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Re: ZFC really really really sucks -- really!
Posted:
Jan 7, 2013 3:59 PM
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On Monday, January 7, 2013 11:14:57 AM UTC-8, Dan Christensen wrote:
> On Monday, January 7, 2013 8:50:09 AM UTC-5, david petry wrote:
>
> > An article by Nic Weaver is worth a read:
> > http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.1680v1.pdf
> > Here's a quote:
> > "An essential incorporation of impredicative mathematics in basic physics would involve a revolutionary shift in our understanding of physical reality of a magnitude which would dwarf the passage from classical to quantum mechanics [...} the likelihood of ZFC turning out to be inconsistent [is] much higher than the likelihood of it turning out to be essential to basic physics. The assumption that set-theoretically substantial mathematics is of any use in current science is simply false"
> > By "impredicative mathematics", he means mathematics with the powerset axiom.
> I think you need a powerset axiom to formally construct the set of functions mapping a given set to another -- e.g. the set of continuous functions on the reals. Isn't that important to be able to do?
I suppose it is surprising to classically trained mathematicians, but it is not necessary to define a set of all continuous functions, nor even a set of all real numbers, to develop the mathematics used in science.
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