SCI.MATH POLL - uncountable infinity
in [Physics]
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From: George Greene on 8 Jun 2010 01:25 On Jun 6, 2:31 am, Transfer Principle <lwal...(a)lausd.net> wrote: > Therefore, any poster who doesn't like Cantor's Theorem > ought to consider NFU instead of ZFC. Nobody ought to consider NFU period for any but the most theoretical of reasons. For example, in NFU, the set of all 1-element subsets of a set is NOT the same size as the set! You canNOT prove the existence of the function mapping x to {x} for every x in some domain-set S. What you really want to consider, far more generically than NFU, is set theory with a universal set. There are plenty of web-pages devoted.
From: Aatu Koskensilta on 8 Jun 2010 21:32 Transfer Principle <lwalke3(a)lausd.net> writes: > I am confident that ZF is consistent, because I believe that if ZF > were inconsistent, a proof of this would have been found by now. Why? This is not uncommon idea but on closer scrutiny there's not much to recommend it. > If it does turn out that ZF is inconsistent, then there would have > been some underlying reason that the proof wasn't discovered for over > a century after the axioms were first given. What's there to rule out the possibility that the simplest proof of a contradiction in ZF is inhumanely complex, utterly beyond our comprehension, invoking, say, an obscure instance of Pi-20^20^20^20^4546^3214532 + 4145624^7542 + 897412 replacement? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Bill Taylor on 9 Jun 2010 02:28 On Jun 9, 1:32 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > What's there to rule out the possibility that the simplest proof of a > contradiction in ZF is inhumanely complex, utterly beyond our > comprehension, invoking, say, an obscure instance of > Pi-20^20^20^20^4546^3214532 + 4145624^7542 + 897412 replacement? Common sense? ----------------------------------------------------- Bill Taylor W.Taylor(a)math.canterbury.ac.nz ----------------------------------------------------- Q. Why did the chicken cross the Moebius strip? A: To get to... to... -----------------------------------------------------
From: Aatu Koskensilta on 9 Jun 2010 02:30 Bill Taylor <w.taylor(a)math.canterbury.ac.nz> writes: > Common sense? How does common sense rule out the possibility that the simplest proof of a contradiction in ZF is inhumanely complex? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: |-|ercules on 9 Jun 2010 02:47
"Aatu Koskensilta" <aatu.koskensilta(a)uta.fi> wrote ... > Bill Taylor <w.taylor(a)math.canterbury.ac.nz> writes: > >> Common sense? > > How does common sense rule out the possibility that the simplest proof > of a contradiction in ZF is inhumanely complex? > The question of the decade! hint: common sense will easily refute most of the popular derivations of ZF. IF ZF told you to jump off a cliff would you? Herc |