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

Joe Shipman shipman at
Thu Feb 17 20:26:14 EST 2000

Matthew Frank wrote:

> 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.

On what do you base your opinion that a more satisfying mathematical treatment
of quantum field theory will be easy to recover predicatively?

There is a good place to start -- as I said before, QED (unlike other QFT's)
is precisely formulated mathematically, lacking only a convergence theorem.
Another theory to try to "predicativize" is General Relativity.  If Feferman
or someone else can redevelop these two theories (which are quite a bit more
complex than classical mechanics or classical electrodynamics) within
predicative mathematics, I will be much more inclined to agree with you.

-- JS

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