FOM: attitudes of core mathematicians and applied model theorists toward f.o.m.

Mark Steiner marksa at
Wed Jan 26 16:36:11 EST 2000

	The intolerance of arguing that field X is of interest only if it
contributes to MY field is regrettable, but widespread.

	Philosophy also sufferences from such intolerance.  I recall being
deeply offended by Steven Weinberg's book, Dreams of a Final Theory,
which contains a chapter, Against Philosophy.  This chapter argues that
philosophy has made no contribution to particle physics since 1945.
(Neither has chicken soup, but he has no chapter on that.) Even where a
scientist claims to be, or appears to be, influenced by philosophical
ideas, I have to agree with my friend Juliet that the connection may be
more causal/psychological than logical.  Nevertheless, it's great if a
philosophical idea sparks creativity in another field.  (Harvey has
written that he employs even discredited philosophical ideas to gain
insights, and that's fair enough.)  And, I don't deny that a scientific
piece of work can occasionally be ALSO or CONTAIN real philosophy.  No
one in his right mind would deny that Frege's Grundlagen is BOTH great
philosophy and also great f.o.m.  Though Goedel's work has enormous
philosophical interest (I'm teaching an entire course next semester on
the philosophical significance of Goedel's theorem), his philosophical
remarks on intuition, though they may well have INSPIRED his
mathematical work, are not in themselves great philosophy.  Goedel's
claim to fame as a philosopher (meaning philosophical achievement, not
just "philosophical acuity") should be made out by arguing that his
foundational work itself embodies philosophical analysis in the way that
Frege's did.
	Finally, as Mara Beller has documented in her new book, Quantum
Dialogue (Chicago), much of the philosophical patter of scientists may
be "politically" motivated.  Often a scientist will use philosophical
ideas to ensure the reception of an otherwise unpopular theory.
Einstein's use of positivist conceptions in arguing for the relativity
of simultaneity should be examined skeptically, in light of his later
realism with respect to spacetime and perhaps quantum mechanics.  In his
argument with Einstein, Bohr used instrumentalist/verificationist
arguments as a weapon (argues Beller), where previously he had shunned
such arguments.  In the case of the quantum revolution, Beller
concludes, you can almost never take philosophical pronouncements by
scientists at face value--you have first to see who the scientist is
reacting to and why.
	I think that core mathematicians should appreciate that
foundationalists are uniquely capable of conveying to others the great
interest of mathematics itself.  The same goes for philosophy; a more
reasonable role for philosophy vis a vis science is to interpret and
analyze scientific ideas in such a way as to highlight their
"intellectual interest" and importance.    In doing so, we need not go
overboard, as Kant did, and proclaim that our favorite scientific theory
is inevitable or a priori.

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