FOM: "collection" as a basic mathematical concept
Stephen G Simpson
simpson at math.psu.edu
Thu Jan 22 15:01:30 EST 1998
I wrote:
> 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.
Charles Silver responded:
> I don't mean to quibble, but isn't the *basic* or *foundational*
> concept that of a "collection" rather than of a "set"? ....
My list was tentative. My purpose in presenting it was to delimit
f.o.m. in what seems like a reasonable way, so that the discussion on
the FOM list wouldn't randomly wander all over the mathematical and
intellectual landscape.
I would have no objection if you were to modify my list and replace
"set" by "collection". I said "set" rather than "collection", because
I wanted to acknowledge that set theory is the current orthodoxy. But
I'm not particularly content or dogmatic about this orthodoxy, and we
could certainly discuss alternative foundational schemes based on a
notion of "collection" other than sets. What did you have in mind?
How about foundational schemes based on "predicate"?
-- Steve
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