How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent(EASYPROOF)
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From: Alan Smaill on 3 Jul 2010 14:12 Nam Nguyen <namducnguyen(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). -- Alan Smaill
From: Alan Smaill on 3 Jul 2010 14:36
Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Alan Smaill wrote: >> Nam Nguyen <namducnguyen(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. But everyone, including you and me, goes around making assertions which they believe to be the case, but don't have incontrovertible proof for. > Why couldn't they admit they _in fact_ don't know that PA is > consistent? I don't have a proof that PA is consistent that can convince anyone who will not accept reasoning principles that go beyond PA. I haven't seen anyone claim anything beyond that. What happened to your Zen phase? -- Alan Smaill |