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Well, my complaint was, that 30 years after Goedel showed mathematics was not exactly planted on solid bedrock, mathematicians were still pretending that it was.  

I had no complaint about internal consistency--but what we were getting was faith.  In a sense there was no choice about that, but I thought that in that case we should own up to it.  

Then again, a non-formal proof of consistency, might serve, but--and now I am wandering off-topic, perhaps those funny little symbols were not as important as everybody thought?  I was slowly coming around to the intuitionist view that mathematics should be comprehensible.  Even if the intuitionists treated Cantor very badly--which they did--they weren't wrong about everything.  Hilbert's project had its uses, but the core of it had failed.  It was time to let mathematics be done in a style appropriate to its content.  

So during this period, it was the logicians, not the mathematicians, who were my guides.  They wanted proof of consistency but knew they had not gotten it, and owned up.  They knew they needed to do something about it, too, even if what they did lay outside of logic.  

The Fates are kind.

by Gaianne on Wed Jan 2nd, 2008 at 02:51:24 PM EST
[ Parent ]
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
[ Parent ]

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