FOM: Tennant on set-theoretic and other foundations

Tue Feb 24 15:08:27 EST 1998

   Neil, Tragesser does not owe us an impossibility proof that some branch of
mathematics cannot be reduced to set theory; he merely needs to challenge us by
specifying a branch of mathematics and claiming it cannot be reduced to set
theory--if we cannot rebut the claim his position holds up.
   Your proposal to respect the need to prosecute branches of mathematics in
their own intrinsic terms must come to terms with the empirical observation
that almost all branches of mathematics have benefited strongly from interaction
with the terms and methods of other branches, often far removed, in ways that
cannot always be recast into "intrinsic" terms (the most obvious examples come
from Reverse Mathematics; another example is the apparent necessity of analytic
methods in number theory [are these always eliminable?]). -- Joe Shipman

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