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: comp.theory,sci.logic Subject: Re: H(D,D) cannot even be asked about the behavior of D(D) --- Truth Itself is not Broken. (Just misunderstood) Date: Sat, 15 Jun 2024 09:44:15 -0500 Organization: A noiseless patient Spider Lines: 49 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 15 Jun 2024 16:44:16 +0200 (CEST) Injection-Info: dont-email.me; posting-host="65be3053bb2d9b452c13d5ddc3153d90"; logging-data="3682461"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX194mMIcGslK0rlTQdDogtI5" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ety6FvVaz4nTo6Ku9+lyRHKRX9w= In-Reply-To: Content-Language: en-US Bytes: 4215 On 6/15/2024 8:52 AM, Richard Damon wrote: > On 6/15/24 8:26 AM, olcott wrote: >> On 6/15/2024 6:48 AM, joes wrote: >>> Am Fri, 14 Jun 2024 21:39:50 -0500 schrieb olcott: >>> >>>> The key aspect of all of this is that if the halting problem is correct >>>> then truth itself is fundamentally broken. Since truth itself cannot >>>> possibly be fundamentally broken it must be fallible human >>>> understanding >>>> of truth that is actually broken. >>> I've got bad news for you, and you're a century late. Gödel proved that >>> not all true statements are provable. It sure would have been nice. >>> >> >> He didn't even prove this. >> He proved that a statement that can be expressed in PA >> cannot be proving in PA that is not true in PA yet can be >> proved in matamath thus is true in metamath. > > No, you are just showing you don't know what you are talking about. > > You have admitted that you don't even understand the actual statement he > was using, but can only understand it as the simplication through > implication in the meta-thoery. > > G, the statement about the non-existance of a Natural Number 'g' that > satisfied the specified relationship. > > It can be shown (in the meta-theory) that no such number can exist, so G > must be true. Either the number 'g' exists or it doesn't so their can be > no middle ground, and it if is shown (in the meta theory) that if such a > number 'g' existed, then we could build a proof (as encoded in the > finite number 'g') in PA that PROVES CONCLUSIVELY no such number exist. *This is the crux of your correct insight* > There can not be a number that proves that itself doesn't exist, so > there must not be such a number. > There can be no proof in PA that G cannot be proven in PA because such a proof in PA requires a sequence of inference steps in PA that prove that they themselves do not exist. *To sum this up in my terminology G has no truthmaker in PA* -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer