McCreason - 16 April 2008 12:38 AM

Was mathematics made up by people, incorporated into culture and society and then handed down through the generations? Ideas are memes. Is not mathematics an idea? It is an invented explanation and intrepetation of the abstract, no? 2 plus 2 equals 4. Only if we say so and believe it and tell our kids it is so.

This is an uninformed (I don’t mean that in a negative sense, just that it slides over many issues) gloss of a view of mathematics that has come up over the past 30 - 40 years generally going under the heading of social constructivism. It is rooted in Wittgenstein’s views of language and mathematics. The basic issue has to do with the reality of mathematical objects and the universality of mathematical truths. When you say that mathematics is made up by people, there is an ambiguity: we make up symbolic systems and formal rules for symbol manipulation—those are human constructions but, as with language, do the constructs (in this case the definitions, axioms, and theorems) refer to something out there in an independent reality, or are they simply made up playthings? Is the Pythagorean theorem universally true, or is it just a human construction that might be false in some other part of the universe? In the former case, saying that mathematics is a meme is like saying Mount Everest is a meme and ignoring the real physical mountain.