FOM: reply to the "list 2" crowd

[Charles Silver]

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
>   knowledge." 
>   ....  
>   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? 

Charlie Silver
Smith College