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Platonism, Naturalism, and Mathematical Knowledge by James Robert Brown

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4    Just Metaphor?

Lakoff's Language1

 In their book Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000), George Lakoff and Rafael Núñez consider the nature of mathematics in the framework of cognitive science. Contemporary cognitive science has revolutionary consequences for the philosophy of mathematics, especially the fact that mathematics involves conceptual metaphor. At least, so they say. They further claim that their results not only refute traditional Platonism about mathematical entities like numbers, but also provide a completely new philosophy (and even a new pedagogy) of mathematics that can take its place (2000, 9).

I will argue to the contrary, that findings in cognitive science that have ...

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