Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: Keith Thompson Newsgroups: comp.theory Subject: Re: Simply defining =?utf-8?Q?G=C3=B6del?= Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Date: Sun, 02 Aug 2020 18:04:39 -0700 Organization: None to speak of Lines: 78 Message-ID: <87sgd48rq0.fsf@nosuchdomain.example.com> References: <87ft9bd1nz.fsf@bsb.me.uk> <87a6zjcu95.fsf@bsb.me.uk> <874kprcno2.fsf@bsb.me.uk> <87h7trb36f.fsf@bsb.me.uk> <87wo2m80lf.fsf@bsb.me.uk> <87y2n17r40.fsf@bsb.me.uk> <87wo2j42ek.fsf@bsb.me.uk> <87wo2i2jyk.fsf@bsb.me.uk> <87lfiy2bmg.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="86706e5582ecee2408f4b05921e91782"; logging-data="27881"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1//7LiOoaC/Y57cvRlR49Pb" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux) Cancel-Lock: sha1:rHz2j+VbuoGOD0j7T7vecCPCX0U= sha1:q53kqDJ/Vhsamphr789JocRcUN8= Xref: csiph.com comp.theory:22092 olcott writes: > On 8/1/2020 6:24 PM, Ben Bacarisse wrote: >> olcott writes: >> >>> On 8/1/2020 3:24 PM, Ben Bacarisse wrote: >>>> olcott writes: >>>> >>>>> On 7/31/2020 7:48 PM, Ben Bacarisse wrote: >>>>>> olcott writes: >>>>>> >>>>>>> I never claimed to have an all knowling membership algorithm. >>>>>> >>>>>> You claimed an impossible membership algorithm. Even some very narrowly >>>>>> defined sets of strings don't have membership algorithms. >>>>> >>>>> It only seems that way because these strings are members of the empty >>>>> set. The set of all integers > 10 and < 3. >>>> >>>> You are lost. These are trivial. Of course there is a membership >>>> algorithm for those. >>> >>> ∀x ∈ ℤ (x > 10 ∧ x < 3) >> >> What's that supposed to tell me? Do you doubt that a membership >> algorithm exists for the set of integers > 10 and < 3? I am pretty >> certain you don't think so, so why are you arguing the point? > > You must be high on crack to believe that there are ingters that are > simutanously less than three and greater than 10. Be less rude. I presume you don't really believe that Ben thinks there are any integers that are less than 3 and greater than 10. He has said nothing to imply that he does think that. Now it's possible that Ben might write something that implies, or seems to imply, that he holds that belief. (I don't think he has, but he could. We all make mistakes.) If he did write such a thing, it would not be plausible to assume that Ben actually believes that there are integers simultaneously less than 3 and greater than 10. It would be far more reasonable to assume that Ben unintentionally wrote something that implies that. Or it's possible that you misinterpreted what he wrote (no shame in that, we all make mistakes). Given such an occurrence, you could *ask for clarification*. For example, "Ben, what you wrote seems to imply that there are integers that are simultaneously less than 3 and greater than 10. Of course we both know there aren't. Can you clarify?" Replying with "You must be high on crack" just makes you look foolish. Looking at what Ben *actually wrote*, and summarizing it in my own words, he said that there is a membership algorithm to determine whether a given integer is a member of the set of integers that are both less than 3 and greater than 10. Expressing it in code (because I'm a programmer), we might write: bool IsGreaterThan3AndLessThan10(int n) { return n < 3 && n > 10; } or, equivalently: bool IsGreaterThan3AndLessThan10(int n) { return false; } Before that, Ben said that *some* sets of strings do not have membership algorithms, and you tried and failed to refute that by showing a set (that happens to be empty) that *does* have a membership algorithm. To be clear, Ben said that some sets have membership algorithms, and some do not. Your single example is not relevant. You also wrote ∀x ∈ ℤ (x > 10 ∧ x < 3) for some reason that neither Ben nor I can discern, and that you have declined to explain coherently. (It is, of course, a false statement. I presume you know that.) [...] -- 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 */