[FOM] The boundary of objective mathematics
Paul Budnik
paul at mtnmath.com
Sat Mar 14 12:19:01 EDT 2009
Timothy Y. Chow wrote:
> I'm curious about this "increasing scepticism" that you speak of. Do you
> have any statistical evidence of increasing scepticism? Or it is just a
> rhetorical flourish?
>
Its an impression I have based on limited evidence. Soloman Feferman
expresses his doubts about the CH near the end of his paper "Does
Mathematics Need New Axioms?"
(math.stanford.edu/~feferman/papers/newaxioms.pdf ). There use to be a
web page that gave the opinions of various prominent mathematicians on
CH. Several of them expressed doubts about whether it was objectively
true or false. I cannot now find the page so it may no longer exist.
When I was a student (admittedly quite some time ago) I had the
impression that the vast majority of logicians thought CH was an
objective question.
> ... In one direction, I could argue
> that as far as we know, the continuum hypothesis might play a key role in
> the physical world. ...
>
Einstein, Feynman, a recent Noble Prize winner Gerard 't Hooft and many
others have come to suspect that physics is ultimately discrete or
digital (see http://www.mtnmath.com/digital.html for quotes and
additional names). Thus it is at least a respectable philosophical
position to take. Potential infinity is very useful in developing
mathematics and our universe could be potentially infinite.
Paul Budnik
www.mtnmath.com
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