[FOM] FOM: set theory

[Fred Richman]

Martin Davis wrote:
 
> Dean Buckner wrote:
 
>> My view is that set theory is wrong, in the sense it does not
>> capture our ordinary intuitions about sets and things.
 
> This makes about as much sense as saying that physics is wrong
> because it doesn't capture our ordinary intuitions about work and
> energy. A scientific discipline is not intended to capture our
> ordinary (fallible) intuitions, but rather to improve on them.
> Particularly on FOM, set theory is of special interest in
> providing a foundation for mathematics where "our ordinary
> intuitions" have proved utterly misleading.
 
I'm struck by the tacit claim here that set theory, or perhaps
mathematics itself, is a "scientific discipline." I've never been
comfortable with lumping mathematics in with the sciences. I don't
consider myself a scientist. How do other people on the FOM list feel
about this?

I think it reasonable to attack set theory on the grounds that it does
not capture our ordinary intuitions. Keep in mind that our intuitions
change as we explore the consequences of various assumptions. If, at the
end of the day, our theory is completely out of whack with our
intuition, then something needs to be done. That is not so much the case
in physics, where the physical universe might be governed by
incomprehensible rules, or no rules at all.

--Fred