Wednesday, September 06, 2006

Rumbling

Kurt Godel proved the consistency of first order logic in 1930. That's odd.

First, logic was considered a foundation for reason for over two thousand years, yet nobody knew if you could derive a contradiction by using its axioms.

Second, it took over two thousand years to prove the consistency of FOL, and it took a genius to do it.

What if the consistency of FOL was still not proved? It seems the equivalent of building houses on the side of an active volcano. They might be inhabitable for a long time. Then the eruption could come and sweep everything away.

Well, Godel proved the consistency of FOL, so we can all sleep soundly in our beds at night.

What's that rumbling I hear?

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