> 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
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.5.446 / Virus Database: 268.18.15/728 - Release Date: 20/03/2007
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (010)