> The intuition, which has been articulated by many first rate > mathematicians at least since Poincare', is that we should not > try to talk about things that we can't actually talk about. >
Frege once characterized the empty set as a "forest without trees".
Modern mereology follows Lesniewski in denying the existence of an empty set.
Shall these be accepted as arguments to ban speaking of zero?
> Cantorian set theory, which purports to prove that there exist > uncountable sets > (and hence sets containing more things than we can actually > talk about) is then seen as nonsense on an intuitive level. >
Cantor's diagonal argument exposes a difficulty in treating the continuum as being the same as the sequence of natural numbers -- that is, as treating infinity ambiguously.
To disentangle this issue mathematically requires a theory of transfinite arithmetic.
Even if Cantor viewed his own conception in terms of realism, why do you presume that this is required of everyone else?