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Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 16 Sep 2008 11:30:43 -0400
Message-id: <48CFD123.3010506@xxxxxxxxxxx>
Pat,    (01)

On that point I certainly agree with you:    (02)

 > Your construction takes a Kripke structure - no mention there
 > of a language or a signature - and begins by mentioning a set
 > of [sentences] ..  And my point is simply that no such set is
 > defined by the Kripke structure. You still have not defined it.
 > Until you do, your construction isn't well-defined.    (03)

That is closely related to something that I have been saying for
years:  A Tarski-style model is a set of entities and a set of
relations among those entities.  Those entities and relations
are *approximate* representations of aspects of the world
according to some ontology.  But they do not have an existence
in the world that is independent of the ontology that we use
to characterize them and identify particular instances.    (04)

We have argued about that point before, and logicians and
philosophers have taken many different positions on it.
Although I do not believe that the real world *is* a model,
it is at least conceivable that some people might make that
claim.  But to claim that some imaginary possible worlds have
an objective existence that can determine truth or falsity in
our formalisms is beyond my "Will to Believe".    (05)

 > What is the signature of the language? Does it have binary
 > relations in it? Etc. . It's not enough to say 'use FOL' or
 > some such reply.  That does not determine a set of sentences.    (06)

My answer is that I think of Kripke-style possible worlds as
a collection of Tarski-style sets of entities and relations.
Those relations determine the signature and ontology.    (07)

I'll confess that if you think those possible worlds have an
independent existence in a Platonic heaven, I cannot imagine
any formalizable way to map them into a Dunn-style model.    (08)

So my claim reduces to this:    (09)

  1. A Kripke-style model in which each "possible world" is
     a Tarski-style model (with a set of entities D and a
     set of relations R over D) can be mapped to a unique
     Dunn model.    (010)

  2. But I do not know how to define or even think coherently
     about a Kripke-style model that consists of possible worlds
     that have an objective existence independent of any particular
     ontology that would determine the Tarski-style pairs (D,R).    (011)

If you claim that there is a meaningful notion of a Kripke model
that is independent of any ontology, then I'd like to know how you
think it could be mapped to anything computable or formalizable.
If you can do that, I suspect that the same methodology would
uniquely determine a Dunn-style model.    (012)

John    (013)

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