Wednesday, December 14, 2005
Communication from John Sowa on lattice of theories
John (Sowa) and ONTAC working group
I am posting your note to [303] in my web log.... but I have a major question I need to ask .. before I can take the next step...
the lattice 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...
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?
How does one know in the general case? 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 philosophical debate, but a search for a way forward for an ontology community that is really stuck in a very real sense.
Again, the issue is about the formation of categories in the natural world and in the mental world and the involvement of these categories in "theories" so the induction of new natural type seems to be a precursor to a "theory in its natural form" (what ever that is). Here by "induction" I mean something like metabolic induction where what is "caused" depends on what is "there".
I have included a few of the people I trust on these issues... and ask if any one has a precise statement that can be posted into the discussion.
Dick Ballard?, Paul Werbos?.... Ben .... ?
Lattices
I love this kind of mathematics, but I am not sure that the common notion of a theory...
like my personal theory as to why I have been consistently failing
to make my point about Edelman's notion of degeneracy to the
ONTAC working group....
can be "ordered" as part of a formal lattice.
Are you, or are you not, ,making the mistake that we attribute to the early Wittgenstein?
If not, why not....
I suspect that the answer leads into something new, and interesting.
and simpler.
Paul Prueitt