Pat Hayes schrieb:
>> I guess Pat Hayes is working within the latter
>> kind of contexts; it is a pity that it misleads him into thinking that
>> "what you can represent as a set, is a set".
> All I mean by this is that its "being" a set is simply saying that it
> can be described using set theory; and if it can be so described, then
> it is a set, pretty much by definition. There is no independent,
> metaphysical notion of "being a set", any more than there is of being
> a group (in the mathematical sense); if something satisfies the
> axioms, then it is indeed one of the things described by those axioms.
> That is all I meant. Bungean aggregates do not satisfy those axioms;
> mereological sums do not; ergo, these are not sets.
Fine. But I think your way of talking is a bit too incautious even in
the paragraph above. No concrete entities can satisfy the axioms of set
theory, only sets can. But, of course, set-theoretic representations of
concrete things might satisfy the axioms. (01)
Ingvar J (02)
IFOMIS, Saarland University
home site: http://ifomis.org/
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