FOM: Cantor and Hilbert knew what they were talking about jshipman at
Thu Dec 4 12:17:38 EST 1997

Cantor and Hilbert certainly felt that CH was meaningful, and I do NOT think
that there was anything essentially wrong with their thinking on this matter.
It's sour grapes to say because we can't decide it that it is inherently vague
or essentially indefinite.  I know what a set of integers is, and I know what a
countable ordinal is, and I darn well know what a 1-1 correspondence between the
sets of integers and the countable ordinals would be!  The only possible
vagueness you could charge me with is "you don't know what ALL the sets of
integers (as a totality) and ALL the countable ordinals (as a totality) really
are", but if I really know what I'm talking about when I talk about the members
of two sets I ought to be allowed to say "the sets are the same size" without
being criticized for vagueness or indefiniteness.  Cardinality is an utterly
fundamental notion.  GCH of course is an entirely different matter because it
talks about arbitrarily large sets.  (I always thought GCH was silly, it's
false for the finite cardinals so you have to include an ugly infinity clause).
If ZFC doesn't suffice for CH, so what?  What's privileged about ZFC?--J Shipman

More information about the FOM mailing list