[FOM] Cantor's "hidden" views

Martin Davis martin at eipye.com
Sun Feb 19 12:08:54 EST 2006

Arnon Avron wrote:

 >I think that Hilbert, Dedkind, Weyl etc deserve more credit than
 >thinking that if only they knew Cantor's hidden views they would never
 >have seen problems in set theory.

Cantor wrote Hilbert with an attempted proof of CH in which he used the 
absolute infinite in the argument. I believe (but don't remember clearly) 
that he wrote to Dedekind in the same vein. That's how hidden Cantor's 
views were.

What really upset Hilbert in particular was Russell's demonstration that at 
the bottom of Cantor's paradox was an antinomy that on the face had nothing 
to do with the infinite. (Arnon, is of course quite right that it was the 
comprehension principle that caused the trouble).

Martin Davis

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