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Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Tue, 16 Sep 2008 12:36:40 -0500 (CDT)
Message-id: <alpine.OSX.1.00.0809161215360.2480@xxxxxxxxxxxxxxx>
On Tue, 16 Sep 2008, John F. Sowa wrote:
> Chris,
> Dunn was just using the word "law" as a convenient synonym for
> "necessary truth".    (01)

Not according to his semantics.    (02)

> CM> The problem for turning this into a Dunn model is: when do we
> > have a "mere" necessary truth and when do we have a law?
> In Kripke models, the necessary truths in any world w are those
> sentences that are true in every world accessible from w.  The
> mapping from a K-model to a D-model would put all those sentences
> into the set L of the laws of w.    (03)

But my point is that your mapping is only *one* of several possible ways
to construct the laws of a corresponding D-model.    (04)

> CM> ... (though I'm working old memories of Dunn's semantics).
> > If so, there is in general no unique mapping from a Kripke model
> > to a Dunn model.
> I have the original book somewhere in my house.  Unfortunately, I
> did not put it back on the shelf next to several other yellow books
> from North-Holland Press.  So I can't find the original quotation.
> But I can't recall anything Dunn said that would distinguish a law
> of w from a statement that is necessarily true in w.    (05)

He doesn't have to.  The distinction is simply a consequence of his
definition.  The laws of a world are defined to be a subset of the
truths.  The necessary truths of a world w are the truths of w that are
also true in all accessible worlds (where accessibility in Dunn's
semantics is determined by the laws: <F',L'> is accessible to <F,L> if L
is a subset of F', i.e., if the laws of <F,L> are facts of <F',L'>.) But
the necessary truths of a world needn't coincide with the laws of the
world.  All of the laws of a given world are necessary at that world;
but not all of the necessary truths of a world need to be laws of the
world.  Tautologies, in particular, needn't be included among the laws
of any world, but they will all turn out to be necessary simply because
the facts of all worlds have to satisfy the usual boolean truth
conditions.    (06)

> (Dunn had read my papers, he thanked me for promoting his work, he
> invited me to give a talk at Indiana U., and he did not say that my
> interpretation was inconsistent with what he had said.)    (07)

Your interpretation of Dunn's work may be fine.  I am questioning your
claim that every Kripke model determines a *unique* Dunn model.    (08)

-chris    (09)

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