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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
From: Marshall on 9 Jun 2010 09:33
On Jun 8, 11:47 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
> "Aatu Koskensilta" <aatu.koskensi...(a)uta.fi> wrote ...
>
> > Bill Taylor <w.tay...(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?

ZF told Aatu to jump off a cliff? Oh man, I am so there.


Marshall

From: BURT on 9 Jun 2010 15:23
On Jun 9, 6:33 am, Marshall <marshall.spi...(a)gmail.com> wrote:
> On Jun 8, 11:47 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
>
> > "Aatu Koskensilta" <aatu.koskensi...(a)uta.fi> wrote ...
>
> > > Bill Taylor <w.tay...(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?
>
> ZF told Aatu to jump off a cliff? Oh man, I am so there.
>
> Marshall

All infinities are the same. They are all uncountable.

Mitch Raemsch
From: Transfer Principle on 9 Jun 2010 20:42
On Jun 8, 6:32 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Transfer Principle <lwal...(a)lausd.net> writes:
> > 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?

Ah yes, I do acknowledge that a proof may be difficult to find
if it involves large numbers. Indeed, this is exactly what Ed
Nelson is doing. He is attempting to find a proof that PA is
inconsistent, involving the large numbers that appear via the
operation of tetration.
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