[FOM] On Epistemology of Mathematics

[Jon Awbrey]

Dmytro,

C.S. Peirce provided a framework for thinking about
belief and knowledge in mathematics, more generally
about the process of inquiry that "fixes belief" in
science and even in ordinary common sense reasoning.
He did this in a way that largely avoids the errors
of "psychologism" -- that Frege even more pointedly
criticized -- specifically, the tendency to confuse
a normative science like logic with a corresponding
descriptive science like psychology.

Jon Awbrey

Dmytro Taranovsky wrote:
 >
> In deciding which axioms to use in mathematics, we should reflect on not merely
> why they are necessary and true, but also what causes humans to believe their
> truthfulness.
 > ...
> My view is that humans have a universal capacity to think
> that allows us to go beyond the recursive limitation.
> 
> Dmytro Taranovsky
> http://web.mit.edu/dmytro/www/main.htm

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