How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent(EASYPROOF)
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From: herbzet on 3 Jul 2010 15:12 Nam Nguyen wrote: > herbzet wrote: > > Nam Nguyen wrote: > >> Nam Nguyen wrote: > >>> herbzet wrote: > >>>> Marshall wrote: > >>>>> herbzet wrote: > >>>>>> What is PA + (1)? > >>>>> The successor to PA. > >>>> The more I look at this, the funnier it gets. > >>> Same here. > >>> > >>>> Make it stop! > >>> Right. _Stop_ believing you "know" _exactly_ what the natural numbers be! > >> Seriously, relativity in sciences (including mathematics) isn't an > >> one-man conviction in "sci.logic", "sci.math". The mere mentioning > >> of the 5th postulate, Hilbert-era's truth-equals-provability, SR, > >> QM, should be a reminder that belief of any absoluteness in sciences > >> is an ancient belief, which is no longer adequate for describing physical > >> reality, or abstraction. > >> > >> If we scorn or laugh at the relativity of the standardness of a purported > >> "model" of L(PA), a.k.a collectively as "the natural numbers", then we're > >> no better that those who laughed at Riemann's ideas, at SR, at QM's uncertainty. > >> At least those people had a valid excuse: they were in a different time in > >> the past. We don't have such excuse! > >> > >> Seriously, all the nasty bickering aside, think about the whole thing logically. > >> Think about the 4 reasoning Principles: > >> > >> - Principle of Consistency. > >> - Principle of Compatibility. > >> - Principle of Symmetry. > >> - Principle of Humility. > >> > >> Would you think these are nonsensical principles honestly speaking? > > > > Probably. > > > > Who said anything about "absolute knowledge"? I think you're > > tilting at a windmill. > > Oh, but by FOL definition of a formal system consistency, it must be > either absolutely true or absolutely false that PA is consistent! > (Ditto for inconsistency). True -- it is a theorem of FOL that phi xor ~phi for any FOL formula phi. > Of course nobody should prevent you from saying: > > "I don't know"! Sometimes I do know. > See how easy when we're truthful to ourself! Well, I try as best I can. -- hz |