In article <firstname.lastname@example.org>, david petry <email@example.com> wrote:
> 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.
I suppose it is surprising to classically trained physicists and other scientists, but it is not necessary to apply mathematics to physics or other sciences to justify its existence, nor is mathematics limited by the needs of classically trained physicists and other scientists. --