[FOM] CH and mathematics

[hendrik@topoi.pooq.com]

On Mon, Jan 21, 2008 at 12:16:18PM +0200, Alex Blum asked:
> And  are the truth conditions of CH any less clear than that of 2+1=3?

My intuitions and experience with set theory have told me, at least, 
that I have very little good intuition about sets, especially infinite 
sets defined by predicates (or impredicates, to back-form a word).  In 
fact, when it comes to infinite sets, about the only understandings we 
have are those derived from proofs, based on axioms postulated by 
analogy with finite sets.  Over the years of reading proof theory, model 
theory, and the like, it has become more and more clear to me that I 
don't really know what a set is when we get to these more abstract 
realms.  If it's something defined by axioms, then it's just a question 
of whether it can be proved from those axioms (whichever ones one 
chooses).

But we have a lot of experience with small finite integers, dating back 
through millennia of accounting to the very beginnings of mathematics.
We don't need to understand anything about infinities to understand 
2+1=3.

-- hendrik