David Bernier wrote: > Am I right that the axiom schema of replacement is necessary to > assert the existence of some large "small cardinals"?
> As far as believing in the axioms of set theory, I think > first one needs to get at least acquainted with > first order logic.
There is no need to know any formal logic to understand or believe the axioms of set theory. Of course, if one is interested in their formalizations in ZFC a bit of logic is in order.
> Perhaps a good number of mathematicians don't have the > time, inclination, etc. to, e.g., read about > FOL, ZFC enough to be able to say confidently: > "Yes, I know why each of those axioms was introduced."
That certainly is true.
-- Aatu Koskensilta (email@example.com)
"Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus