FOM: real numbers and the real world

[Matthew Frank]

Allen Hazen mentions the view "that reformulating physics in [Hartry
Field's] `nominalistic' way made physical explanations more perspicuous."

I find this view implausible at the moment (unless "perspicuous" means
"perspicuous for someone worried about nominalizing classical theories").  
I doubt that anyone would find Field's reformulations of physics more
perspicuous than the standard differential equations.

>From my perspective, Field's great achievement was to give a nice,
geometrical, formal framework (language + axioms) for classical
gravitation of continuous media.  In particular, he showed how to
formulate Poisson's equation in this language.  Field's great achievement
from his perspective (or at least that of some commentators) was to show
that the models for these axioms are just the classically intended models.

Field might have gone further, and shown how to formulate some of the
standard (classical) consequences of Poisson's equation in this language;
further yet, he might have given an elegant derivation in that framework 
of those consequences.  That would convince me of the perspicuity of the
nominalistic perspective.  I think the project would be difficult, but
possible and of mathematical value; so far as I know, no one has attempted
it.

--Matt