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Re: [ontolog-forum] intangibles (was RE: Why most classifications are fu

To: doug@xxxxxxxxxx, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: sowa@xxxxxxxxxxx
Date: Thu, 28 Jul 2011 06:10:50 -0400 (EDT)
Message-id: <0332af08d8614d53afe60ed4b278e9ec.squirrel@xxxxxxxxxxxxxxxxxxxx>


I admit that more work would be needed to transfer all results about
quantified modal logic (QML) to Dunn's semantics.  But there is a very
clean and widely used subset of QML that is trivial to derive from
the laws and facts.

In particular, there is no restriction on what language is used to state
the laws and facts.  For any world w, the facts F can contain any and
every FOL proposition that is true about w, and the Laws L can contain any subset of F that is closed under deduction.

Then any proposition consistent with L is possible, and any proposition derivable from L is necessary.  If L is stated in FOL, you have a version of QML with the modal operators in front of any ordinary quantifiers.  You can also get all the combinations of modal operators, such as necessarily possible or possibly necessarily possible (if anyone would ever find a need for such things).

I admit that one might want to support conditions such as Barcan's
formula for interchanging the order of modal operators and quantifiers.
I haven't explored the details of how and whether that work can be

But before spending any time worrying about such issues, I would like to see any evidence that they serve any useful purpose in understanding the semantics of natural languages as ordinary human beings (i.e., people who have not been exposed to philosophers or logicians) use them.

As far as counterpart theory is concerned, my preference is to assume
(1) two individuals in different worlds with the same name are likely
candidates for being counterparts, and (2) if their significant life
events correspond, they are the same, barring some exceptional conditions that are being discussed by whatever philosophers are discussing them.

As for the question about substitutional interpretations of quantifiers
and counterparts, I would like to note that the puzzles and paradoxes
do not arise in finite or countable domains.  The problems arise in
uncountable domains where there aren't enough names for all individuals.  Yet in our known universe, the number of atoms is finite, and the number of namable combinations is finite.  Even if there are infinitely many multiverses, no physicist has ever suggested that they are uncountable.

The only place where uncountable things arise is in mathematics, and
no mathematicians use modal logic for their proofs.  I would very much like to see any example where a substitutional interpretation fails
for empirical science, human NL usage, or NLP.

Meanwhile, there are a host of very significant issues about the use
of modal operators in NLs that are much easier to handle with Dunn's
semantics than Kripke's.  The prime example is with multiple modalities, which frequenly occur in ordinary language.

With D's semantics, they can be handled just by partitioning the laws L
into subsets L1,...,Ln for n different modalities.  With K's semantics,
you need to assume multiple accessibility relations, and trying to
justify or explain even one such relation is problematical.


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