FOM: Math and Physics

Thu Apr 16 17:33:43 EDT 1998

Feferman reports in "When a little bit goes a long way: logical foundations of
scientifically applicable mathematics" that most of the math involved in
physical theories can be formalized in a weak type theory W that is conservative
over PA.  I have some questions about the import of this:
 1) (To Sol if he's still listening): Does this apply to Quantum Electrodynamics
and General Relativity, the two most fundamental fully mathematized physical
theories?  (Other Quantum Field Theories aren't fully rigorized yet).
 2) Let's postulate that a physical theory PT formulated in W is "true".  Does
the existence of a reduction from W to PA mean (as Feferman implies) PT confers
no "ontological rights" (Quine's term) on mathematical entities of higher type
than integers?  I'd say no, unless the reduction "preserves comprehensibility".
 3) Does it make a difference to the f.o.m. whether there is a "Theory of
Everything" of the type physicists seek?  (I claim it does.)
 4) "How far up" can the following extramathematical considerations confer
definiteness on mathematical entities? a)physical realism b)logicism c)theism JS

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