FOM: Reply to Feferman on Cantor and Hilbert jshipman at
Thu Dec 4 15:56:32 EST 1997

   Of course I didn't mean that Cantor and Hilbert never made mistakes, just
that they knew what they meant when talking about real numbers, countable
ordinals,  the collection of all real numbers, and the collection of all
countable ordinals, and that what they meant was not incoherent.  I was
referring to their thinking on the matter of CH's MEANINGFULNESS, not its TRUTH.
   Sol's remarks from and about Cantor don't disprove this -- Cantor was
apparently a particularly strong theistic Platonist regarding mathematical
existence, but there is nothing wrong with that.  And the Axiom of Choice, to
which the Well-Ordering theorem is straightforwardly equivalent, is regarded by
many as a law of thought (I regard my own favorite form of AC, "a product of
nonempty sets is nonempty", as pretty darn self-evident though I might not go
quite so far as to call it a Law of Thought).
   As for Hilbert, his "proof" of CH isn't so different from assuming V=L, and
although his "program" depended on a conjecture disproved by Godel, that is not
evidence he was confused or indefinite.                      -- Joe Shipman

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