Dr. DB has cleverly put the ball in the Platonists' court. A Platonist
has to admit that some mathematical creatures are not real, since
he constructs unreal objects himself whenever he produces a proof
by contradiction. If he tries to retreat to D-Platonism, he has to
say where to draw the line between what "exists" and what "does
not exist." The line was clear to Dedekind but it is not clear to me.
When are you talking "about" something? It isn't merely a
question of integers vs. real numbers. Dr. de Bruijn has pointed out
that there is another dimension to the problem. Even "natural"
numbers occur in hypothetical constructions which are designed to
be impossible, like ants in an M.C. Escher drawing. And yet it's all
supposed to be part of _the real world_ !
Is it abuse to ask a Platonist to acknowledge this problem?
Lyle