Re: The Difference between a Set and an Element

On Fri, 12 Jan 2007 18:36:06 GMT, Nam D. Nguyen <namducnguyen@xxxxxxx>
said:
...
The concept of *set* can be as he says fundamental mathematical
concepts should be: that doesn't stop the members of sets being as
concrete as you like.

It does stop "members of sets being as concrete" because concepts
should be abstract.

You seem to be assuming two things here: (1) that sets are concepts; (2)
that a set with concrete members is not abstract. Re (1), the set
{5,17,1383} for example certainly doesn't *seem* to be anything like a
concept. I mean, sets are just (in general) arbitrary collections of
things, right? There doesn't seem to be anything particularly
conceptual about them at all. 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.

Re (2), while some philosophers (e.g., Penelope Maddy) do indeed think
that sets with concrete members are concrete, or are at least spatially
located, there is certainly no obvious inconsistency in the view that
they are abstract, the concreteness of their members notwithstanding.
(If you think otherwise, you'll need to provide an argument.)

Period. (I hate to use that word "Period", but what choice do I have
when incorrectness keeps persisted?).

Oh, that's an easy one. You *argue* for your position instead of
dogmatically asserting it to be true with no justification. Maybe
you'll have better luck á la Bill O'Reilly by following unargued
assertions with a resounding "Shut up!" :-)

Remember the word "concept" should be used with "of":

Really? What's wrong with "Fido falls under the concept DOG"? How
about: "A concept is an abstract entity"? Or: "The concept that 'red'
calls to mind is very different from the concept that 'snow' calls to
mind"?

there is an indirectness-gap between a concrete object and the concept
*of* it. (Sigh! Before one accuses somebody else as being foolish, as
you've done so in the other post, why doesn't one *carefully* review
what has been said, or review the natural-language (such as English)
usage of the word in question?)

Fine advice. Vide above.

.

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