[FOM] CH and mathematics

joeshipman@aol.com joeshipman at aol.com
Mon Jan 28 01:22:05 EST 2008

Pitwosky's work by design had no testable predictions differing from 
standard quantum mechanics -- its value was philosophical, in showing 
that one could replace physical weirdness (spooky actions at a distance 
or failures of experimenters' free will or faster-than-light 
communication) with mathematical weirdness related to (but stronger 
than) Banach-Tarski type phenomena.

To the extent one takes the metaphysics and philosophy seriously, one 
can also use his work to argue for certain ZFC-independent mathematical 
propositions as necessary to make the physics work, vindicating a 
remark of Godel's that new axioms for set theory might come to be 
accepted on the basis of their fruitfulness in physics. (Technically, 
this depends on my result that "spin-1/2 functions" of the type 
envisioned by Pitowsky can not be shown to exist within ZFC; but I do 
not personally argue that spin-1/2 functions exist because I do not 
agree with the metaphysical assumptions of Pitowsky's model.)

-- JS

-----Original Message-----
From: hendrik at topoi.pooq.com
> 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).

Did it have any testable predictions?

-- hendrik
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