halting problem proof, via diagonalization?
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From: Daryl McCullough on 8 Aug 2008 19:16 julio(a)diegidio.name says... >So you cannot add anything significant, you just reiterate your >insults to my intelligence. Never mind, it was anyway very >"instructive". Look, Cantor made a precise claim, and he gave a rigorous proof of that claim. You made a fuzzy claim (one that didn't actually contradict what Cantor said), and you gave a false proof of that fuzzy claim. I guess it's not nice to insult your intelligence, but you clearly don't know what you are talking about. -- Daryl McCullough Ithaca, NY
From: MoeBlee on 8 Aug 2008 19:20 On Aug 8, 3:50 pm, ju...(a)diegidio.name wrote: > On 8 Aug, 23:41, MoeBlee <jazzm...(a)hotmail.com> wrote: > > On Aug 8, 3:09 pm, ju...(a)diegidio.name wrote: > > > > On 8 Aug, 19:10, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > > > On Aug 8, 10:23 am, ju...(a)diegidio.name wrote: > > > > > > > To make a long story short: we are not interested in the "limit entry" > > > > > > (whatever that may be), but in the fact that the diagonal differs from > > > > > > each and any entry in the list. > > > > > > Interested or not, you cannot just dismiss it. The "limit" entry makes > > > > > just as much sense as the above (or the below) "[for] every entry in > > > > > the list". Is the list "infinite" or is it not? I am saying, yours is > > > > > not a valid objection. > > > > > Whether the list is infinite or NOT, the anti-diagonal is not on the > > > > list. > > > > You keep saying so as if it were the starting point, while that's the > > > result to get. The first problem is indeed in your general way of > > > argumentation. > > > We state exactly the premises and rules of inference. I've been that > > saying over and over, because YOU are not responsive to the poing > > (instead you just complain about the repetition of my answer while you > > don't ADDRESS my answer). > > > One more time: > > > Theorems of Z set theory are from an explicit set of premises (axioms) > > and an explicit logic (the inference rules). Yes, if you fault the > > axioms and/or inference rules, then you don't have to accept the > > theorems. But that is a separate question from what is or is not a > > theorem from whatever given set of axioms and inference rules. > > > PLEASE LISTEN THIS TIME: > > > You and I have NO DISAGREEMENT that if you fault the axioms and rules, > > then you don't have to accept the conclusions. BUT, then an > > INTELLEGENT discussion starts with you saying just which axioms and > > rules you don't accept, and then perhaps to tell us what axioms and > > rules that you instead propose to derive theorems of mathematics. > > > > > Otherwise, you are free to mention EXACTLY what premises in the > > > > proof or what rule of logic used you disagree with. > > > > The diagonal argument is broken in its essence, and this comes before > > > your axioms, another problem of yours. > > > You see. You didn't answer the question. You won't say what axioms or > > rules you disagree with. Okay, fine, so we just leave it at that. > > Since the axioms and rules entail a conclusion you disagree with, > > there is at least one, though unspecified axiom or rule, that you > > don't accept. > > > > But I am not trying to disprove > > > *you*. Here I have provided the simpliest of the arguments based on > > > the naturals and induction, to build the very same list and the very > > > same diagonal as Cantor's, with quite opposite results: > > > No, you have not. Please, we keep telling you, but you keep evading, > > that your "argument" doesn't work because it uses an UNDEFINED notion > > of a 'limit'. We DEFINE the use of limits EXACTLY. But your just > > SAYING "in the limit case" is not a mathematical argument. It is using > > mathematical sounding terminology, but without defintion of the sense > > of a limit that would apply. > > > > and they are > > > very natural results. You have not been able to provide a meaningful > > > objection that is one. > > > Please, it is INSULTING that you say that when people have taken the > > time to SPECIFICALLY articulate the objections to your "argument". > > > > Somewhere else, though, you have finally > > > admitted that there exists such a thing as constructive theories. So > > > all the fuzz for nothing? > > > Because, as far as I know, such constructive mathematics does not work > > by just going around using mathematical sounding terminology such as > > vacuously spouting about some UNDEFINED "limit case". > > > > > Then we could at > > > > least say, "Yes, given that you don't accept those premises and rules > > > > of logic, you don't have to accept the theorem that is proved from > > > > them. Now, what premises and logic DO you accept for the purpose of > > > > deriving mathematical conclusions?" See, that would be productive. But > > > > we can't get there if all you do is use UNDEFINED hocus pocus about > > > > "limit induction", and amphiboly in your symbolisms, along with > > > > recriminations about what dishonest idiots mathematicians are. > > > > Let's be serious. I have given the simpliest of the arguments. Can you > > > spot any significant flaw? > > > So you will never actually READ the posts given to you, I guess. We've > > said over and over and over that the flaw is using an UNDEFINED notion > > of 'limit'. > > > > If not, then I guess it's really the time > > > to revisit Cantor's... and then I can see what is the fuzz for. > > > > How do you dismiss constructive theories? > > > I DON'T dismiss well presented constructive theories. And I very much > > DO appreciate the importance of constructivism in mathematics. What I > > do dismiss is an argument that just uses mathematical sounding > > terminology without properly defining it. > > > > I'd be very interested in > > > learning what eventually there is to lose. > > > Constructivism has drawbacks and advantages, while classical > > mathematics also has its drawbacks and advantages. That is a rich area > > for discussion, but it requires at least