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

[sowa@xxxxxxxxxxx]

Chris,

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
transferred.

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.

John
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