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.nat-lang,sci.lang.semantics Subject: Re: Simply defining =?iso-8859-1?Q?G=F6del?= Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Followup-To: comp.theory Date: Tue, 21 Jul 2020 01:52:11 +0100 Organization: A noiseless patient Spider Lines: 192 Message-ID: <87tuy1ofk4.fsf@bsb.me.uk> References: <87a7001bhr.fsf@nosuchdomain.example.com> <87sgdrz49w.fsf@nosuchdomain.example.com> <874kq7yug9.fsf@nosuchdomain.example.com> <4dKdnXavpI9eu4zCnZ2dnUU7-S3NnZ2d@giganews.com> <87ft9qy3cn.fsf@nosuchdomain.example.com> <87imelefjh.fsf@bsb.me.uk> <87d04ser16.fsf@bsb.me.uk> <875zakwk73.fsf@nosuchdomain.example.com> <87v9ikcjdv.fsf@bsb.me.uk> <87k0yzcmhl.fsf@bsb.me.uk> <8fKdndiKLplIMYnCnZ2dnUU7-RvNnZ2d@giganews.com> <87ft9not86.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="0eaeff4ffd7c44356abe7202ef35462e"; logging-data="13724"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+BDbtT69Q8pMIN/jS730ZUa6gO6cUhLlU=" Cancel-Lock: sha1:NtT1mzL9/SvKw9/in7yrse5KTs0= sha1:ufhUgao8O6vOGA+szkGJkTsH+dU= X-BSB-Auth: 1.49d437aedb02d85df2a4.20200721015211BST.87tuy1ofk4.fsf@bsb.me.uk Xref: csiph.com comp.theory:21829 comp.ai.nat-lang:2520 olcott writes: > On 7/19/2020 8:44 PM, Ben Bacarisse wrote: >> olcott writes: >> >>> On 7/19/2020 2:51 PM, Ben Bacarisse wrote: >> >>>> Stop changing the subject. This is what is what you said: >>>> >>>> | Undecidability as it is currently used in math and computer science is >>>> | like the problem of deciding which of the two Boolean values represent >>>> | the current time. >>>> >>>> You should acknowledge that you are wrong. I suppose you could try to >>>> defend this claim, but the very fact that haven't even addressed it in >>>> any subsequent post suggests you can't (or have no intention of doing >>>> so). >>> >>> - Undecidability as it is currently used in math is >>> - like the problem of deciding which of the two Boolean values represent >>> - the current time. >>> >>> The solution set is required to come from the intersection of disjoint >>> sets. >> >> No, the term is used to mean problems with yes/no answers for which >> there is no effective decision procedure. Every instance of every >> undecidable problem has a correct yes/no answer. There is never any >> requirement for the solution to come from any set other than {yes, no}. > > Every time that I prove that I am right everyone says blah blah blah > no you are not. You have not proved that decidable means what you say it means. You can't because it means what the textbooks say it means. The answer is always a simple yes/no and there is always a correct answer. >> Every instance of every >> undecidable problem has a correct yes/no answer. > > If you can't prove that the Liar Paradox is exactly one of true or > false and still assert that the liar paradox is definitely true or > false I will take this to mean that you know that you are lying. The liar paradox is not a decision problem. Decision problems are /defined/ to have correct yes/no answers. You have been told this enough times that your refusal to the term correctly makes it clear you are being deliberately obtuse. > The reasonable thing for you to do here is acknowledge that the liar > paradox when properly formalized may be the exception to the rule that > >> Every instance of every >> undecidable problem has a correct yes/no answer. The liar paradox is not an example of a decision problem. >> There is a slightly different meaning when applied to a theory, but that >> can be re-phrased as decidable in the sense above. Indeed, that's what >> Turing's famous paper was about. > > Here is exactly how true and unprovable cannot coexist: > ∀M ∈ Models ∀T ∈ Theories ∀φ ∈ Formulas > (Satisfied(M, T, φ) → (T ⊢ φ)) Oh, please stop writing these silly poems. It's not a good look. Because you don't know how to write symbolic mathematics you can't see the silliness -- you string the symbols together in a way that is suggestive of what is in your head, but the effect to others who know more is as if you've written "People called Romanes they go the house". Taking a guess at what your symbols are intended to convey, you have been given an example where your implication fails. There are models of Q for which the formula ∀x∀y x+y=y+x is "satisfied" but, famously, Q does not prove ∀x∀y x+y=y+x. >> What is of interest -- your Big Lie -- is two Turing machines that stand >> in a special relationship to each other (discussed at length in 2018). >> You claimed to have two such TMs and you did not. In fact there is no >> code in any accepted notation that has the property you claimed. This >> is why we've never seen it. You don't have it. > > Changing an x86 intepretor into a UTM takes time. > I did take three months off You could, of course, have posted the "actual Turing machines", "fully encoded" (your words) at anytime in the last 18 months, except of course you lied and you never had "actual Turing machines", "fully encoded". >>>> Determining if a context free grammar is ambiguous is a famous >>>> undecidable problem. The answer in all cases is a simple yes/no binary >>>> choice. It is never in any way like "deciding which of the two Boolean >>>> values the current time". >>> >>> All of those cases that reduce to the halting problem are simply >>> decidable. >> >> No. There is a theorem that says otherwise. > > There is a key gap in the reasoning of this theorem, a loophole that > has been undiscovered for many decades. Again you make yourself look ignorant. Theorems don't have gaps, arguments and proofs do. The halting theorem would still be a theorem even if Linz's proof (and all those just like it) were shown to be wrong. Indeed, Linz's proof does have a minor error in it. Anyway, it, and a whole host of interrelated theorems, remain theorems, with dozens of interlocking and overlapping proofs, none of which have been shown to have any serious flaws. (I say that because an embarrassingly large number of published proofs do have minor, fixable, flaws.) >> But let's put the fact that you don't accept these well-known theorems >> to one side. The term "undecidable" means not computable by a TM (or >> equivalent) so what sorts of functions are not computable in PO-land -- >> in the land of someone who thinks at least all the conventional >> uncomputable functions are computable? If there aren't any, what use is >> the term? If there are, give an example of one (no waffle please -- >> actual mathematics preferred). > > In Definition 12.1 Linz specifies this H(Ĥ,Ĥ) as this q0WmW where q0 > is the start state of H, Wm is the Turing machine description of the > input to H and W is the input to Wm. > > I will show how this is computable by filling in the "..." state > transitions with x86 code: > > H.(Ĥ,Ĥ) ... qy // Halts > H.(Ĥ,Ĥ) ... qn // Does not Halt Why won't you answer my question? Could you not resist the opportunity make another idle boast? I asked if there are any uncomputable functions in PO-land? Will you say? >> Note that I have deliberately switched from "decidable set" to >> "computable function". You don't know how to use the term "deciable" in >> relation to sets, so I think it will save me having to correct lots of >> detailed errors if you talk about uncomputable functions instead. > > ∃H ∈ Turing_Machine_Descriptions > ∀φ ∈ Turing_Machine_Descriptions > ∀w ∈ finite_strings > (H.Halts(φ,w) ∨ ¬H.Halts(φ,w)) 'Beauty is Truth, Truth Beauty' that is all ye know on earth, and all ye need to know. >>>>> The conventional self-referential halting problem counter-example most >>>>> clearly defined by Linz as specific state transitions is definitely >>>>> decidable (Linz 1990:319) >>>> >>>> Whatever this is supposed to mean >>> >>> The class of machines specified by the Peter Linz H_Hat is decidable. >> >> Yes. As you've been told before, that class is empty and the empty set >> is a decidable set. Of course, you don't mean what you said. You mean >> something else but you don't know how to say it (I do, by the way, but I >> can't be bothered to write out your impossible claim for you yet again). > > H.q0 wM w ⊢* H.qy > H.q0 wM w ⊢* H.qn Argh!! Again you fail to use the key part of this notation. I have explained, time and time again, that without the criteria for each case these lines are useless. (And they are technically wrong as well but the correct ones have what you probably consider to be "extraneous detail".) > When we make this whole thing perfectly concrete fully encoding every > single detail then and only then is it impossible for things to slip > through the cracks of human understanding. You lied about having done that 18 months ago. To cover that lie you've been making excuses for why you have to write a whole steaming pile of X86 code just so you can bury whatever error it is you have made. The "actual Turing machines" that you had "fully encoded" no later than 15th Dec 2018 would have backed up your claim unambiguously. But that claim was a lie, so they were never posted. (I'll grant you this: I think you were simply mistaken or deluded in December 2018, but by mid January the next year it was clear that you knew you were wrong because the story started to change.) -- Ben.