FOM: "Unreasonable effectiveness..."; CAT vs. SET
pratt at cs.Stanford.EDU
Fri Jan 30 16:05:32 EST 1998
From: <wtait at ix.netcom.com>
>Although I probably appreciate the motives for this proposal---I have
>certainly felt that no new ground has recently been cultivated
Do you mean that literally, or only that no one has yet said, "Oh, *now*
I understand what you've been saying."? I would agree with the latter
(which is a disappointment).
>In his Grundlagen, Canter wrote that no one need police mathematics
>against the creation of bad mathematics; if it is bad, no one will pay it
>heed and it will just die away.
Death is undecidable for mathematical topics. Hamiltonian mechanics
seemed to be still-born, but roared into life a century later. There
are many other such examples.
Elegance is another such undecidable predicate. You may judge category
theoretic foundations as inelegant (or worse), but it is quite on
the cards given the way fashions change in mathematics that a future
generation of foundationalists could render the reverse verdict about
sets. There is certainly no objective reason to judge category theory
as inelegant, the definitions are simple enough.
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