Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: Ben Bacarisse Newsgroups: comp.theory Subject: Re: Simply defining =?iso-8859-1?Q?G=F6del?= Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Date: Wed, 29 Jul 2020 00:51:29 +0100 Organization: A noiseless patient Spider Lines: 60 Message-ID: <87k0ynb3lq.fsf@bsb.me.uk> References:

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<87y2n3b8tz.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="eb5022662cee60539f7271085a052fb7"; logging-data="17367"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+9O0ZPbZ1df3nK9XxD5OfqENrruysOozg=" Cancel-Lock: sha1:pXTaR9y7CXY7Mjl/psW5IgUwfGo= sha1:mQvCa/MxT590sW5Eyn6dqMu5FxA= X-BSB-Auth: 1.e4fbfcb324acac455eb4.20200729005130BST.87k0ynb3lq.fsf@bsb.me.uk Xref: csiph.com comp.theory:22000 olcott writes: > On 7/28/2020 4:58 PM, Ben Bacarisse wrote: >> olcott writes: >> >>> On 7/28/2020 11:40 AM, olcott wrote: >> >>> That you cannot possibly imagine a particular individual human out of >>> the set of humans seems quite disingenuous. >> >> That you can think I can't imagine a a particular individual human out >> of the set of humans seems to suggest you don't know what I'm saying. >> >>> It seems so disingenuous that you have seemed (from my perspective) to >>> have turned into an internet troll. >> >> You need to decide. If you think I am a troll, you should not reply. >> You will be wasting your time. >> >> If you think I am a knowledgeable person who has offered to help you work >> through a textbook then you need to apologise. >> >> ∃b ∈ Balls ∃c ∈ Courts (b ∈ c ∧ your(c)) > > Recently you have been perfectly reasonable Is that what passes for an apology in PO-land? > except on the relation "father of" referring to an order pair > of unique individuals in the domain of humans. If you keep subtly altering what you say, my objection will be subtly different too. You will think I'm changing my mind (or being disingenuous) but I'm just responding to what you actually write. Here, I am glad to see you have written "father of" as if it were and ordinary English phrase. That's what Mendelson did, so I am happy to assume you mean the same relationship he did. If, instead, you make it look like a symbol (as you have done) and maybe give it arguments (especially arguments that look like constants in Mendelson's notation) it becomes a predicate or a formula and could mean anything depending on the interpretation. > if {a26, a87} are a pair of baby girls then we can know that the > "father of" relation is not satisified by the ordered pair . You are free to make up your own notation, but you are using two symbols that Mendelson uses for constants. This can lead to confusion. Humans very often have names, so you could have said "if {Jane, Aisha} are a pair of baby girls then we can know that the "father of" relation is not satisified by the ordered pair ". Has you said that, I'd just say "yup". As it is, I have to ask why are you using what look like constants as elements of the domain? If you don't what to be specific, at least write <(a26)^M, (a87)^M>. -- Ben.