[FOM] Berkeley and Weyl/Arnon as critics of foundations

Martin Davis martin at eipye.com
Sun Feb 19 19:54:21 EST 2006

While Berkeley's critique confined itself to the methods, he did not 
quarrel with any of the results. It is striking that just about everything 
that was done with dubious methods in the 17th and 18th centuries survived 
essentially intact after the coming of epsilon/delta. Even some of Euler's 
seemingly outlandish summations of series (e.g. 1/2 = 1-1+1-1+1-1+...) were 
incorporated into summability theory. But Weyl/Arnon advocate a methodology 
which at the outset excludes most of set-theoretic mathematics including 
work done by such outsiders as Paul Erdös.


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