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 V24 (Are we there yet?) Date: Mon, 13 Jul 2020 17:52:22 -0700 Organization: None to speak of Lines: 47 Message-ID: <87wo363ol5.fsf@nosuchdomain.example.com> References: <2tCdnb0urbddzpfCnZ2dnUU7-b_NnZ2d@giganews.com> <87k0z85tt0.fsf@nosuchdomain.example.com> <87d0505kmk.fsf@nosuchdomain.example.com> <5Lmdnehh4P6hLZbCnZ2dnUU7-LdQAAAA@giganews.com> <87365vnik3.fsf@bsb.me.uk> Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit Injection-Info: reader02.eternal-september.org; posting-host="4502a91299fcc6f473e7c6cd344f8c9a"; logging-data="9237"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+wjjglMHp3jlm7AJWHYCH7" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux) Cancel-Lock: sha1:3Kd4EWQvCQcpjWdoDY4DiDWJNaY= sha1:y+UUddfCQI4bvc0rsbeTn81Jq4c= Xref: csiph.com comp.theory:21638 comp.ai.philosophy:21969 comp.ai.nat-lang:2376 olcott writes: > On 7/13/2020 5:42 PM, Ben Bacarisse wrote: >> olcott writes: >>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>> >>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >>> Boolean value. >> >> Would you like to learn why that's wrong, or would you rather just keep >> repeating it? >> >> If you'd like to learn, you have to be a student. I'd ask a student to >> consider an instance of x + y = y + x in Q, for example this one: >> >> S0 + SS0 = SS0 + S0. >> >> and I'd ask them: what can you say about this formula in Q? > > How do you get from point "A" to point "B" when no path from point "A" > to point "B" exists? YOU DON'T !!! > > How do you show that an expression of language is true when there is > no mapping from this expression to Boolean values? YOU DON'T !!! > > How do you show that an expression of language of a formal system is > true in this formal system when there is no mapping in this formal > system from this expression to Boolean values? YOU DON'T !!! Please stop shouting. The post to which you're responding doesn't ask what you can say about x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) in Q. It asks what you can say about S0 + SS0 = SS0 + S0 in Q (or, using more standard notation, 1 + 2 = 2 + 1). What you can say about S0 + SS0 = SS0 + S0 in Q, if I'm not mistaken, is that it's both true and provable. It doesn't even touch on the points of disagreement that have been consuming this newsgroup. I'm sure that Ben has more things to say once that's established, things that you'll undoubtedly disagree with, but let's just start with S0 + SS0 = SS0 + S0, shall we? Without the shouting. -- 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 */