Pop-math author par excellence Keith Devlin drops Platonism.
In doing so, Keith edges a bit closer than I’d like to the social-contruction arguments of Reuben Hersh. I seriously doubt that “other cognitive creatures in another part of the universe might have different mathematics.” I don’t think, when we eventually get to the Lesser Magellanic Cloud, we shall find that two plus two equals five over there, or that the angles of plane triangles add up to 190 degrees. In any case, according to Martin Seligman (see below) there’ll be no-one there to discuss the matter with.
Still, the anti-Platonism is surely correct. The beginning of mathematics is abstraction — forming those stable mental structures we call “concepts” from repeated observations of the world around us. Abstraction, and math, then advance by forming hierarchies of concepts, the concepts at each level dealing with the concepts at the lower as if they were objects in the physical world. That is, as Keith points out, the only way we are equipped to treat them. The fact that we can only think about concepts as if they were objects, does not mean they are objects, though. Score one for Nietzsche. Still, anyone who seizes on this as an excuse to teach “feminist math” or “African math” should be tarred, feathered, and run out of town on a rail.
Devlin’s piece is one of many brief contributions to science webzine Edge.org’s Annual Question round robin: “What Have You Changed Your Mind About? Why?” addressed to notable intellectuals, with a bias towards the human sciences. For an exceptionally high quotient of interesting ideas to words, this is hard to beat. Try, according to your own interests:
What a feast of egg-head opinionating!
If there’s a common tendency running through many of these pieces, it is the fast-rising waters of naturalism, released by a half-century of discoveries in genetics, evolutionary biology, and neuroscience, submerging every other way of looking at the human world.
We are part of nature, a twig on the tree of life. If we are to have any understanding of ourselves, we must start from that. Final answers to ancient questions are beginning to come in. You may not be happy about the answers; but not being happy about them will be like not being happy about Heisenberg’s Uncertainty Principle. Sing it, Bobby:
Come gather ‘round people
Wherever you roam
And admit that the waters
Around you have grown
And accept it that soon
You’ll be drenched to the bone.
If your time to you
Is worth savin’
Then you better start swimmin’
Or you’ll sink like a stone
For the minds they are a-changin’.