How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
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From: herbzet on 3 Jul 2010 14:04 "R. Srinivasan" wrote: > Fortunately for me, at least a few quantum physicists who matter were > interested in (a new interpretation of) quantum physics, and that is > why I got my work published. I am pleased for you. Congratulations! -- hz
From: Charlie-Boo on 3 Jul 2010 14:12 On Jul 3, 10:39 am, William Hale <h...(a)tulane.edu> wrote: > In article > <6edea512-8a83-4c88-834e-a4ab9f77e...(a)z8g2000yqz.googlegroups.com>, > > Charlie-Boo <shymath...(a)gmail.com> wrote: > > On Jun 29, 10:22 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > Charlie-Boo <shymath...(a)gmail.com> writes: > > > > What is that formal expression? > > > > To find out you need to read a logic book. > > > Then why don't you (anyone) name one that has it? You can't name a > > book that has the proof or even the theorem spelled out, and you can't > > give it yourself, or even an outline. Yet you claim it can be done. > > Is that Mathematics? I thought statements had to be proven in > > Mathematics. > > I thought outlines were given, but you then asked for more detail, even > going as far to ask for it to be written completely formal, starting > from the axioms of ZFC without using any previous theorems. So far I believe only one person has even listed some ZFC axioms that will supposedly be used. When I asked what they will be used for and how they are essential, why PA can't do it because of them (which must be so due to Godel's 2nd), I got nothing in return. An authentic, intelligent, productive, normal, sane discussion would go something like this: 1. Someone posts a summary - high level overall - that gives the proof and how ZFC will formalize it. The axioms needed and how they are needed. 2. Others can ask question, get clarification or more details. 3. The information flows back and forth, freely. And what do we see here? 1. BS references that have no ZFC in the proof. 2. An explanation that refers to some theorem without mention of ZFC. 3. Mention of ZFC with no proof or theorem. 4. "Read a logic book." 5. "Figure it out yourself." If there were such a proof, people could have given and discussed it in less time than has been spent on BS and sarcasm. But they haven't. What do you conclude? When I discuss my results, I give as much detail and answer as many questions as people want - sometimes for days. I have nothing to hide. C-B > > > > > > C-B > > > > It appears the generous > > > explanations various people have provided for your benefit in news are > > > not sufficient. > > > > -- > > > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > > > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus- Hide quoted text - > > - Show quoted text -
From: Charlie-Boo on 3 Jul 2010 14:28 On Jul 3, 2:05 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > And you won't post it, alas, so people could quickly and easily see it > > and debunk it like the other BS references. > > You want me to post Ross Bryant's Master's Thesis? You'll find it online > at: > > http://www.cas.unt.edu/~rdb0003/thesis/thesis.pdf Thanks. But where does he show proof lines with ZFC as their justification? He refers to ZFC and makes claims regarding it, but all of his proofs and arguments are presented in normal mathematical terms with no reference to ZFC. 100 pages full of proofs and a handful of references to ZFC doesn't do it. C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Charlie-Boo on 3 Jul 2010 14:31 On Jul 3, 2:28 pm, Charlie-Boo <shymath...(a)gmail.com> wrote: > On Jul 3, 2:05 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > Charlie-Boo <shymath...(a)gmail.com> writes: > > > And you won't post it, alas, so people could quickly and easily see it > > > and debunk it like the other BS references. > > > You want me to post Ross Bryant's Master's Thesis? You'll find it online > > at: > > > http://www.cas.unt.edu/~rdb0003/thesis/thesis.pdf > > Thanks. But where does he show proof lines with ZFC as their > justification? He refers to ZFC and makes claims regarding it, but > all of his proofs and arguments are presented in normal mathematical > terms with no reference to ZFC. > > 100 pages full of proofs and a handful of references to ZFC doesn't do > it. And the proof that it can't be carried out in PA? > C-B > > > > > -- > > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus- Hide quoted text - > > - Show quoted text -
From: MoeBlee on 3 Jul 2010 16:19
On Jul 2, 8:00 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > I myself accept the proof of Con(PA) > (though I still believe that the presence of epsilon_0 in any > proof of Con(PA) is suspicious, I don't know what you find suspicious about it. Anyway, we don't need to deploy epsilon_0. > What Charlie-Boo needs, therefore, is some evidence that > convinces him that if one were to work out all the steps, one > can eventually prove Con(PA) in ZFC, just as one can eventually > find googolduplex digits of sqrt(2)+sqrt(3). So far, no poster or > book has so convinced him. Therefore, there is no reason for > him to believe that such a proof exists. Of course. But it's just a mathematical theorem that virtually anyone who is informed in the basics of the subject can do for himself. No one can give a proof for Charlie-Boo that will convince him, since a proof of this theorem depends on lots of terminology, formulations, and previously proven theorems in Z set theory, which he refuses to learn (let alone the predicate calculus). You don't expect someone to prove in a post or two some result in mathematics such as analysis, abstract algebra, etc. that requires first learning the basics of those subjects, do you? Same fop mathematical logic. Morevover, Charlie-Boo is asking for a LITERAL formal proof. But you understand how impractical and senseless that is, since you understand that for purposes of communication and practicality mathematicians give informal proofs such that an adequately informed reader can see that the informal proof can be perfectly formalized in practice if we wished to spend the time and labor or at least in principle. MoeBlee |