FOM: Evolution and reason; math and the brain

Wed Apr 1 17:47:55 EST 1998

Let me add to Tennant's Uniformity Postulates for Logic and Mathematics the
following account of how these quasi-Platonic systems S and T could be
accessible to us, copied from a posting I sent to the Hersh splinter group.
*<If there is an abstract Platonic mathematics it does NOT follow that we have
no access to it.  Remember first of all that our scientific theories are
formulated mathematically and make experimental predictions.  When fully
formalized they have a mathematical part M and a physical part P.  An
experimental result confirms the conjunction (M&P) but we empirically observe
that M is common to all physical theories and extremely stable over time
compared to P--historically progress has practically always been made by
modifying P rather than M.  The common stable mathematical core may be regarded
as hard-won knowledge about the Platonic realm depending on the empirically
justified principle "the Universe is intelligible".  Secondly, we have access
to the part of math reducible to logic by definition.>*  Feferman argues that M
needn't go beyond PA; I'd say logic already gives PA. Neil, do S and T imply PA?

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