david petry <email@example.com> writes:
> 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.
Well, then, do so!
What does it matter to you that others prefer using a theory that you don't like? Just go ahead and show how easily it can be eliminated. And then, knowledgeable folk can determine whether it is worthwhile to do so, just to ease your own personal philosophical views.
There are, as I understand, people who investigate just what bits of ZFC are inessential for, say, real analysis. These folks are doing real work. All you do is occasionally drop by with your silly metaphors about the computer as a microscope and whine about the fact that others don't give a damn about your pretty, little ideas.
Go do something and show the results if you want to make a change.
-- Sam Vimes could parallel process. Most husbands can. They learn to follow their own line of thought while /at the same time/ listening to what their wives say.... At any time they could be challenged and must be ready to quote the last sentence in full. -- Terry Pratchett