jshipman at bloomberg.net
Thu Nov 20 09:57:19 EST 1997
Vaughan disagrees with me that an inconsistency in ZF would be "a bigger
earthquake than Godel's" and says it "would be an earthquake for set theory,
but it would be business as usual for 99.99% of mathematics".
First of all, I strongly disagree with the implication that set theory is no
more than 0.01% of mathematics! If you apply an extremely crude criterion like
counting Ph.D.'s, this seems off by a couple of orders of magnitude.
Secondly, Godel's results did not affect "business as usual" (at least not so
far, though if Harvey's current projects pan out they will) so that doesn't
invalidate my comparison. My criterion for the earth-shatteringness of a result
is how many textbooks would have to be rewritten and the answer is "a great
many of them" (since replacement used informally all over the place though not
in a necessary way). Has there EVER been an example of a principle of
mathematical reasoning used widely for many decades being refuted?--Joe Shipman
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