[FOM] extramathematical notions and the CH
Nik Weaver
nweaver at math.wustl.edu
Sun Feb 3 13:51:27 EST 2013
Tim Chow wrote:
> Physicists, of course, already have enough evidence that ZFC is consistent
> that they don't need to do anything further before the corks start popping.
Really? I wasn't aware that physicists had any evidence that ZFC is
consistent.
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? But surely you're aware that the mathematics
underlying all experimentally relevant physical theories can be
formalized in much weaker, predicative, systems. (I use the qualifier
"experimentally relevant" out of politeness. The point could be put
more forcefully.)
If that is what you mean, you could just as well say that physicists
have evidence that supercompact cardinals exist, since the mathematics
underlying our physical theories can be formalized in ZFC + "there
exists a supercompact cardinal". If indispensability arguments show
anything, it is that we have experimental confirmation of the consistency
of the weakest formal systems in which our physics can be formalized, not
of systems which are much stronger than what is needed.
Nik Weaver
More information about the FOM
mailing list