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Embodied mathematics is what you are describing I think. The idea is that mathematics arises out of ordinary experience extended by metaphor. It charts a pretty
by roywiggins 11y ago
Embodied mathematics is what you are describing I think. The idea is that mathematics arises out of ordinary experience extended by metaphor. It charts a pretty satisfying middle ground between Platonism and Fictionalism. Mathematics is a story, but it is "at the bottom" tied into our experience of everyday reality. Do real numbers exist? Probably not, but the the continuum is like a long stick you can make marks on.
Can you have a trillion apples, so you know that a trillion + a trillion is two trillion? No, but you can reason about "trillion" as existing metaphorically.
- hyperpape 11y agoThat actually just sounds like good old fashioned nominalism or fictionalism--you'd have to sketch out a more detailed story, but I don't think it's actually distinct.
- roywiggins 11y agoI'm (probably badly) summarizing Lakoff & Nunez's book: https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From Neither are capital-P Philosophers, and I don't remember if they actually make a claim that their ideas are philosophically distinct from fictionalism- they're more worried about platonists! The other approach I'm fond of is saying mathematical objects exist but only inside the heads of mathematicians. As long as mathematicians share a particular idea and can talk about it, it's math. So when I point to the real numbers, I'm pointing at a real thing: the shared idea of them. There's no Platonic realm, but they exist in the mind. It parallels how mathematics is really done (a proof is only a proof if it convinces mathematicians) so I find it compelling on that front.