[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

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