From: Hal Finney (hal@rain.org)
Date: Mon Nov 10 1997 - 11:46:47 MST
Alex Tseng, <alextseng@rocketmail.com>, writes:
> I'd like to agree that there is no way for proving the CH
> to be either true or false, a la Godel ; which states if we construct
> a proof that is either incomplete or inconsistent...and dealing with
> infinities, I have no expirence,...can anyone shoot me down?
> to show that a proof construct to prove or disprove CH will
> be either incomplete or inconsistent,thus a never-ending story
> ( just like this discussion on INFINITIES seems to heading towards
> some infinite point....hey hey hey )
Kind of hard to extract meaning with all the ellipses... not sure where
thoughts start or end... godel's theorem wasn't used to prove the ch
was unprovable... didn't have anything to do with that, except godel
the man was interested... proof was by models... find a way of modelling
axioms+ch within standard theory, no problems... find a way of modelling
axioms+opposite of ch within standard theory, no problems... kind of like
how it was done with noneuclidean geometry, capische... say, this is
sure easy... i see why people post like this... no need to organize or
anything... hope you're getting a lot of useful info out of this...
> Am I making any sense here,...Let me try to put it in another way...
> a quasi-layman approach,... to say just like the Quantum Physics says
> that we cannot determine exactly one property of a particle without
> losing the accuracy of another property of the same measured partical
> ...can be said to be analogous to Godel's Incompleteness theorem
> which says one can never generate a complete theory without
> inconststencies and vici-versa.....!!!
> So just like adding one to one equals two on paper
> is actualize by puting one apple beside another making 2 apples....!
Don't think these have anything to do with each other... any more than
any other situation which has two alternatives... qm lets you trade off
the accuracy of measurements of one property against accuracy of other...
it's continuous... godel's theorem is all or none... besides, nobody is
interested in inconsistent axiom sets... they don't really count... so
godel's theorem really just says that no sufficiently complex theory is
complete... it's not really a duality... also this is the old way of
looking at qm... lots of us like many worlds...
> Does Godel put a limit to what we can actually say about CH and
> other related matters,....I think it does ?! Pls help out
> ( if so put a limt to this discussion on Infinities or mine !? )
No, godel's theorem is not really practical... doesn't actually generate
any practical undecidable propositions... all are monstro massive...
main point is philosophical that such must exist... in practice have to
do it the old fashioned way... have to prove the proposition undecidable...
sometime i'll tell you how it was done for noneuclidean geometry... really
good story... unfortunately these ellipses are too small to contain it...
> Not to lose sight of our extropian objectives, is how these
> infinities or INFINITIES will even affect our extropian objectives
> or put limits or no limits to our objectives,....
Some relation to quantum computing... theoretically a quantum state can have
infinite information... not just aleph null, but real numbers... some people
think this is much more than aleph null... in practice environmental noise
probably makes it finite... but maybe if the whole universe were your state...
there'd be no environment... then maybe you could go beyond aleph null in
your calculations... just a crazy thought... gotta watch these ellipses...
that means three dots btw... think i'm getting dizzy... better stop now...
Wow, what a trip.
Hal
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