Okay… I now know what an ordinal number actually is. And I’m trying to make more sense out of your comment...
So, re-reading this:
or even be uniquely specified by second-order axioms that pin down a single model up to isomorphism the way that second-order axioms can pin down integerness and realness, is something we have rather less evidence for
So if I understand you correctly, you don’t trust anything that can’t be defined up to isomorphism in second-order logic, and “the set of all countable ordinals” is one of those things?
(I never learned second order logic in college...)
Hmmm…
::goes and learns some more math from Wikipedia::
Okay… I now know what an ordinal number actually is. And I’m trying to make more sense out of your comment...
So, re-reading this:
So if I understand you correctly, you don’t trust anything that can’t be defined up to isomorphism in second-order logic, and “the set of all countable ordinals” is one of those things?
(I never learned second order logic in college...)