How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent (EASY PROOF)
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From: herbzet on 3 Jul 2010 01:56 MoeBlee wrote: > herbzet wrote: > > MoeBlee wrote: > > > herbzet wrote: > > > > MoeBlee wrote: > > > > > herbzet wrote: > > > I'm migrating to the terms "demonstration" or "derivation" > > for "formal proof". > > Okay. By 'proof' in this context I had meant formal proof. I know that, and you know that, and I know that you know that, and you know (I think) that I know that, etc. etc. But I was thinking about the fat lady in the second row who might get confused on that point. We're talking, after all, about whether the proof in ZF(C) that PA is consistent is in any sense a more compelling proof (of the consistency of PA) than the "proof" in some unnamed and informal meta-theory that PA is consistent if ZF(C) is. Or something like that. The whole thing is nonsense, anyway. Clearly, PA is consistent, or at least, its consistency is at least as evident as the consistency of any system which purports to prove it. Harrumph. -- hz
From: Nam Nguyen on 3 Jul 2010 02:29 herbzet wrote: > > MoeBlee wrote: >> herbzet wrote: >>> MoeBlee wrote: >>>> herbzet wrote: >>>>> MoeBlee wrote: >>>>>> herbzet wrote: >>> I'm migrating to the terms "demonstration" or "derivation" >>> for "formal proof". >> Okay. By 'proof' in this context I had meant formal proof. > > I know that, and you know that, and I know that you know that, > and you know (I think) that I know that, etc. etc. > > But I was thinking about the fat lady in the second row > who might get confused on that point. We're talking, > after all, about whether the proof in ZF(C) that PA > is consistent is in any sense a more compelling proof > (of the consistency of PA) than the "proof" in some > unnamed and informal meta-theory that PA is consistent > if ZF(C) is. > > Or something like that. > > The whole thing is nonsense, anyway. Clearly, PA > is consistent, or at least, its consistency is > at least as evident as the consistency of any > system which purports to prove it. Sometimes it's much ... much simpler and more logical, humble, humanistic to admit we don't know what we can't know, rather than pretending to possess some sort of an immortal knowledge. Suppose someone states "There are infinitely many universes and each has harbored a planet with intelligent life in its history." If there actually are infinitely many universes we can't know such fact. PA's consistency is like such a statement: if it's consistent, you can't never know that. Period.
From: MoeBlee on 3 Jul 2010 16:08
On Jul 2, 5:13 pm, Charlie-Boo <shymath...(a)gmail.com> wrote: > Why don't you do it here? What's in it for ME? MoeBlee |