Re: SUO: Thoughts and judgments
Robert,
Fine. I agree that the lattice of all possible theories, which
was first suggested by Tarski's student Adolf Lindenbaum, is indeed
a important contribution to the organization of an ontology.
REK> The advantage that I had in mind was one of conceptual
organization. The
> truth concept lattice allows us to conceptually organize our theories in a
> way that provides a flexible ontological framework for the "infinite lattice
> of theories" that you advocate. Axiomatizations for the two mathematical
> contexts of large classifications and large concept lattices, which provide
> a rough framework for representing the truth concept lattice notion, appear
> in the IFF Classification Ontology
And by the way, Peirce did write down axioms for various kinds of
graph structures, including lattices, although he didn't use that term.
If someone had suggested the idea of organizing theories in a lattice
with morphisms from one to another, it would probably have taken him
all of two minutes to get the point and to start itemizing all the
implications.
John