Re: [CL] The Decidability Fetish
Dear Michel,
This is in response to your comment (see below) "As a matter of fact it
would be worth the trouble to abandon Set Theory and replace it with Topos
Theory -- a start has already been made by Lawvere". As you know the SUO
project aims to specify an upper ontology that will provide a structure and
a set of general concepts upon which object-level domain ontologies can be
constructed.
The SUO IFF project was the first proposal passed by the SUO working group.
Using a categorical approach, it is being developed to represent the
structural aspect of the SUO. The IFF, whose architecture consists of
metalevels, namespaces and meta-ontologies, provides a principled framework
for the modular design of object-level ontologies via a descriptive category
metatheory. Over its four year lifespan the IFF project has been developed
in several phases.
Now the IFF is in the third phase of its development. A central task in this
third phase is the reorganization of the IFF metastack (core hierarchy)
http://suo.ieee.org/IFF/metastack/version20040707.html. As seen for example
in the presentation of finite limits in the IFF Top Core (meta) Ontology
(IFF-TCO) and the presentation of exponents in the IFF Upper Core (meta)
Ontology (IFF-UCO), this reorganization uses an ``adjunctive
axiomatization'' style. It is anticipated that the adjunctive axiomatization
in the new IFF metastack, will provide the metastack with better structure,
and will simplify the IFF-KIF meta-language core by not requiring the
definite descriptive operator.
The ``adjunctive axiomatization'' style follows the conceptual lines
expressed in the book *Set for Mathematics* by Lawvere and Rosebrugh, which
presents the category of sets in terms of Topos Theory. The third phase of
the IFF development is presenting the IFF descriptive metatheory in terms of
Topos Theory.
Robert E. Kent
rekent@ontologos.org
----- Original Message -----
From: "Michel Eytan" <eytan@UMB.U-STRASBG.FR>
To: <sowa@bestweb.net>
Cc: <standard-upper-ontology@LISTSERV.IEEE.ORG>
Sent: Thursday, August 26, 2004 2:13 AM
Subject: Re: [CL] The Decidability Fetish
> Thus spake John F. Sowa at 6:51 pm -0700 on 25-08-04 re Re: [CL] The
> Decidability Fetish:
>
> > PH> Wrong on two counts. First, it is not true that every
> > > segment of a tea party is a tea party. Second, it is not
> > > obvious (and indeed I think it is false) that time is
> > > in fact a mathematical continuum. It is certainly false
> > > that what one might call conceptual time is a continuum.
> >
> > I agree with Pat about tea parties: the act of stuffing
> > the dormouse into the tea pot may be part of a tea party,
> > but it is not, in itself, a tea party.
>
> And I strongly agree that time is *NOT* a mathematical continuum. Several
> years ago I had written up a sketch of how it could be better modelized as
a
> *sheaf*.
> More generally I believe we need to review many, many items modelized by
> Physics: the "material point" (inexistent, only parts of space-time have
> meaning), the use of the real line $R$ (not only for time but for
everything
> "measurable"), etc, etc.
> As a matter of fact it would be worth the trouble to abandon Set Theory
and
> replace it with Topos Theory -- a start has already been made by Lawvere
but
> it's a major undertaking demanding a team not a mere individual.
>
> > John
>
> Cheers
> --
> Michel Eytan eytan@umb.u-strasbg.fr
> I say what I mean and mean what I say