Obections to Cantor's Theory (Wikipedia article)
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From: Han de Bruijn on 25 Jul 2005 05:38 David Kastrup wrote: > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: >> [ ... ] But mathematical axioms start to behave _as if_ they >> were physical laws, as soon as they become being _applied_ to >> i.e. physics. > > Oh nonsense. It is not the mathematics that draws the connection > between its axioms and the physical world, but the physicists. The mathematics or the physicists, whoever does it. Han de Bruijn
From: David Kastrup on 25 Jul 2005 05:43 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > David Kastrup wrote: > >> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: >>> [ ... ] But mathematical axioms start to behave _as if_ they >>> were physical laws, as soon as they become being _applied_ to >>> i.e. physics. >> Oh nonsense. It is not the mathematics that draws the connection >> between its axioms and the physical world, but the physicists. > > The mathematics or the physicists, whoever does it. No skin of the mathematicians' nose. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum
From: Han de Bruijn on 25 Jul 2005 05:47 David Kastrup wrote: > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: >> >> It's not that bad. The Theory of Relativity didn't invalidate the >> use of Newtonian Mechanics with designing bridges and cars. > > There is no room for a bit of error in the tenth place if you are > factoring primes. OK. If you want no error in the tenth place, use Relativity :-) >> And what would be wrong with a mathematics which evolves in time, >> like everything else in life ? > > That's like saying what is wrong with a building that evolved in time, > like everything else in life? Let's use sand instead of bricks. > > You don't get anywhere serious if your structures keep crumbling down. Structures of _life_ tend to be _growing_ instead of crumbling down, that is: iff you keep them healthy and well. Han de Bruijn
From: David Kastrup on 25 Jul 2005 05:56 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > David Kastrup wrote: > >> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: >>> >>> It's not that bad. The Theory of Relativity didn't invalidate the >>> use of Newtonian Mechanics with designing bridges and cars. >> There is no room for a bit of error in the tenth place if you are >> factoring primes. > > OK. If you want no error in the tenth place, use Relativity :-) > >>> And what would be wrong with a mathematics which evolves in time, >>> like everything else in life ? >> That's like saying what is wrong with a building that evolved in >> time, >> like everything else in life? Let's use sand instead of bricks. >> You don't get anywhere serious if your structures keep crumbling >> down. > > Structures of _life_ tend to be _growing_ instead of crumbling down, > that is: iff you keep them healthy and well. That's why mathematics is not tied to changing entities. If you find in nature that conservation of mass does not hold, that does not disturb addition in math. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum
From: Robert Low on 25 Jul 2005 06:00
Han de Bruijn wrote: > Clearly, it has never crossed their minds that such a nice relationship > between topology and calculus could possibly esists. Apart from trivialities like de Rham cohomology and the Atiyah-Singer Index theorem, anyway. |