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## Re: [ontolog-forum] standard ontology

 To: "[ontolog-forum] " Pat Hayes Wed, 11 Feb 2009 17:54:31 -0600
 On Feb 11, 2009, at 4:42 PM, Rich Cooper wrote:Possible worlds are useful constructs in commercial databases, but numbers aren’t a problem; arithmetic is all that’s necessary.  So mathematizing the concept of 4 isn’t very useful there.  Number theory isn’t very useful to most companies. True, but so what? Nobody is suggesting formalizing number theory, only allowing numbers into the universe of discourse at all. I want to be able to talk about numbers, its pretty hard to do without them. So Numbers are the first thing I would drop from an FO, and use them only as descriptive (adjectival) values in relations. If you are using them that way, they are in the ontology. Pat Sincerely,Rich CooperEnglishLogicKernel.comRich AT EnglishLogicKernel DOT com  From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat HayesSent: Wednesday, February 11, 2009 1:53 PMTo: [ontolog-forum] Subject: Re: [ontolog-forum] standard ontology  On Feb 11, 2009, at 10:41 AM, Chris Partridge wrote:PatH,Last time you raised the question of numbers, and I responded, Chris Menzeltold me off for raising something NOT relevant. Note to ChrisM - PatH raisedthis.1. Are there certain things like e.g. numbers and possible worlds? 2. Are they abstract or concrete? Even the first may be controversial, but even if you agree thatthese thingsexist, whether they are considered abstract or not is a differentquestion(and arguably more controversial). Whether they exist or not, I think  you have to say that numbers arenot concrete. You can't weigh seven. As I think you must know there is a Fregean concept of number (where 2 isthe set of all sets with two members). Well, you can't weigh a set, either. This Fregean proposal has modernsupporters - e.g. Crispin Wright http://en.wikipedia.org/wiki/Crispin_Wright. There is debate about whether sets are abstract - David Lewis asks why wecannot say the set of cars in the car park is located in the car park - andif it is located, it cannot be abstract. Hence, there is an account ofnumbers that says they are not abstract. As you know, the fact that there is an account of X does not make that account likely, intuitive, or even consistent with many other widely held positions. Philosophy is full of minority reports. All the cases I've read of treating sets as concrete seem to me to be cases of getting sets and mereological sums muddled together. Lewis' example has a clear reply: the cars are located there; all of them are located there; but it does not follow that the set is; just as if we say that there are four cars in the car park, it doesn't follow that four is in the car park. We can loosely say this, being careless (as we all often are) about ontic commitment, but the intended meaning is clear. As Barwise once asked me: look around the office: how many sets can you see? Question back to Lewis: are all the subsets of the set of cars also in the parking lot? What about the power set? Etc.. (Yes answers seem more and more silly; no answers have no rational justification, if you accept that the first set is there.)There seems to me to be gap between the mathematician's notion of number andthe common sense (or engineer's) notion. Seems to me that the former is simply a precise and formalized version of the latter. But we ought to distinguish the mathematician's notion (they talk of "the natural numbers" without blinking an eyelid) from the philosopher-of-mathematics' notion, which is typically altogether more tenuous and abstract.  For historical reasons, mathematicians wanted mathematics to be devoid ofontological commitment. Actually I think for practical reasons. Trying to actually DO mathematics more or less forces one to think in Platonic terms, or go slightly mad. So, if I say there are four books on the table - howthis four relates to the (set of?) books is unclear. Its the cardinality of the set. This seems to me to be about as clear as anything can be. Its much clearer than explaining the relationship of the books to, say, their color or their authors.(Ditto, the 4lb ofapples on the table.) Assume there is an abstract thing that is the numberfour - how does it get related to the books/apples? Hope you see theproblem. No, I don't. There is no problem here that I have ever been able to discern. The answers to these questions are obvious, even to a child. The relation between the books on the table and four is, that the number of them is four. There are four of them. If you count them, you will get to four, then stop. The cardinality of the set of books on the table is four. If you pair them up with the sequence of names "one", "two", etc.,, you will find that that final item in the sequence is "four". And so on. All these are different ways of saying the same, obvious, thing. What mystery or problem is there here?   (For the record, this kind of finding problems where no problems exist is what made me tire of academic philosophy. The real world is hard enough to understand, without having to deal with ethereal non-issues arising from an overdeveloped sense of awe at the most trivial observations. But carping aside: whatever qualms one might have about the underpinnings of the last century or so of mathematics, surely just on pragmatic grounds, it can hardly be gainsaid that numbers are very useful: so useful, that asking anyone from a child counting bricks to any engineer to do without them is asking too much to justify even the most serious philosophical scruples. Note: this is simple for the Fregean. It seems to me that engineerswould be happier with a Fregean approach for counting and weighing.Maybe one cannot practically weigh seven (or locate it - as it is far tooscattered). Its not in the spatiotemporal universe at all. "Scattered" isn't meaningful applied to a number. But similar problems occur for things like the mereological sumof all milk (or gold, or water). These are also too scattered, but seem tome irredeemably concrete. If you believe in mereological sums like this, then they are indeed scattered. But it still makes sense to ask what is the total mass of gold in the universe, for example. Such estimates do in fact exist, I believe, though they are of course impossible to verify directly. But the total mass of seven? Pat  Chris_________________________________________________________________Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1JTo Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx ------------------------------------------------------------IHMC                                     (850)434 8903 or (650)494 3973   40 South Alcaniz St.           (850)202 4416   officePensacola                            (850)202 4440   faxFL 32502                              (850)291 0667   mobilephayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes    _________________________________________________________________Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1JTo Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx ------------------------------------------------------------IHMC                                     (850)434 8903 or (650)494 3973   40 South Alcaniz St.           (850)202 4416   officePensacola                            (850)202 4440   faxFL 32502                              (850)291 0667   mobilephayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes
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 Current Thread Re: [ontolog-forum] standard ontology, (continued) Re: [ontolog-forum] standard ontology, Christopher Menzel Re: [ontolog-forum] standard ontology, John F. Sowa Re: [ontolog-forum] standard ontology, Matthew West Re: [ontolog-forum] standard ontology, Pat Hayes Re: [ontolog-forum] standard ontology, Matthew West Re: [ontolog-forum] standard ontology, Chris Partridge Re: [ontolog-forum] standard ontology, Christopher Menzel [ontolog-forum] (no subject), Chris Partridge Re: [ontolog-forum] standard ontology, Pat Hayes Re: [ontolog-forum] standard ontology, Rich Cooper Re: [ontolog-forum] standard ontology, Pat Hayes <= Re: [ontolog-forum] standard ontology, Azamat Re: [ontolog-forum] standard ontology, Rich Cooper Re: [ontolog-forum] standard ontology, John F. Sowa [ontolog-forum] (no subject), Chris Partridge Re: [ontolog-forum] Possible Worlds, John F. Sowa Re: [ontolog-forum] Possible Worlds, ravi sharma Re: [ontolog-forum] standard ontology, Pat Hayes Re: [ontolog-forum] standard ontology, Christopher Menzel Re: [ontolog-forum] standard ontology, Pat Hayes Re: [ontolog-forum] standard ontology, Azamat