Re: SUO: Re: Foundations for Ontology
>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,
That all depends on who I'm talking to. If I am talking to
a nominalist, I say that a proposition is an equivalence
class of sentences in some language(s) for which appropriate
"meaning-preservation transformations" have been defined
(see Ch. 5 of my KR book).
If I am talking to someone who has read Peirce, I talk
along Peircean lines: A proposition is a sign type that
serves as the interpretant of a declarative sentence in some
language (formal logic or natural language).
If properly formalized, I believe that these two definitions
have equivalent effects -- ergo, according to CSP, they are
> and that you use "theory" to mean
> a collection of axioms, not a collection of sentences.
I use the term theory as the deductive closure of a collection
of propositions (see above) which have been singled out as
>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?
Since I am talking about theories expressed in FOL,
material implication and semantic entailment give me
exactly the same consequences. See Ch. 2 of my KR book,
where I first talk about the lattice of all possible
theories. It is essentially a Lindenbaum lattice.
In the partial ordering of the lattice, a more generalized
theory T1 (closer to the top) is implied by any theory T2
that is more specialized than T1; i.e., every proposition
in T1 is implied by the collection of axioms in T2. Also,
every model of T2 is also a model of T1.
This is all spelled out in my KR book.