[FOM] Friedman Macintyre

[Walt Read]

Thanks for posting these.

Pursuing ``foundations" as a general topic is an ambitious but
intellectually risky business unless it keeps close to the
practitioners of the field.  It's especially so for ``foundations of
physical science". The grounding for physics is the real-world.
Physicists sometimes talk about aesthetic criteria for a theory but
the bottom line is conformity to experiment. Math is in a different
situation because of questions about the nature of the existence of
mathematical objects. Historically consistency was often used to
justify existence. What I'm getting from Macintyre and Voevodsky is
that (at least some) mathematicians no longer see consistency as the
_sine qua non_ of theory. This might be due to ``foundational
fatigue", post-Godel acceptance of limitations, the rise of the
constructive point of view or maybe just a desire for novelty. But if
it's representative of mathematicians generally, then it represents a
shift in what would constitute foundations *for* math, if not *of*.
Other foundations come from other goals. In some ways, the attitude
seems closer to the physics view. We don't worry so much about showing
that our methods can never fail us as that they don't fail us in the
(more limited) situations where we actually use them. Of course,
classic FOM has methods for dealing with this but the emphasis may be
changing.

1. Assume consistency is no longer a core issue for mathematicians.
How does that change what foundationalists do, if at all?

2. Is completeness also less important? Compactness? That would change
the conventional view of formalizing mathematics.

-Walt

On Sun, Jun 12, 2011 at 10:13 AM, Añon Barfod <ianon at cim.com.uy> wrote:
> Since the Con(PA) thread snowballed from reflections on the Vienna
> meeting, you might be interested in the talks:
>
> http://videolectures.net/godelfellowship2011_friedman_ppf/
>
> http://videolectures.net/godelfellowship2011_macintyre_fcm/
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