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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 <polcott333@gmail.com> 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: <v4k9bv$3gc4t$5@dont-email.me> References: <v45tec$4q15$1@dont-email.me> <v4d991$3qbnc$1@i2pn2.org> <v4da12$1sioe$1@dont-email.me> <v4dbmf$3qbnc$3@i2pn2.org> <v4dcd6$1sioe$3@dont-email.me> <v4df0h$3qbnd$1@i2pn2.org> <v4dhf5$1tsdf$2@dont-email.me> <v4dja1$3qbnd$5@i2pn2.org> <v4djhf$1tsdf$6@dont-email.me> <v4dk7b$3qbnc$8@i2pn2.org> <v4dl3b$225kb$1@dont-email.me> <v4dn5u$3qbnd$8@i2pn2.org> <v4dop4$22o4a$2@dont-email.me> <v4dq07$3qbnc$12@i2pn2.org> <v4dqq0$2353n$1@dont-email.me> <v4el9m$3rsd6$3@i2pn2.org> <v4f3ec$2akmh$2@dont-email.me> <v4g65a$3tn6q$1@i2pn2.org> <v4g6vr$2ic0g$1@dont-email.me> <v4gc0b$3tn6r$6@i2pn2.org> <v4gcjc$2msea$1@dont-email.me> <v4geab$3tn6r$8@i2pn2.org> <v4gg0s$2nim8$2@dont-email.me> <v4ha63$3v16r$2@i2pn2.org> <v4hfq9$2sdqr$5@dont-email.me> <v4ijlc$kqh$1@i2pn2.org> <v4injg$348ha$1@dont-email.me> <v4iraj$kqh$4@i2pn2.org> <v4isva$392jh$2@dont-email.me> <v4itis$kqh$7@i2pn2.org> <v4iutm$39bc0$1@dont-email.me> <v4jv2n$222a$2@i2pn2.org> <v4k18r$3f0hc$4@dont-email.me> <v4k6ag$2218$7@i2pn2.org> 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: <v4k6ag$2218$7@i2pn2.org> 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