FOM: reply to the "list 2" crowd
csilver at sophia.smith.edu
Thu Jan 22 07:25:54 EST 1998
On Sat, 17 Jan 1998, Stephen G Simpson wrote:
> It seems that the "list 2" crowd is upset. Perhaps they didn't expect
> anyone to catch on to their game.
> A brief history of "list 2":
> I proposed to define f.o.m. (= foundations of mathematics) as "the
> systematic study of the most basic mathematical concepts and the
> logical structure of mathematics, with an eye to the unity of human
> I presented a tentative list of the most basic mathematical
> concepts: number, shape, set, function, algorithm, mathematical
> axiom, mathematical proof, mathematical definition.
I don't mean to quibble, but isn't the *basic* or *foundational*
concept that of a "collection" rather than of a "set"? Don't you (and
Harvey) wish to claim that kids naturally arrive at this concept via
counting and so forth? If so, I wouldn't think it can be a technical
notion (as I think "set" is) that they arrive at naturally. It must be an
informal, intuitive notion. Do you agree?
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