In the midst of a rather interesting discussion of the notion of Aristotle’s Unmoved Mover, Leah Libresco went on a mild digression about the philosophy of mathematics that I couldn’t let go of, and feel compelled to respond to. She says:
I take what is apparently a very Platonist position on math. I don’t treat it as the relationships that humans make between concepts we abstract from day to day life. I don’t think I get the concept of ‘two-ness’ from seeing two apples, and then two people, and then two houses and abstracting away from the objects to see what they have in common.
I think of mathematical truths existing prior to human cognition and abstraction. The relationship goes the other way. The apples and the people and the houses are all similar insofar as they share in the form of two-ness, which exists independently of material things to exist in pairs or human minds to think about them.
The notion that there’s something special about math – that it has some sort of metaphysical significance – only makes sense if you ignore the history of how we uncovered math to begin with. It was, despite Leah’s protestations, exactly just the abstraction of pairs and triplets and quartets, etc. The earliest known mathematics appear to be attempts to quantify time and make calendars, with other early efforts directed towards accounting, astronomy, and engineering.
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