Date: Jan 7, 2013 2:14 PM
Author: Dan Christensen
Subject: Re: ZFC really really really sucks -- really!

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?

Dan
Download my DC Proof 2.0 software at http://www.dcproof.com