[FOM] CH and mathematics

Alasdair Urquhart urquhart at cs.toronto.edu
Fri Jan 25 09:24:49 EST 2008

Tim Chow wrote:

> Since Joe Shipman is involved in this discussion, I probably don't need to
> jump in with this, but physicists Itamar Pitowsky and Stanley Gudder have
> used the continuum hypothesis to construct a "local hidden-variables"
> theory.

I think it is more accurate to say that Itamar Pitowsky is a philosopher
of physics.  Pitowsky's construction uses the Banach-Tarski paradox to 
construct a highly nonstandard "quasi-probability" function that is then 
employed to construct the theory.  The function has odd features, for
example, in his model, two events can have quasi-probability 1 
but their intersection quasi-probability 0 (p. 2320).

Whatever one thinks of this result, it is very, very far removed
from the mainstream of physics and so I don't 
think it provides clear evidence of the relevance of set theory to 
physics.  I don't mean this as a criticism of Pitowsky, who states
explicitly: "The proposed model is by no means intended as an
alternative to quantum mechanics" (p. 2317).

Alasdair Urquhart

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