Hi Thomas, I got back to working on ontology, and I'd like to give an answer to one of your previous remarks. Your last e-mail was a bit harsh but I'm hoping that you will find my view worthwhile. ;)
"Thomas Bushnell, BSG" wrote: > > I think that logic has a great deal to do with semantics. > > I think that the mathematical notion Category Theory has a great deal > to do with logic and semantics. > > And I don't think that the mathematical notion "Category Theory" has a > great deal to do with the traditional philosophical notion of > "Category". As I read the views of Category Theorists themselves, I found out that their views were quite parallel with yours. They thought of metaphysics to be a distinct sphere of endeavor from that of mathematics as is the general attitude of a mathematician. In countless encounters, mathematicians did admit that they held their task as a subjective and intuitive effort rather than an objective "hard" science and that it had a boundary of its own. That its use did not necessarily indicate a relation with another field. I may use mathematics to explain a sociological phenomenon, but mathematics is not related to sociology; it remains separate. I believe most would claim such even for physics which itself has given way to new branches of mathematics. Anyway, mathematicians would mostly tell me mathematics != philosophy in strong words. Unfortunately, I have to disagree :) The creators of mathematical theories, which have been used in AI to explain how facts of world are to be represented, would say that the terms they have used are only borrowed. *The semantic content is entirely different* That I believe is also what you have stated in various ways. That the term "category" in Category Theory is very different from Category in study of ontology in philosophy. That is precisely where I think we *should* be skeptical about. After thinking about Feyerabend's view of scientific practice, I reached the following argument: Artificially separating mutually related theories into predefined domains of theories is not a fruitful methodology. It isn't because it is the enforcement of a particular "progress" methodology. That it is the correct way to draw a hard line between the philosophy and science of "a thing". I cannot offer a proof of my argument why this methodology is wrong, because it has to be a "historical" rather than an analytical one. That I am not very skilled at; and I have limited space in this e-mail. In the context of our discussion, I think my argument would imply something of the following sort: We should not exclude the possibility that a "new theory" of categories, be it more metaphysical or more mathematical, depends on an important relation between the mathematical Category and philosophical Category regardless of whether prominent philosophers or mathematicians deny such a relation. That was a cumbersome sentence, but I can't word it better now :) The simpler statement would be that in new research we should utilize ideas from both worlds and try to exploit similarities as well as differences between them. I know this sounds confusing but I think it is an "anything goes" argument for research. We should not inhibit scientific practice before it happens. I've written this small piece because I was inspired by a work of Nicola Guarino. If you're interested I can send you links to some of his papers. Of course you can take a look at his work yourself. At this location there are many papers authored by him: http://www.ladseb.pd.cnr.it/infor/ontology/Papers/OntologyPapers.html Merry Christmas, -- Eray (exa) Ozkural Comp. Sci. Dept., Bilkent University, Ankara e-mail: [EMAIL PROTECTED] www: http://www.cs.bilkent.edu.tr/~erayo