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Re: [ontac-forum] Theories, Models, Reasoning, Language, and Truth - del

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Thu, 15 Dec 2005 15:10:35 -0600
Message-id: <20051215211035.GF57447@xxxxxxxx>
On Thu, Dec 15, 2005 at 08:23:02AM -0700, Paul S Prueitt wrote:
> the latttice of theories, developed by Tarski and Sowa.. and others,
> seem to assume that every element of any possible theory can be
> compared in a subsumption relationship.... and thus the lattice...    (01)

They can be.  That the subsumption relation is a lattice is important,
of course, because that allows for the possibility of theories T1 and
T2 such that neither subsumes the other.    (02)

> Rosen talked about the largest model, and I always hated that, because
> I never felt comfortable with the issue of relevance, and ordering .
> One theory is Larger than another theory?  How can one say that?    (03)

T1 is larger than T2 if every theorem of T2 is a theorem of T1 but not
vice versa.    (04)

> How does one know in the general case?      (05)

One might not.  For instance, at the moment we don't know whether Peano
Arithmetic + Goldbach's Conjecture is larger than Peano Arithmetic.    (06)

> Well I should say that my friend Peter Kugler talked about Rosen
> talking about the largest model.    Perhaps Judith Rosen has time to
> help us a little on some issues....  This is not a philosophyical
> debate, but a search for a way forward for an ontology community that
> is really stuck in a very real sense.    (07)

Where is the sticking point, exactly?    (08)

-chris    (09)

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