Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth Date: Tue, 25 Feb 2025 23:02:13 -0600 Organization: A noiseless patient Spider Lines: 67 Message-ID: References: <7e532aaf77653daac5ca2b70bf26d0a3bc515abf@i2pn2.org> <0f7cd503773838ad12f124f23106d53552e277b8@i2pn2.org> <651817a6f69ac3ebe6f1525f2e8588c6aa164c7b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Wed, 26 Feb 2025 06:02:14 +0100 (CET) Injection-Info: dont-email.me; posting-host="be1a41fcc27cfa869ea1b51d56f1df7a"; logging-data="2555772"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18BnqH0a+PwhAUHN5fYlJHS" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:mSxmaqEN+EbmVspYLM9FwFCxNbo= X-Antivirus-Status: Clean In-Reply-To: <651817a6f69ac3ebe6f1525f2e8588c6aa164c7b@i2pn2.org> Content-Language: en-US X-Antivirus: Norton (VPS 250225-8, 2/25/2025), Outbound message On 2/25/2025 10:21 PM, Richard Damon wrote: > On 2/25/25 4:10 PM, olcott wrote: >> On 2/25/2025 9:35 AM, Mikko wrote: >>> On 2025-02-24 21:44:10 +0000, olcott said: >>> >>>> On 2/24/2025 2:58 AM, Mikko wrote: >>>>> On 2025-02-22 18:42:44 +0000, olcott said: >>>>> >>>>>> On 2/22/2025 3:25 AM, Mikko wrote: >>>>>>> On 2025-02-22 04:44:35 +0000, olcott said: >>>>>>> >>>>>>>> On 2/21/2025 7:05 PM, Richard Damon wrote: >>>>>>>>> On 2/21/25 6:19 PM, olcott wrote: >>>>>>>>>> On 2/20/2025 2:54 AM, Mikko wrote: >>>>>>>>>>> On 2025-02-18 03:59:08 +0000, olcott said: >>>>>> >>>>>> >>>>>>>>>> Tarski anchored his whole proof in the Liar Paradox. >>>>>>>>>> >>>>>>>>> >>>>>>>>> By showing that given the necessary prerequisites, The >>>>>>>>> equivalent of the Liar Paradox was a statement that the Truth >>>>>>>>> Predicate had to be able to handle, which it can't. >>>>>>>>> >>>>>>>> >>>>>>>> It can be easily handled as ~True(LP) & ~True(~LP), Tarski just >>>>>>>> didn't think it through. >>>>>>> >>>>>>> No, it can't. Tarski requires that True be a predicate, i.e, a truth >>>>>>> valued function of one term. >>>>>> >>>>>> It does not matter a whit what the Hell his misconceptions >>>>>> required. >>>>> >>>>> It is not required by any misconception. It is required by the >>>>> meanings of the words and symbols, in particular "predicare" >>>>> and "~". >>>> >>>> That none of modern logic can handle expressions >>>> that are not truth bearers is their error and >>>> short-coming. >>> >>> Why should any logic permit formulas that are not truth-bearers? >>> (Of course, term expressions are not truth-bearers.) >>> >> >> Undecidable expressions are only undecidable because they >> are not truth bearers. Logic ignores this and faults the >> system and not the expression >> > > Nope. And "expressions" are not "undecidable", but "Problems" are. > A specific problem instance is a single finite string expression input to a specific decider. > You seem to have a fundamental problem with the meaning of the words, > likely because you can't handle the needed abstractions. > > Of course, since you don't understand what a "program" is, you never > were on a good track. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer