FOM: attitudes of core mathematicians and applied modeltheoriststoward f.o.m.

[Mark Steiner]

charles silver wrote:
>
>     Doesn't non-standard analysis show that Berkeley was wrong and Leibniz
> was right?
>
> Charlie

	I'm a little hesitant to write answers in this field, but I doubt that
the core mathematicians are running out to buy the calculus textbook
based on infinitesimals.  More seriously, I suggest that nonstandard
analysis could never have existed without the rigor in f.o.m. which
mathematicians developed in the 19th century partly as a result of
Berkeley's criticisms and partly because of internal pressures (e.g.,
mathematicians were not sure that they had proved certain theorems or
not).  Once analysis is known to be consistent, you can play games with
conservative extensions.

	There's also an historical/foundational question which I believe the
historian Prof. Bos from the Netherlands deals with--namely, whether
Leibniz theory of infinitesimals is actually the Robinson theory.
Something to do with second and third order infinitesimals I vaguely
recall.  I'd welcome clarification, because I know there are experts out
there.

Mark