SUO: Re: Foundations for Ontology

[Jon Awbrey <jawbrey@oakland.edu>]

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John,

Thanks for the link -- knew that you musta been upto something good.

In trying to integrate the presentation that you give of model theory
and the lattice of theories with the model theory that I learned in
days gone by, I do run into a couple of problems, which require me
to try and classify different people's usages of various key words,
like "proposition" and "theory", in ways that I can always remember.

On this pass over your presentation, I am getting a clearer sense
that you use "proposition" to mean the sign-like thing, not the
abstract logical object, and that you use "theory" to mean
a collection of axioms, not a collection of sentences.
Also, your lattice of theories seems to be oriented
according to the number of models that a theory has.
Are those impressions correct so far as they go?

This seemed to be a crucial passage:

| By repeated contraction, expansion, and analogy, any theory or collection of beliefs
| can be converted into any other.  Multiple contractions would reduce a theory to
| the empty or universal theory at the top of the lattice that contains only the
| tautologies that are true of everything.  Multiple expansions would lead to
| the inconsistent or absurd theory  at the bottom of the lattice, which
| contains all axioms and is true of nothing.

Thanks,

Jon

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