[FOM] Convincing math-blind people that math is different

Jon Awbrey jawbrey at att.net
Tue Dec 23 22:32:13 EST 2014

Re: Tim Chow
At: http://www.cs.nyu.edu/pipermail/fom/2014-December/018455.html


My interest in the thought of C.S. Peirce leads me to spend a good deal of my time explaining the 
mathematical side of his work to people with more philosophical than mathematical backgrounds and 
also to spend a certain amount of time hoping to coax people with the necessary mathematical skills 
into paying more mind to the distinctive features of his thought.

I experience mostly failure in negotiating that two-cultural divide, to the point where I begin to 
believe in the incommensurability of paradigms.  But it does seem that many of the less mathematical 
people are able to understand one of Peirce's points about the qualitative difference in the nature 
of mathematical inquiry, namely, that the reason we are able to achieve certainty and exactitude in 
mathematical reasoning is because we are reasoning relative to hypotheses that we ourselves make. 
This is how we finesse the uncertainty that would otherwise arise from exposing our theories to 
empirical encounters.  Whether Gödel changed all that I cannot say.




More information about the FOM mailing list