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Re: [ontolog-forum] Ontological Assumptions of FOL

To: Pat Hayes <phayes@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ingvar Johansson <ingvar.johansson@xxxxxxxxxxxxxxxxxxxxxx>
Date: Mon, 19 Mar 2007 10:35:39 +0100
Message-id: <45FE596B.3090105@xxxxxxxxxxxxxxxxxxxxxx>
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)

Ingvar Johansson
IFOMIS, Saarland University
     home site: http://ifomis.org/
     personal home site:
     http://hem.passagen.se/ijohansson/index.html      (03)

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