FOM: Re: predicativist, constructive physics -- reply to Frank and Ketland
Matthew Frank
mfrank at math.uchicago.edu
Thu Feb 17 19:00:24 EST 2000
Two responses:
Ketland notes "Hellman thinks that certain statements about manifolds are
not even *expressible* in Z_2". This is only because Hellman defines
manifolds as topological spaces with a maximal atlas of coordinate charts.
But there is no obstacle to discussing manifolds in Z_2 as spaces which
simply have an atlas of coordinate charts. This is a slight variant of
the standard definition, but in practice has no effect.
Shipman mentions quantum field theory as an objection to Feferman's
program of predicative physics. When I discussed the success of that
program, I said that I felt "all the theorems of mathematical physics can
probably be recovered predicatively and in ACA_0." So I do not count
quantum field theory as an objection: when someone finds a more
satisfying mathematical treatment of it, I think it will be easy to
recover it predicatively. I also doubt that particularly impredicative
thinking will be particularly useful in coming up with such an account.
--Matt Frank
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