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Re: [ontolog-forum] Ontological Assumptions of FOL

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Chris Partridge" <mail@xxxxxxxxxxxxxxxxxx>
Date: Tue, 20 Mar 2007 19:33:18 -0000
Message-id: <00c201c76b26$9e22f990$0200a8c0@POID7204>
Chris,    (01)

> On Mar 20, 2007, at 12:22 PM, Chris Partridge wrote:
> >> On Mar 19, 2007, at 5:25 PM, Chris Partridge wrote:
> >>> ...
> >>> A number of points:
> >>> 3) If one has a Fregean notion of number, then as the set of all
> >>> (actual and possible?) sets with 17 members would have an infinite
> >>> number of members - working out the density would be difficult, if
> >>> not impossible.
> >>
> >> This is a red herring.  All that the Fregean (or, for that matter,
> >> *any* set theoretic) representation of the numbers buys you is a
> >> class of well-defined objects that collectively model the axioms of
> >> Peano Arithmetic; they provide a convenient answer to the question,
> >> "What are the numbers?".  You don't actually have to "manipulate"
> >> them in any sense that requires that they themselves be represented
> >> in a computer, you just *do* arithmetic.
> >>
> >>> But not absolutely meaningless. However, I have already agreed
> >>> numbers pose problems.
> >>
> >> Why?  Arithmetic is undecidable, of course, but so is first-order
> >> logic, so I take it that that is not the sort of problem you have in
> >> mind.  If anything, because the ontology of the numbers -- a.k.a.
> >> Peano Arithmetic -- is universally agreed upon, they pose far fewer
> >> problems than most domains.
> >
> > If you look further up the discussion, you will see that this
> > comment was in
> > the context of trying to deny the existence of abstract objects.
> > Pat offered
> > numbers as his favourite example of abstract objects. If you see no
> > problem
> > in making numbers (integers, rationals, reals, transfinite ...)
> > concrete, I
> > am interested. To repeat Pat's question, Where is the number one
> > located?
> I haven't the foggiest idea what relevance the question of the
> metaphysical status of natural numbers (or anything else, frankly)
> has to do with ontological engineering.      (02)

If you have a problem with this as a topic, moan at Pat and ask him for an
explanation, as he raised it. Not me.    (03)

If we need to talk about
> number in the development of a useful ontology, we include axioms for
> them; end of story.  Under what real world circumstances is anyone
> *ever* going to agonize over the metaphysical implications of their
> sums and products?  Under what real world conditions would any
> practical benefit accrue from even broaching the question of the
> existence of abstract entities?      (04)

Another disingenuous point :-).
Whether something is abstract or concrete is a useful question - if it is
meaningful. In ontological engineering, it might be irrelevant to ask what
the symbols in the logical axioms refer to. In data modelling, it is
regarded as good practice. Indeed, it is often a starting for determining
interoperability. Knowing whether something is abstract or concrete can
sometime be of some helping in determining what one might be referring to.     (05)

>A certain amount of philosophizing
> is unavoidable in ontological engineering, but it seems to me that
> this issue, while interesting and important in academic philosophy,
> is badly misplaced here.    (06)

> Chris Menzel
>     (07)

Chris    (08)

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08:07    (09)

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