Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: Keith Thompson Newsgroups: comp.theory,comp.ai.philosophy,comp.ai.nat-lang,sci.lang.semantics Subject: Re: Simply defining =?utf-8?Q?G=C3=B6del?= Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Date: Mon, 20 Jul 2020 20:03:20 -0700 Organization: None to speak of Lines: 39 Message-ID: <87lfjdtvrb.fsf@nosuchdomain.example.com> References: <871rl8dyg1.fsf@bsb.me.uk> <87lfjfovhm.fsf@bsb.me.uk> <87365mui5o.fsf@nosuchdomain.example.com> <9PCdnZ43HJ8Qy4vCnZ2dnUU7-a2dnZ2d@giganews.com> Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit Injection-Info: reader02.eternal-september.org; posting-host="9cb5fddfb6baba36cf4dbcb45e564783"; logging-data="13232"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+PVX3GB/qrGozCnVMUlZQB" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux) Cancel-Lock: sha1:lplMJ7s0iKtgd0ManQYQ8/sif2Q= sha1:u2/KeQNysKRJM0Af4PGafMK9+GI= Xref: csiph.com comp.theory:21835 comp.ai.philosophy:22165 comp.ai.nat-lang:2524 olcott writes: > On 7/20/2020 1:59 PM, Keith Thompson wrote: >> olcott writes: >>> On 7/20/2020 12:15 AM, André G. Isaak wrote: >>>> On 2020-07-19 22:52, olcott wrote: >>>>> Here is the formalization of the sentence: "This sentence is a theorem" >>>>> φ ↔ ⊢φ >>>> >>>> That isn't a formalization of 'this sentence is a theorem'. It is a >>>> statement about some other formula, φ, which you have not given an >>>> interpretation. >>> >>> Like the liar Paradox and Gödel's >>> We are therefore confronted with a proposition which asserts >>> its own unprovability.15 >>> The truth teller paradox has no interpretation. Its meaning is vacuous. >> >> Do you understand that >> φ ↔ ⊢φ >> is *not* a formalization of "this sentence is a theorem? That nothing >> in that formula means "this sentence"? >> >> Yes or no, please. >> >> [...] > > φ ↔ ⊢φ > φ is logically equivalent to its own provability. Response ignored. Yes or no, please. If you respond to be above question starting with either "yes" or "no" or "neither yes nor no would be an accurate answer" with some attempt to explain why, I will consider replying. -- Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com Working, but not speaking, for Philips Healthcare void Void(void) { Void(); } /* The recursive call of the void */