How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
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From: Charlie-Boo on 29 Jun 2010 09:06 On Jun 29, 8:28 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > George Greene <gree...(a)email.unc.edu> writes: > > I really don't think that the model existence theorem is going to leap > > out at him here. > > Pretty much any elementary text contains an account of the set theoretic > construction of the various number systems. It's a trivial exercise to > verify the axioms of PA hold in the structure of naturals. Combined with > the soundness of first-order logic this immediately yields the > consistency of PA. Can that be carried out in ZFC? Who has? I've asked like 5-10 times. The only answers I've gotten were YES then changing the subject or a BS reference (for $400.) Elementary, trivial? See - more fuckhead nonsense (condescending.) A: If it's trivial then give it. DUH: Mathematicians don't give trivial proofs. A: When's the last time you read a math book? 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 29 Jun 2010 09:15 On Jun 29, 8:30 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > herbzet <herb...(a)gmail.com> writes: > > "Jesse F. Hughes" wrote: > > >> But, Walker, you really have the wrong impression of me. I come to > >> sci.math mostly to read the cranks. I'm not proud of that fact > > > *I* am proud of you, that you would make this startling announcement. I say the cranks are the ones who give BS references, make unsubstantiated statemements and who practice arguing ad hominem. Agreed? Or are you so base that you won't admit to even principles of morality? C-B > Coincidentally, I am reading /Idiot America/ by Charlie Pierce. The > book has much to do with cranks, though not of the mathematical sort so > much as the political and other sorts. There's a vaguely relevant > passage. > > The value of the crank is in the effort that it takes either to refute > what the crank is saying, or to assimilate it into the mainstream. In > either case, political and cultural imaginations expand. Intellectual > horizons expand. > > Now, contrary to Walker's fantasy, none of the cranks here have > anything worth "assimilating" into mathematics, of course, but there is > something to be said with the effort required to refute a bad argument. > Of course, no one here really thinks that any argument will effectively > end a crank's pursuit of nonsense, but that is nonetheless the > intellectually interesting bit. > > Of course, I'm really here for lower entertainment. I want posts about > the Hammer, about how surrogate factoring moves the stock market, about > the most influential mathematicians on the planet. But still I pretend > to care about arguments, if only for appearance's sake. > > -- > Jesse F. Hughes > > "Most of my research is irreducibly complex." > -- James S. Harris
From: Charlie-Boo on 29 Jun 2010 09:17 On Jun 29, 8:34 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Transfer Principle <lwal...(a)lausd.net> writes: > > 1. Is there a proof in ZF-Inf+~Inf that every set is finite? > > It appears I once posted a proof. It relies, in an essential way, if I > recall correctly, on the axiom of replacement. You recall incorrectly. It actually consisted of drawing of little girls playing outside your window. 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 29 Jun 2010 10:06 On Jun 29, 8:58 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > How about when you said that Gentzen proved PA consistent using ZFC? > > No one ever proves anything using ZFC in the sense of producing formal > derivations. What about the MetaMath web site - or do you think it's BS as some do? > Rather, they prove mathematical theorems using mathematical > principles formalized in ZFC. By certain elementary considerations we > know the formalizations of such theorems are formally derivable in ZFC. Ok. What is the reference to the proof in ZFC of PA consistency doing it that way? 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 29 Jun 2010 10:15
On Jun 29, 9:14 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > On Jun 28, 8:58 am, Frederick Williams <frederick.willia...(a)tesco.net> > > wrote: > > >> Yes, you can: take Gentzen's proof (or Ackermann's etc) and formalize > >> it in ZFC. > > > Give the slightest bit of details. > > Read a logic book. What is the title of a book that includes it? > >> It has everything to do with V_omega. > > > That's not a ZFC axiom. > > Indeed. It is a set. What are the essential ZFC axioms that are used that PA would need to carry out the proof? C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |