > > The details are permitted to differ. > Instead of using any single order of logic we simultaneously represent an arbitrary number of orders of logic in a type hierarchy knowledge ontology. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer