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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