[FOM] extramathematical notions and the CH

Timothy Y. Chow tchow at alum.mit.edu
Tue Feb 5 11:34:36 EST 2013

Nik Weaver wrote:

> Really?  I wasn't aware that physicists had any evidence that ZFC is 
> consistent.

The comment was slightly flippant, because physicists don't care about the 
question.  But if they had reason to care, I think they'd be satisfied 
with the current evidence.

> Is this a version of the "indispensability" argument which says that
> confirmation of physical theories amounts to confirmation of Con(ZFC)
> because the mathematics underlying our physical theories can be
> formalized in ZFC?

No, certainly not.  The evidence I had in mind was, people have looked for 
a contradiction and haven't found one.  If you want to dress this up in a 
way that has more of a "laboratory science feel," then program up a 
computer to look for the contradiction for you.  Keep it running until 
your grant runs out.

> If that is what you mean, you could just as well say that physicists
> have evidence that supercompact cardinals exist

"Supercompact cardinals exist" isn't Pi^0_1.  But I would say that 
physicists have evidence that supercompact cardinals are *consistent*.


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