Re: Zeno's Pardox

["Roger Koppl" <KOPPL@xxxxxxxxxxxxxxx>]

Professor Carmo asks about Zeno's paradox and economics.

Israel Kirzner has long had an argument about infinite regress in the
chosing of maximization frameworks.  He uses the argument to support
his idea of "alertness."  I don't recall if Israel makes the link
explicit, but it's pure Zeno.  See his 1973 book _Competition and
Entrepreneurship_ Univ. of Chicago Press.

A less direct link, but still worth considering might be
Morgenstern's Holmes/Moriarty example.  See his essay entitled
something like "Perfect Forsight and Economic Equilibrium" in
Schotter edited _Selected Economic Writings of Oskar Morgenstern_ NYU
Press circa 1976.

It might even be worth your while to read some of the chapters of
Bell's _Men of Mathematics_ for his lucid discussion of Zeno.  Zeno's
paradoxes are paradoxes of the infinite.  One of the perennial
dividing lines in math is between those who will and those who will
not buy into the notion of a "completed infinity."

I hope something here is helpful.

Roger