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Personally I think we'd be well served by taking a constructivist approach to mathematics. A lot of the apparent paradoxes and monsters of functional analysis go away if you take a constructivist approach. Which, in fact, is good for applied mathematics such as physics because a lot of conundrums just melt away.

We have met the enemy, and he is us — Pogo
by Migeru (migeru at eurotrib dot com) on Wed Jan 2nd, 2008 at 03:10:32 PM EST
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