Dr. Podnieks had interesting remarks to make about the psychology of
mathematical intuition and the development of mathematical theories
and their relation to the sciences; most of these are perfectly
comprehensible from a platonist standpoint.
The one thing which I found rather forced was the idea that the
natural numbers are in any sense a product of human psychology; also,
while one might be able to distinguish two theories of the natural
numbers in history, neither of them is likely to be exactly
first-order arithmetic; I suspect that the ancient theory would be
more limited than first-order, if it could be identified precisely at
all, while, since second-order arithmetic was proposed before
first-order arithmetic, there would never have been any time when
first-order arithmetic was actually the dominant model.
This is a philosophical topic which I find fascinating; I'm not
certain what its relevance to QED may be. I suppose that our scruples
on the reality of the objects of mathematics may have something to do
with the kinds of root theories we adopt? Also, the operational
definition in a recent posting of the dichotomy between Platonism and
formalism in terms of what kinds of objects we take ourselves to be
manipulating was instructive.
--Randall Holmes