Tuesday, March 12, 2019

Embodied math

Continuing the last post, Platonists think math in inherent to the universe and something we discover. Recall  this FB IPS thread on cognitive science and just how that is so. E.g.:

I was just re-reading some of Lakoff & Nunez, Where Mathematics Comes From. Even in math there is no one correct or universal math. There are equally valid but mutually inconsistent maths depending on one's premised axioms (354-55). This is because math is also founded on embodied, basic categories and metaphors, from which particular axioms are unconsciously based (and biased), and can go in a multitude of valid inferential directions depending on which metaphor (or blend) is used in a particular contextual preference. Hence they dispel the myth of a transcendent, Platonic math while validating a plurality of useful and accurate maths.

However Lakoff & Nunez do not see the above as relativistic postmodernism (pomo) because of empirically demonstrated, convergent scientific evidence of universal, embodied grounding of knowledge via image schema, basic categories and extended in metaphor. They see both transcendent math and pomo as a priori investments.


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