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: Tue, 21 Jul 2020 11:31:04 -0700 Organization: None to speak of Lines: 71 Message-ID: <87a6zsu3dj.fsf@nosuchdomain.example.com> References: <871rl8dyg1.fsf@bsb.me.uk> <87lfjfovhm.fsf@bsb.me.uk> <87365mui5o.fsf@nosuchdomain.example.com> <9PCdnZ43HJ8Qy4vCnZ2dnUU7-a2dnZ2d@giganews.com> <87lfjdtvrb.fsf@nosuchdomain.example.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="10127"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19uBox4om8krJau5mfoqHph" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux) Cancel-Lock: sha1:7yVlviJ1FTTavtLcfBMFiG3l0pU= sha1:bU3K4UKQyyTxteXjfDF8qkBs0+c= Xref: csiph.com comp.theory:21845 comp.ai.philosophy:22177 comp.ai.nat-lang:2533 olcott writes: > On 7/20/2020 10:03 PM, Keith Thompson wrote: >> 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. > > You claimed: >>>That nothing in that formula means "this sentence"?<<> > I proved that you are wrong. There is not yes or no to it. Proving something requires more than just asserting it. > Do you understand that house bricks are a kind of baby kitten? > (yes or no). > > "Yes" you understand and agree, "no" you fail to understand. Neither "yes" nor "no" *in the sense that you've insisted on redefining those words* is accurate. I understand and disagree. Obviously. If I ignore your redefinition of "yes" and "no", then my answer would be "no", followed by a clarification (I do not "understand" things that I believe to be false). Note how I directly addressed the question that you asked. Try it some time. >> 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. So you claim that "φ ↔ ⊢φ" is a formulation of "This sentence is a theorem". In the English sentence "This sentence is a theorem", the phrase "This sentence" presumably refers to the sentence itself. In "φ ↔ ⊢φ", φ does not refer to the sentence itself, but to some other sentence. Let's name the sentence "φ ↔ ⊢φ" S. Then S asserts that φ is logically equivalent to φ's own provability. S is not a statement about S. If interpreted in English, S would not include the phrase "this sentence"; rather it might include the phrase "that sentence" to refer to φ. -- 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 */