[FOM] Freiling's axioms
John McCarthy
jmc at steam.stanford.edu
Fri Sep 3 22:42:26 EDT 2004
I now understand why set theorists don't like Freiling's axioms.
I just don't share their taste.
Their intuitions come from within set theory.
The intuitions behind Freiling's axioms are from ordinary
mathematics, i.e. probability theory, not from set theory.
Godel wrote that new intuitions would be required to settle the
continuum hypothesis. I don't know whether he would have liked
Freiling's.
I do believe that set theory is the appropriate foundation for
mathematics, including the AI formalizations of common sense knowledge
and reasoning. However, my intuitions don't come from set theory
itself.
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