FOM: Re: predicativist, constructive physics -- reply to Frank and Ketland

[Matthew Frank]

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