[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
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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