[FOM] 461: Reflections on Vienna Meeting

[Walt Read]

>
> 10. To begin with, ZFC forms an unexpectedly comprehensive and definite
> model of mathematical practice, which is clearly sufficient to draw a number
> of startling and deep conclusions about the nature of mathematical practice.
> Our great physical theories also have this property - they are clearly
> sufficient to draw a number of startling and deep conclusions about the
> nature of physical phenomena -  and none of them come close to reflecting
> all physical phenomena that we seek to analyze.
>

   Is the defense of ZFC that it's a good "tool to inspire insight"?
Somehow it seems unlikely that that could have been the original
intent.

   There is a profound difference between mathematical "theories" and
physical theories and therefore between mathematical practice and
physical practice. The reality of physics is assumed to be outside of
us and only accessed indirectly. We need to be constantly testing our
hypotheses. The reality or "reality" of mathematics (depending on your
philosophical position) is assumed to be directly accessible. Unless
you're prepared to assert that PA is a set of working hypotheses which
are falsifiable as we get more experience with specific numbers, any
comparison of mathematical practice and physical practice is
superficial at best and misleading in the main. Surely Zermelo et al.
were looking for an actual foundation, something to reliably build
everything else on, not insights into mathematical practice,
falsifiable by sociologists of mathematics.

-Walt