[FOM] Convincing math-blind people that math is different
jawbrey at att.net
Tue Dec 23 22:32:13 EST 2014
Re: Tim Chow
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.
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