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Re: [ontolog-forum] Ontological Assumptions of FOL

 To: "'[ontolog-forum] '" "Chris Partridge" Tue, 20 Mar 2007 19:33:18 -0000 <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) -- 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 08:07    (09) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (010) ```
 Current Thread Re: [ontolog-forum] Ontological Assumptions of FOL, (continued) Re: [ontolog-forum] Ontological Assumptions of FOL, Pat Hayes Re: [ontolog-forum] Ontological Assumptions of FOL, Chris Partridge Re: [ontolog-forum] Ontological Assumptions of FOL, Pat Hayes Re: [ontolog-forum] Ontological Assumptions of FOL, Chris Partridge Re: [ontolog-forum] Ontological Assumptions of FOL, Pat Hayes Re: [ontolog-forum] Ontological Assumptions of FOL, Chris Partridge Re: [ontolog-forum] Ontological Assumptions of FOL, Pat Hayes Re: [ontolog-forum] Ontological Assumptions of FOL, Christopher Menzel Re: [ontolog-forum] Ontological Assumptions of FOL, Chris Partridge Re: [ontolog-forum] Ontological Assumptions of FOL, Christopher Menzel Re: [ontolog-forum] Ontological Assumptions of FOL, Chris Partridge <= Re: [ontolog-forum] Ontological Assumptions of FOL, Chris Partridge Re: [ontolog-forum] Ontological Assumptions of FOL, Ingvar Johansson Re: [ontolog-forum] Ontological Assumptions of FOL, Erick Antezana Re: [ontolog-forum] Ontological Assumptions of FOL, Ingvar Johansson Re: [ontolog-forum] Ontological Assumptions of FOL, Erick Antezana Re: [ontolog-forum] Ontological Assumptions of FOL, Ingvar Johansson Re: [ontolog-forum] Biological space, John A. Bateman Re: [ontolog-forum] Ontological Assumptions of FOL, Pat Hayes [ontolog-forum] offline question, Smith, Barry Re: [ontolog-forum] Ontological Assumptions of FOL, Erick Antezana