FOM: g.i.i.; f.o.m.; genetic defects; ignorance; the boxing match

[Charles Silver]

On Sun, 11 Jan 1998, Stephen G Simpson wrote:

>   2. As a tentative list of the most basic mathematical concepts, I
>   offered the following:
>   
>      list 1:
>   
>      number
>      shape
>      set
>      function
>      algorithm
>      mathematical axiom
>      mathematical proof
>      mathematical definition
>   

	To my mind "set" is utterly distinct from the other members of
this list.  I don't wish to argue that "set" is *not* basic, but if it is,
it is basic in an entirely different sense than the others.  I won't go
through all the items in the list, but it seems to me that each concept,
with the exception of "set", can be argued to be "epistemically basic".
That is, each concept (except "set") is arguably rooted in certain
fundamental conceptions in our minds that arise naturally.  I don't think
the concept of "set" comes to our minds in such an epistemically primitive
way.  Rather, it seems to me, the concept of "set" reflects a later
mathematical development.  Using the concept of "set" (plus some axioms
*about* sets), one can unify other mathematical concepts in a desirable
fashion.  In this way and in many others, "set" can be considered "basic". 
But, I don't see it as being basic in the same way as "shape" is, for
example.  Steve, could you please explain your reasons for including "set"
in the above list?

Charlie Silver
Lecturer in Logic
Smith College