Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.logic Subject: Re: This is how I overturn the Tarski Undefinability theorem Date: Tue, 3 Sep 2024 22:28:07 -0400 Organization: i2pn2 (i2pn.org) Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 4 Sep 2024 02:28:07 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="771834"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird Content-Language: en-US In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 4579 Lines: 96 On 9/3/24 8:44 AM, olcott wrote: > 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 But Prolog can not express ALL logical statement. > >> 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. But the set of Prolog operations are limited compared to logic. > >> Consequently some goals may evaluate >> to true in some implementations and false in others, for example >> >>   L = [L]. >> > >