How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent(EASYPROOF)
in [Logic]
|
Prev: How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent(EASY PROOF)
Next: How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent(EASYPROOF)
From: Nam Nguyen on 3 Jul 2010 09:53 herbzet wrote: > > 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. While having such a "seeing", do you "see" if PA + (1) is consistent? I mean, how far can you go with such "seeing"?
From: Nam Nguyen on 3 Jul 2010 10:10 herbzet wrote: > > 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. IOW, mathematical reasoning is just a gambling that never ends!
From: herbzet on 3 Jul 2010 10:22 Nam Nguyen wrote: > herbzet wrote: > > 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. > > While having such a "seeing", do you "see" if PA + (1) is consistent? > > I mean, how far can you go with such "seeing"? What is PA + (1)? -- hz
From: herbzet on 3 Jul 2010 10:22 Nam Nguyen wrote: > herbzet wrote: > > 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. > > IOW, mathematical reasoning is just a gambling that never ends! You find something doubtful in the proof of the infinitude of primes? -- hz
From: Nam Nguyen on 3 Jul 2010 11:11
Marshall wrote: > 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. That's all you and a few others have: just "saying". Well, JJ, JSH, etc.. have "said" a lot of things "a bazillion times" too. What would make you be different from them, as far as "saying" is concerned? You'll never get it. No? |