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 04:11 Nam Nguyen wrote: > herbzet wrote: > > 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. I see a model for PA: the natural numbers. I conclude PA is consistent. I would say I know this to a mathematical certainty. -- hz
From: Marshall on 3 Jul 2010 11:03
On Jul 3, 1:11 am, herbzet <herb...(a)gmail.com> wrote: > Nam Nguyen wrote: > > > 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. > > > > [...] PA's consistency is like such a statement: if it's consistent, > > you can't never know that. Period. > > I see a model for PA: the natural numbers. I conclude PA is consistent.. > > I would say I know this to a mathematical certainty. We've all said this to Nam a bazillion times. He's doesn't get it. Marshall |