Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.logic Subject: Re: The key undecidable instance that I know about Date: Mon, 10 Mar 2025 07:04:54 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <7cd6d8a1477fce2ef564f74f49ebbff8074ad11b@i2pn2.org> References: <3b57384a57c71e1880fe3f1df975003c1d743c07@i2pn2.org>

<9a2fbcc7a803bc91d320117f8c8e03e03799e9b3@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 10 Mar 2025 11:04:55 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="3714055"; 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: 6486 Lines: 146 On 3/9/25 11:39 PM, olcott wrote: > On 3/9/2025 8:57 PM, Richard Damon wrote: >> On 3/9/25 6:28 PM, olcott wrote: >>> On 3/9/2025 4:43 PM, Richard Damon wrote: >>>> On 3/9/25 4:08 PM, olcott wrote: >>>>> On 3/9/2025 2:24 PM, Richard Damon wrote: >>>>>> On 3/9/25 1:15 PM, olcott wrote: >>>>>>> Is the Liar Paradox True or False? >>>>>>> >>>>>>> LP := ~True(LP) >>>>>>> >>>>>>> ?- LP = not(true(LP)). >>>>>>> LP = not(true(LP)). >>>>>>> >>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>> false. >>>>>>> >>>>>>> Its infinitely recursive structure makes it neither true nor false. >>>>>>> >>>>>> >>>>>> >>>>>> The liar's paradox isn't an "undecidable" instance, as >>>>>> "undecidable" is about a problem that has a true or false answer >>>>>> that can not be computed for every case. >>>>>> >>>>> >>>>> Tarski thought that is was undecidable and anchored his >>>>> whole proof in it. >>>>> >>>>> 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 >>>> >>>> Note, he says to construct the antinomy of the liar in the >>>> METALANGUAGE representing the statement x in the LANGUAGE. Thus "x" >>>> is *NOT* the liar, but something that with the additional >>>> information of the metalanguage can be reduced to it. >>>> >>> >>> "the antinomy of the liar in the metalanguage" >>> >>> {the antinomy of the liar in the metalanguage} >> >> So, you admit you don't understand what that means? >> >> Do you understand the differene between the metalanguage and the >> language? >> >> You do understand that the whole proof is about the Truth Predicate in >> the LANGUAGE, not the Metalanguage. >> >>> >>> And my understanding of his metalanguage that I have >>> had for several years and just refreshed from the >>> original source material does seem to prove that >>> this does mean that Tarski did anchor his whole >>> proof in the antinomy of the liar. >> >> And clearly you don't understand the meaning of the metalanguage. >> >> Note, the antinomy of the liar in the metalanguage is a result that >> comes from the actual statement "x", that is in the language gets >> manipulated based on new concepts from the metalanguage allowing it to >> be simplifed. >> > > That does not really show any depth of understanding. > You might have greater depth, yet did not show it yet. No, your reply, by not addressing *ANY* of > >> Your ignorance of how that is done is NOT an error on Tarski's part, >> just stupidity on yours. >> > > Yet you never said how it should be done, thus I > have no way to tell what you say is not pure bluster. > Maybe because what you want to define can't be. Tarski shows how to derive that part in the earlier work. It is clear that you just don't have the brains to understand that discussion, and it isn't my job to educate you on that, particularly when you have declared that you idea of logic fundamentally disagrees with the actual rules of logic, so you fundamentally don't understand how to use logic. > That you refer to my stupidity yet fail to point out any > mistake seems to be strong evidence that you are clueless. Sure I have pointed out your error. You are just too stupid to recognize the. > >>> >>> Until you provide ALL OF THE REASONING PROVIDING >>> ALL OF THE DETAILS OF EXACTLY HOW I AM WRONG >>> it seems reasonable to conclude that you do not >>> have any of these details and only have pure bluster. >>> >> >> Not my job. >> >> You need to point to the actual logical step you think Tarski got >> wrong, not a conclusion you disagree with. >> > > Yu failure to understand what i said is not my mistake, I.E. your claim is that you don't understand the error pointed out to you means the error wasn't pointed out to you. Part of your problem is you create a world of strawmen as you start with the fraud that claim you get to redefine the basic words of the logic system, which you don't. A Basic property of logic is that you can't prove something if your premises aren't true. > >> In particular, you need to show a claim he makes that is not supported >> by what he has shown or from valid logical reasoning. Note, you can't >> alter the rules of logic to be something different than what Tarski is >> using, or you are just admitting that you don't know what you are >> talking about. >> > > LP := ~True(LP) DOES SPECIFY INFINITE RECURSION. Yex, but isn't the way to express the statement "x" Thus, your agruments that LP isn't validly defined is just a strawman. > >> Note, the paragraph you quote from page 248 isn't making a new claim, >> but is pulling forward from his previous work, so if you disagree with >> that step, you need to show how it doesn't follow from that previous >> work, or the error in that previous work. Your not understanding it is >> n0t finding an error in it. > >