Re: The Difference between a Set and an Element

Chris Menzel schrieb:

Granted, there might be those who would
say that {5,17,1383} is the concept of being identical to 5, 17 or 1383
(though I think that would be an odd thing to say). So consider
instead, for example, an arbitrary infinite set S of natural numbers for
which -- unlike, say, {5,17,1383} or the set of prime numbers -- there
is no description that characterizes exactly the members of S, and no
procedure that lists them. What concept is S? Sure doesn't seem like
anything I'd call a concept.

I agree with you insofar as, in the Fregean sense, sets are objects and
not concepts.
As we know, there isn't a set for every concept.
But isn't it the case that there is a (defining) concept for every set,
as Gödel conjectured:

"A plausible conjecture is: Every set is the extension of a concept."

[Kurt Gödel - quoted in: Wang, Hao (1996). /A logical journey: From
Gödel to philosophy/. Cambridge, MA: The MIT Press. (p. 245)]

#PH

.