How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
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From: George Greene on 27 Jun 2010 13:59 On Jun 24, 2:01 pm, Charlie-Boo <shymath...(a)gmail.com> wrote: > And the ZFC part is the DATA STRUCTURES of this "programming > language". When programmers need to go beyond aleph-1 integers DAMN, you're stupid. PROGRAMMERS NEVER need to go beyond aleph-1 integers. Indeed, they never even MAKE IT UP to aleph-ZERO integers! COMPUTERS ARE FINITE! Jeezus.
From: George Greene on 27 Jun 2010 14:00 On Jun 24, 5:01 pm, Charlie-Boo <shymath...(a)gmail.com> wrote: > Read the first 3 sentences of Godel's famous 1931 article (not famous > enough, unfortunately.) YOU are TELLing US to READ something?? I'm sorry, it doesn't work that way. You ASK us a QUESTION about this, if you have read it. We doubt this, frankly, since you obviously haven't understood it.
From: Charlie-Boo on 27 Jun 2010 14:14 On Jun 27, 1:29 pm, Frederick Williams <frederick.willia...(a)tesco.net> wrote: > Charlie-Boo wrote: > > Hey Frederick, I bet you $449.94 that Gentzen's book doesn't contain a > > proof that PA is consistent, carried out in ZFC. You on? > > No, but I do claim that it could be formalized in ZFC. > > > Or do you say things that you don't believe? > > Yes, but I don't think that's relevant here. How about when you said that Gentzen proved PA consistent using ZFC? C-B > -- > I can't go on, I'll go on.
From: Frederick Williams on 27 Jun 2010 14:22 Charlie-Boo wrote: > > On Jun 14, 11:45 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > Charlie-Boo <shymath...(a)gmail.com> writes: > > > Since PA can't prove something as simple as that, how could anyone be > > > so stupid as to claim ZFC/PA is a good basis for all of our ordinary > > > math? > > > Who makes this claim? You're hallucinating. > > Read the first 3 sentences of Godel's famous 1931 article (not famous > enough, unfortunately.) While you're at it, maybe even read more than > 3 sentences. Here's the van Heijenoort translation: The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules. The most comprehensive formal systems that have been set up hitherto are the system of _Principia mathematica_ (PM) on the one hand and the Zermelo-Fraenkel axiom system of set theory (further developed by J. von Neumann) on the other. These two systems are so comprehensive that in them all methods of proof today used in mathematics are formalized. So what? -- I can't go on, I'll go on.
From: Frederick Williams on 27 Jun 2010 14:25
Charlie-Boo wrote: > > On Jun 27, 1:29 pm, Frederick Williams <frederick.willia...(a)tesco.net> > wrote: > > Charlie-Boo wrote: > > > Hey Frederick, I bet you $449.94 that Gentzen's book doesn't contain a > > > proof that PA is consistent, carried out in ZFC. You on? > > > > No, but I do claim that it could be formalized in ZFC. > > > > > Or do you say things that you don't believe? > > > > Yes, but I don't think that's relevant here. > > How about when you said that Gentzen proved PA consistent using ZFC? The proof could be formalized in ZFC. I do not claim that Gentzen used nothing but the *language* of ZFC. -- I can't go on, I'll go on. |