two things you are not > > willing to bring: (1) An understanding of the basics of the subject, > > and (2) a willingness to rise from mindless recriminations about > > mathematicians and instead pay attention at least long enough so that > > you understand what various mathematicians - constructivst and non- > > constructivist - are actually saying. > > So you cannot add anything significant, you just reiterate your > insults to my intelligence. Never mind, it was anyway very > "instructive". How insulting! You just included the QUOTES of my SUBSTANTIVE comments and then just SKIPPED all of it to say that all I did was insult your intelligence. AND, for that matter, in my remarks about you personally, I NEVER commented on your INTELLIGENCE. Look, the substantive comments of mine are right there in what you yourself quoted. At this point, after your skipping thsee points yet again, and after my nearly BEGGING you to address the substantive points, I do have to think that indeed you are just trolling for reactions here and are not interested in the actual mathematics or even philosophical aspects of this subject. MoeBlee
From: julio on 8 Aug 2008 19:23 On 9 Aug, 00:16, Balthasar <nomail(a)invalid> wrote: > On Fri, 8 Aug 2008 15:49:27 -0700 (PDT), MoeBlee <jazzm...(a)hotmail.com> > wrote: > > > > > P.S. It is decidedly NOT constructivist to assert the existence of a > > "limit" without CONSTRUCTING it (and just saying "the limit case" is > > decidedly not a construction), let alone, not even defining what > > possible sense you might mean by a "limit" in such a context. > > And, btw., even a constructivist/intuitionist would agree that a number > is not in a certain set (or list) if it differs from ALL (i.e. each and > every) elements (or entries) in the set (or list). ;-) Paralogism. As usual you are assuming what there is to prove, that's what anyone knowing about logic would say. And in my argument I do NOT even assume anything like that, I actually conclude the opposite. Clueless as you can be, can you be sooo clueless? -LV > > Proof (in NJ + identity): > > 1 (1) Ax(x e A -> ~(a = x)) A > 2 (2) a e A A > 1 (3) a e A -> ~(a = a) 1 UE > 1,2 (4) ~(a = a) 2,3 ->E > (5) a = a =I > 1,2 (6) _|_ 4,5 ~E > 1 (7) ~(a e A) 2,6 ~I > > Hence: > > Ax(x e A -> a =/= x) |- a !e A. > > This does even hold in ML (minimal logic) + identity. But obviously id > does not hold in /crank logic/. > > B. > > -- > > "For every line of Cantor's list it is true that this line does not > contain the diagonal number. Nevertheless the diagonal number may > be in the infinite list." (WM, sci.logic)
From: MoeBlee on 8 Aug 2008 19:29 On Aug 8, 4:09 pm, ju...(a)diegidio.name wrote: > On 8 Aug, 23:41, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > On Aug 8, 3:09 pm, ju...(a)diegidio.name wrote: > > > On 8 Aug, 19:10, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > > On Aug 8, 10:23 am, ju...(a)diegidio.name wrote: > > > > > Otherwise, you are free to mention EXACTLY what premises in the > > > > proof or what rule of logic used you disagree with. > > > > The diagonal argument is broken in its essence, and this comes before > > > your axioms, another problem of yours. > > > You see. You didn't answer the question. You won't say what axioms or > > rules you disagree with. Okay, fine, so we just leave it at that. > > Since the axioms and rules entail a conclusion you disagree with, > > there is at least one, though unspecified axiom or rule, that you > > don't accept. > > Reread: you see? You just don't get it, it's out of your universe of > understanding. > > BTW, now you have made a point of denying anything I might be willing > to say, here and elsewhere. No, I have not. I disagree with a number of things you post. I don't have a point to find you wrong on every single thing you've ever said, let alone MIGHT say. > I have already given you a formal > definition of my construction in a another thread, Please state exactly what you are referring to. Please show me your definition of 'limit' in the context of this discussion. > along with any of > the uncountable and meanigless clarifications I was asked for, about > all the details you liked to be told about. Please tell me, for example, where you gave any kind of adequate response to it having been pointed out to you that you conflated two different definitions of 'P' in that other thread. > Result: just reitereted > denial and personal insults. No, that is a lie. Not JUST personal insults. Rather, substantive response, which you keep skipping, plus personal remarks that are not kind but need to be said, since indeed no discussion with you can make progress while you are unwilling to learn the basics of the subject and listen instead of investing yourself in childish recriminations about how "iditotic" mathematicans are. > Balthasar is now your friend. And I am > finished with you both. How childish. What are posting from the fifth grade class computer room? "Bobby is not my friend anymore! Bobby and Tommy are friends, but I'm not their friend!" MoeBlee
From: MoeBlee on 8 Aug 2008 19:31
On Aug 8, 4:23 pm, ju...(a)diegidio.name wrote: > On 9 Aug, 00:16, Balthasar <nomail(a)invalid> wrote: > > > On Fri, 8 Aug 2008 15:49:27 -0700 (PDT), MoeBlee <jazzm...(a)hotmail.com> > > wrote: > > > > P.S. It is decidedly NOT constructivist to assert the existence of a > > > "limit" without CONSTRUCTING it (and just saying "the limit case" is > > > decidedly not a construction), let alone, not even defining what > > > possible sense you might mean by a "limit" in such a context. > > > And, btw., even a constructivist/intuitionist would agree that a number > > is not in a certain set (or list) if it differs from ALL (i.e. each and > > every) elements (or entries) in the set (or list). ;-) > > Paralogism. As usual you are assuming what there is to prove, that's > what anyone knowing about logic would say. And in my argument I do NOT > even assume anything like that, I actually conclude the opposite. > Clueless as you can be, can you be sooo clueless? Okay, go ahead and keep thinking that... MoeBlee |