- From: Oliver Ruebenacker <curoli@gmail.com>
- Date: Sun, 29 Mar 2009 11:48:51 -0400
- To: Pat Hayes <phayes@ihmc.us>
- Cc: W3C HCLSIG hcls <public-semweb-lifesci@w3.org>

Hello Pat, All, On Sun, Mar 29, 2009 at 12:10 AM, Pat Hayes <phayes@ihmc.us> wrote: > On Mar 28, 2009, at 3:52 PM, Oliver Ruebenacker wrote: >> Arithmetic can be described by ontologies. > > Not full arithmetic, because of Goedel's incompleteness theorem. You might > manage with Peano arithmetic, but I doubt it. I suspect you would need at > least complex analysis. Isn't Goedel Incompleteness something that does not apply only to Math, but to Formal Logic in general? Wouldn't that imply that it is a concern for ontology building regardless of whether it is about Math or any other area? The way I understand it: It depends on how deep you want to dig. For example, if you want to talk about the real number one, you could just declare a symbol for it and define in words that this is the real number one and rely on every one agreeing what it is and you will not be confronted with incompleteness. Or you could try to formalize the definition of real numbers by formalizing field axioms. For example, you can base real numbers on set theory, and then you have the choice of naive set theory, which leaves some things undefined, or more sophisticated approaches, and then you would definitely be concerned about incompleteness. >> What would you do? > > I wouldn't. Its far too complicated and too far from existing ontology work. > Statistical ensembles are just way outside the state of the > logical-formalizing art, I would guess. If you can cite any work, however, > I'd be delighted to be proved wrong. Perhaps the question should read: What would you advice to some one who wants to build an ontology to describe pathways for Systems Biology purposes? Take care Oliver -- Oliver Ruebenacker, Computational Cell Biologist BioPAX Integration at Virtual Cell (http://vcell.org/biopax) Center for Cell Analysis and Modeling http://www.oliver.curiousworld.org

Received on Sunday, 29 March 2009 15:49:30 UTC