How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
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From: R. Srinivasan on 3 Jul 2010 11:02 On Jun 30, 11:27 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > "R. Srinivasan" <sradh...(a)in.ibm.com> writes: > > If I had wasted my time trying to dig into the rubbish that you have > > laid out above, I would not have had much time or energy left to deal > > with the kind of stuff that *i* consider worth doing. > > You're of course free to spend your time and energy however you > choose. But why do you think others should take any notice of your > interests and inclinations? > > You are absolutely right. It was very naive and unreasonable of me to expect that logicians should be interested in logic, and that philosophers should be interested in philosophy. In the world of logic and philosophy, nothing is ever that straightforward, as I have found out. 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. RS
From: R. Srinivasan on 3 Jul 2010 11:28 On Jul 3, 8:05 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > R. Srinivasan wrote: > > There are absolute (Platonic) truths in NAFL (e.g. a NAFL theory is > > either consistent or inconsistent) but such propositions are not > > formalizable in the language of a NAFL theory. These must remain as > > metamathematical truths. > > This is where the "alliance" between NAFL forces and the relativists, > so to speak, would end. An inconsistency of a theory should be formalizable, > in the sense there there would be a (finite) syntactical proof for it! > > Sure. Such a proof of a contradiction P&~P would indeed be formalizable in an appropriate NAFL theory T. We can indeed conclude from this formal proof that "T is inconsistent". However, the proposition "T is inconsistent" is not formalizable in the language of T. The notion of provability is not formalizable in T and hence "T |- (P&~P)" cannot be a proposition of T. RS
From: Charlie-Boo on 3 Jul 2010 13:56 On Jul 3, 8:44 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > On Jun 29, 10:16 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > >> It's in Shelah's _Cardinal Arithmetic_ p.3245 - > >> 4325238532. Basically, you just do a triple-fold transfinite > >> recursion over a coherent extender sequence to obtain a suitable > >> premouse, and iterate the upward Mostowski collapsing lemma a few > >> times. To remove the extendible cardinal introduce some Aronszjan > >> trees using Sacks forcing. > > > Where's the part about how ZFC is used to do it? > > Pages 3219845327852387532 - 4321412421. Good. Really. Most people here resort to personal attacks when all of their attempts to BS their way through a problem fail. Humor is much better. C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Charlie-Boo on 3 Jul 2010 13:58 On Jul 3, 8:48 am, Frederick Williams <frederick.willia...(a)tesco.net> wrote: > Charlie-Boo wrote: > > > On Jun 29, 10:16 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > Charlie-Boo <shymath...(a)gmail.com> writes: > > > > Ok. What is the reference to the proof in ZFC of PA consistency doing > > > > it that way? > > > > It's in Shelah's _Cardinal Arithmetic_ p.3245 - 4325238532. Basically, > > > you just do a triple-fold transfinite recursion over a coherent extender > > > sequence to obtain a suitable premouse, and iterate the upward Mostowski > > > collapsing lemma a few times. To remove the extendible cardinal > > > introduce some Aronszjan trees using Sacks forcing. > > > Where's the part about how ZFC is used to do it? > > Woosh. Here's the real woosh: Any idiot knows he's just playing stupid games. But notice how my debunking logic works even for completely nonsensical responses! C-B > -- > I can't go on, I'll go on.
From: Charlie-Boo on 3 Jul 2010 13:59
On Jul 3, 8:48 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > On Jun 29, 9:13 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > >> Charlie-Boo <shymath...(a)gmail.com> writes: > >> > ZFC was designed to avoid paradoxes by making explicit what can be a > >> > set. It doesn't do anything else except what the Peano Axioms give > >> > it. > > >> Does PA give us Borel determinacy? Is Borel determinacy trivial? > > > Prove ZFC can prove it and PA can't. > > The details are explained in Ross Bryant's Master's Thesis. You won't > understand any of it, alas. And you won't post it, alas, so people could quickly and easily see it and debunk it like the other BS references. C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |