On Monday, January 7, 2013 3:59:48 PM UTC-5, david petry 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.