uom-ontology-std
[Top] [All Lists]

## Re: [uom-ontology-std] Note on CLIF draft - approach to scale

 To: uom-ontology-std , "John F. Sowa" Pat Hayes Sun, 17 Jan 2010 00:28:50 -0600 <6331DA2D-F5AA-485B-9D76-3428E1BA8EA2@xxxxxxx>
 ``` On Jan 16, 2010, at 9:49 AM, John F. Sowa wrote:    (01) > Pat, > > I have nothing against using sets, finite or infinite. I was > just making the observation that you can't give an extensional > specification for infinite sets. > > JFS>> ... the integers themselves must be specified by some rules >>> or axioms. > > PH> Most mathematicians would disagree. The natural numbers cannot >> be fully specified by any finite number of axioms, yet we all feel >> that we know what they are, and are quite happy to refer to them. > > I agree. But you can state a finite set of metalevel rules for > generating a denoting expression for each natural number.    (02) Of course, they are called the numerals. Now you have to somehow say that the things denoted by these are precisely the natural numbers, and to do that you have to be able to refer to the natural numbers, and thats what you can't do in any finite axiomatization.    (03) > > For example, I can say that any string of terminal symbols generated > by the following grammar denotes a natural number: > > Terminal symbols: {S, 0} > > Nonterminal symbols: {N} > > Grammar rules: > > N -> 0 > N -> S N > > This is a finite specification that generates a denoting expression > for all and only the natural numbers. You can add a few Peano-style > axioms to get the standard model without the weird number-like things > of the non-standard models.    (04) No you can't. There is no finite axiomatization, in any form, that has just the standard model as its only satisfying interpretation. (Goedel.) And yet, we still feel that we 'know' the standard model. And I'm quite happy to take that for granted and move on.    (05) Pat    (06) > > John > > > _________________________________________________________________ > Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/ > Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx > Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/ > Shared Files: http://ontolog.cim3.net/file/work/UoM/ > Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard > >    (07) ------------------------------------------------------------ IHMC (850)434 8903 or (650)494 3973 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 mobile phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes    (08) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/ Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/ Shared Files: http://ontolog.cim3.net/file/work/UoM/ Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard    (09) ```
 Current Thread Re: [uom-ontology-std] Note on CLIF draft - approach to scale, (continued) Re: [uom-ontology-std] Note on CLIF draft - approach to scale, Pat Hayes Re: [uom-ontology-std] Note on CLIF draft - approach to scale, David Leal Re: [uom-ontology-std] Note on CLIF draft - approach to scale, Pat Hayes Re: [uom-ontology-std] Note on CLIF draft - approach to scale, John F. Sowa Re: [uom-ontology-std] Note on CLIF draft - approach to scale, Pat Hayes Re: [uom-ontology-std] Note on CLIF draft - approach to scale, John F. Sowa Re: [uom-ontology-std] Note on CLIF draft - approach to scale, Pat Hayes Re: [uom-ontology-std] Note on CLIF draft - approach to scale, John F. Sowa Re: [uom-ontology-std] Note on CLIF draft - approach to scale, Pat Hayes Re: [uom-ontology-std] Note on CLIF draft - approach to scale, John F. Sowa Re: [uom-ontology-std] Note on CLIF draft - approach to scale, Pat Hayes <= Re: [uom-ontology-std] Note on CLIF draft - approach to scale, David Leal Re: [uom-ontology-std] Note on CLIF draft - approach to scale, Christopher Menzel