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 11:17 Marshall wrote: > On Jul 3, 7:22 am, herbzet <herb...(a)gmail.com> wrote: >> What is PA + (1)? > > The successor to PA. So do you "see" _with certainty_ that this theory is consistent?
From: Nam Nguyen on 3 Jul 2010 13:12 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!
From: Nam Nguyen on 3 Jul 2010 13:45 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?
From: herbzet on 3 Jul 2010 13:49 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. -- hz
From: Nam Nguyen on 3 Jul 2010 17:25
MoeBlee wrote: > On Jul 3, 11:36 am, Alan Smaill <sma...(a)SPAMinf.ed.ac.uk> wrote: >> Nam Nguyen <namducngu...(a)shaw.ca> writes: >>> Alan Smaill wrote: >>>> Nam Nguyen <namducngu...(a)shaw.ca> writes: >>>>> herbzet wrote: >>>>>> Nam Nguyen wrote: >>>>>>> herbzet wrote: >>>> ... >>>>>>>> No -- I don't "see" if PA + (1) is consistent. >>>>>>> Since inconsistency of a FOL formal system T is merely a finite >>>>>>> proof, you must have "seen" such a proof for PA + (1)? >>>>>> Must I have? >>>>> Of course you must, if you want your technical statement to be credible. >>>>> Why do you ask such a simple question? >>>> You were asking about whether consistency was ' "seen" ', complete >>>> with square quotes. That's not asking about proofs, its >>>> asking about personal intuitions. >>>> And the response was *not* claiming that the formal system is >>>> inconsistent (or consistent, for that matter). >>> But that's my whole point! >>> Why do people, such as MoeBlee, assert >>> that PA is consistent "PERIOD." when they don't have a way to >>> know that for a fact, and _"seeing" is not a fact_ ? >> I don't believe MoeBlee has asserted that -- >> he can answer for himself. > > Not only did I not assert it, I even before reminded Nam that my > remarks in that regard were to convey Aatu's view not necessarily > mine, and even as that was clear in those remarks. > > It's hopeless with Nam. It's actually hopeless with you, when you attacking my position behind Aatu's views. MoeBlee said: > Anyway, Aatu is not saying just that there exists a relative > consistency proof nor just that, say, ZF or some other formal system > proves Con(PA), but rather he's saying that PA IS consistent. He's > saying that aside from whatever FORMAL proofs, PA is consistent - > PERIOD. His basis is for that is not a FORMAL proof, but rather his > conviction that the axioms of PA are true (and not even in confined to > a FORMAL model theoretic sense of truth, but rather that the axioms > are simply true about the natural numbers, as we (editorial 'we') > understand the natural numbers even aside from any formalization. > Haven't you read Franzen's incompleteness book? and when I said of TF's book: > I read part of the book. So? Would wrong become right somehow, or vice > versa? MoeBlee replied: > What would happen is that you would get a better understanding of his > point of view. I'm sorry, MoeBlee, you made a stand and accused me of _not_ having a "better understanding" then the whole thing you said on Aatu's behalf (again without you having been asked by Aatu) was your views, and you were liable to defend it or to concede. AT least it was _you_, not Aatu who accused me as such here! > > MoeBlee |