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 V23 (Newspeak) Date: Sun, 05 Jul 2020 16:40:24 -0700 Organization: None to speak of Lines: 68 Message-ID: <87zh8dbkev.fsf@nosuchdomain.example.com> References: <_LqdnXUL8tmZBp3CnZ2dnUU7-aXNnZ2d@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="40782449c3944e27d96f0e3a01ea599f"; logging-data="22729"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+O0rKAIen2o0kISgt1yYs5" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux) Cancel-Lock: sha1:o950w5jdE3nOh7O7lZA66FFSbag= sha1:EuHpDqrImhAdFZo2wVre/UvCKVM= Xref: csiph.com comp.theory:21461 comp.ai.philosophy:21656 comp.ai.nat-lang:2216 olcott writes: > On 7/4/2020 10:31 AM, André G. Isaak wrote: >> On 2020-07-04 09:06, olcott wrote: [...] >>> Whenever-so-ever there is no connected chain of inference from the >>> WFF premises to the WFF conclusion we have an invalid argument. >> >> But how does that help get around incompleteness? > > In order to use the term "incompleteness" correctly and not as > misnomer a thing must be incomplete relative to something that is > missing. Why? > When Q lacks commutativity then Q is incomplete relative to > commutativity. To assign terms of the art tho meanings having nothing > to do with their base meaning is a bastardization of the communication > process. No, it's a use of well defined terminology in a technical field. There is a long tradition in technical fields of redefining English words with narrower and more precise meanings. (I could give you multiple examples from computer science.) We can either repurpose existing words or invent new ones. Experience has generally shown that repurposing existing words tends to work better. The word "incompleteness" has a well defined and rigorous meaning in the context of mathematical logic. Gödel's incompleteness theorem refers to that meaning, not to any meaning you might see in an English (or German) dictionary. If you dislike the way the English word "incompleteness" is used in mathematical logic, that's fine. If you insist on using the word "incompleteness" in its English sense while discussing mathematical logic, that's just going to cause confusion. You claim to have disproven Gödel's incompleteness theorem. You can do so *only* if you disprove what Gödel stated about incompleteness in the way that word is unambiguously defined in mathematical logic. Nothing you say about "incompleteness" in the sense in which an English dictionary might define it is relevant to Gödel's incompleteness theorem. I'll admit that I don't fully understand a lot of what you've written here. But I wonder whether your refusal to accept the technical use of English words, particularly your refusal to accept the way "incompleteness" is defined in mathematical logic, might be the root of your error. Somebody (I don't remember who) suggested using the otherwise meaningless term "fnord" to refer to the kind of incompleteness Gödel talked about. Would you consider that? Or perhaps you'd consider talking about "Gödel-incompleteness" and restricting its meaning to the technical definition? (Gödel didn't invent the idea, but "Gödel-incompleteness" is as good a term as any.) (Note that using "incompleteness" with a technical sense in the context of mathematical logic doesn't deprive us of the ability to use it with its ordinary English meaning in other contexts.) [SNIP] -- 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 */