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[jon zingale]

>From the article.

"Philosophers have always been divided about the roles of logic (formal
reasoning) and, by extension, of mathematics. There have been empiricists
who regard reasoning as just a tool to help organize the knowledge that
derives from our senses. And there have been rationalists who treat reason
as a mode of mystical, direct access to ultimate truths, one which bypasses
sense experience."

It may be surprising to hear, wrt the paragraph above, I identify as an
empiricist. A psychological (particularly phenomenological) grounding for
mathematics is very important to me. That we have group theory, IMO, follows
from the fact that the world affords us a notion of symmetry (including the
recognition of asymmetry). I am to some extent pragmatist in that the
symmetries I experience are *good enough* to be ontological objects, and the
idea of Symmetry (writ large) is a limit afforded by that pragmatism. Over
the last week, I fell down a Piaget hole thanks to a Jordan Peterson lecture
at the University of Toronto[Ϯ]. While EricC has done quite a bit over the
week to help me to move on from there, I am still left with a deep interest
in how we come to develop the repositories of knowledge that we do,
Mathematics especially. For me, Mathematics is a theory (in the sense of a
systematically organized body of knowledge) and its theorems tell us about
the experience and the intimacy of perception.

[Ϯ] https://www.youtube.com/watch?v=BQ4VSRg4e8w



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