Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: Ben Bacarisse Newsgroups: comp.theory,comp.ai.philosophy,comp.ai.nat-lang,sci.lang.semantics Subject: Re: Simply defining =?iso-8859-1?Q?G=F6del?= Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Followup-To: comp.theory Date: Fri, 17 Jul 2020 02:17:38 +0100 Organization: A noiseless patient Spider Lines: 90 Message-ID: <87wo33ey8d.fsf@bsb.me.uk> References: <87d0505kmk.fsf@nosuchdomain.example.com> <5Lmdnehh4P6hLZbCnZ2dnUU7-LdQAAAA@giganews.com> <87365vnik3.fsf@bsb.me.uk> <87a703lz5c.fsf@bsb.me.uk> <87pn8ykrwq.fsf@bsb.me.uk> <7e-dnQpoj9jkoZPCnZ2dnUU7-UHNnZ2d@giganews.com> <875zapk0bb.fsf@bsb.me.uk> <87lfjkixu6.fsf@bsb.me.uk> <87y2nkguqv.fsf@bsb.me.uk> <87h7u7h54e.fsf@bsb.me.uk> <8rKdnZAbAoVsOo3CnZ2dnUU7-efNnZ2d@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="d774e632b9332d91bd15325dc48bc89e"; logging-data="621"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/BJaaNYgncctKi883It6v9aEkvIfMB5pw=" Cancel-Lock: sha1:JoalobgtMAtjlgC7szy1wExnmLs= sha1:YTgeiUCjVepDvg+0wuXBnPrverg= X-BSB-Auth: 1.9e7c7f0ad89592bb0876.20200717021738BST.87wo33ey8d.fsf@bsb.me.uk Xref: csiph.com comp.theory:21721 comp.ai.philosophy:22070 comp.ai.nat-lang:2445 olcott writes: > On 7/16/2020 10:05 AM, Ben Bacarisse wrote: >> olcott writes: >> >>> On 7/15/2020 7:37 PM, Ben Bacarisse wrote: >>>> olcott writes: >>>> >>>>> On 7/15/2020 12:32 PM, André G. Isaak wrote: >> >>>>>> The example was originally offered by me as x + y = y + x which *is* >>>>>> a WFF of Q. You are the one who keeps insisting on adding extraneous >>>>>> symbols to every formula you come across. >>>>> >>>>> You know that the "extraneous" symbols are not extraneous at all >>>>> because they transform the expression into the commutativity of >>>>> addition and without them the commutativity of addition is not >>>>> expressed. >>>> >>>> No. Commutativity is expressed as ∀x ∀y x + y = y + x (or just x + y = >>>> y + x if you prefer). This expresses the commutativity of the two-place >>>> function symbol + for /any/ theory that has a + operation (Q being the >>>> example we are interested in here). >>> >>> Great. I need this sort of generality. >> >> No, because x+y=y+x is provable, refutable, not provable, not refutable >> or not even well formed depending on the context. To have a sentence so >> general that you can say nothing useful about it will not help you. > > So you forgot that the context is Q? No, I am advising you forget about the gentility and limit yourself to Q. If you do the exercise I suggested you could find out the exact status if x+y=y+x in Q for yourself. >> Understanding what everyone else means by true will help you a lot, but >> you don't seem to want learn. > > The only thing that I want to make sure that I do not ever "learn" is > to believe that the key common misconceptions are true. I don't want you to "learn" anything, I want you to learn. I want you to learn what theories and formulas in them mean. That will enable you to talk about them. You can even reject all out silly meanings like something being true and replace them with your own (though no one will care) but at least you will not appear to be ignorant and will be able to discuss the topic in away other will understand. The reason I am proposing you do some exercises is that you will learn by finding out for yourself. If you can come up with two distinct models of Q for yourself I imagine you will have an "aha" moment. It's a very powerful learning method. > Because of the way that {true} really works {true} and unprovable is > utterly impossible. You have a very limited view of what is possible. If you tried to learn this stuff you would find a whole world of possibilities you have not yet even imagined. > I understand that Q defines natural numbers so that Q does not assume > natural numbers. Q defines them as whatevers that have a successor > function. Ah, so you don't even know what Q is. It does not define the natural numbers. You might have to review the axioms before even trying to come up with one model of Q. >> Can you just state, once and for all, that you have no intention of >> trying to do the exercises that I think will help you to understand this >> subject? That way I can just walk away. I still think there is a tiny >> chance you might want to know what true means to everyone else and why >> neither x+y=y+x (nor its negation) is provable in Q. > > If you can show me what true means to everyone else such that your > explanation very succinctly applies to every formal system that can > possibly exist you can go ahead. There is no point. If you don't know what a model is -- and it seems you don't since coming up with even one model of Q is currently beyond you -- you can't possibly understand what truth means. Just tell me you don't want to do the work and I'll leave you to pontificate about stuff you don't want to lean. If you do want to learn, you might have to ask me what a model is because I don't think you understand the basic idea yet. -- Ben.