Re: Properties, classes, and possible worlds
John, you've started a lot of hares, so I will only try to chase down
those that seem most important.
> Two points: First, the questions we have been discussing are far more
> than "philosophical scruples"; to use Peirce's pragmatic criteria for
> meaning, they have serious implications on how knowledge engineers and
> database administrators do their work.
Granted the issues are important. I just don't think they are important
in the ways you suggest. You seem to think something vital hinges on
our choice of model theory for modal languages, and in particular that
there is something substantially superior about Dunn's model theory. I
disagree. I think different model theories yield different insights,
and that all of them are useful for metatheoretical and/or intuitive
purposes. More on this below.
> Second, Quine wasn't making a blunder in that article I quoted; he was
> using his rhetorical skills to make a serious point. There are many
> times when you and/or I may disagree with his premises, but it is very
> difficult to catch him in a blunder.
Mostly because it is so difficult to catch him in an argument. But
blunder he did in the quote in question.
> >Formal "possible world" semantics is philosophically innocent and is
> >innocuous if used simply for metatheoretical purposes.
>
> Of course, we certainly agree on the formal point. But my concern is
> that the metaphor of "possible worlds" has gone far beyond the
> innocent and innocuous stage to where it has stifled some important
> research that has practical implications for how we do knowledge
> engineering. (If you don't think it has stifled important research,
> please tell me how often you heard about Dunn's 1973 paper before I
> mentioned it.)
Your characterization is tendentious. It just doesn't follow from the
popularity of possible world semantics that Dunn's work was *stifled*.
(On second thought, maybe this explains my own lack of fame and fortune!
;-) Also, you seem to be arguing against possible world semantics as if
it were some sort of homogeneous body of formal and philosophical
theory. To the contrary, "possible world semantics" picks out a *huge*
and varied literature. There are *many* notions of possible world --
from fictionalist accounts, to propositional accounts, to Lewis's
extreme realism -- and *many* different formalisms. To lump them all
together and dismiss them in one fell swoop suggests a grinding axe
rather than careful scholarship.
> When a metaphor is stretched beyond the point of illumination, the
> best strategy is to relegate it to the historical footnotes and to
> replace it with a less misleading term in a proposed standard, such as
> SUO.
In most accounts, the notion of a possible world is not a metaphor. Nor
have you demonstrated that that is all the notion amounts to. Nor are
the better accounts misleading. You may not like them, or you may not
find them illuminating, but they are typically clear and well-defined,
even Lewis's, whom you have not begun to do justice -- I doubt, in
particular, that he ever used the clumsy expression "really real" to
characterize his worlds. (Not that I wish to argue Lewis's virtues. I
would direct interested folks instead to Lewis's excellent, and
infuriating, book, On the Plurality of Worlds.)
> Dunn's semantics, however, does make a significant advance over either
> Kripke's or Hintikka's semantics: it makes the propositions that are
> responsible for the modal effect explicit.
This too is tendentious. In your discussions you have been talking as
if it is obvious that modality is "grounded" in some sense in laws, but
in fact it is at least as intuitive that the reverse is true, that the
law-like character of laws is in fact a primitive modal property -- a
law is (at least) a proposition that *must* be true. Note that the
basis of modality is not an issue I wish to argue with you -- the point
is that, contrary to your rhetoric, modality is a broad, varied, and
difficult phenomenon, there are a variety of formal models and
philosophical theories we can build upon to systematize our intuitions.
All are useful, and none is obviously correct or superior to the others.
> Calling them "laws" is just another metaphor, and I'm willing to call
> them by a more neutral term, such as "axiom" or "constraint". In my
> earlier note, I said that Dunn showed how they could be used to
> replace Kripke's semantics, but I didn't mention the further point
> that the converse is not true.
The same is true of a variety of approaches to modality, including more
detailed and expressive possible world semantics.
> > FOL + S5 entails the Barcan Formula:
>
> Yes, of course. Read my book.
You have pointed us to your book often enough, John. For the sake of
variety, I'll direct folks to the source: A. N. Prior, ``Modality and
Quantification in S5,'' _The Journal of Symbolic Logic_ 21 (1956),
60-62. Prior's work on time and modality cannot be recommended highly
enough.
> >... if you use objectual quantification, and you want unmodified FOL
> >+ S5, you are stuck with possibilia (or some sort of philosophically
> >sophisticated surrogates thereof).
>
> Precisely. In fact, the standard term in database land is
> "surrogate". But those surrogates are set theoretical constructs that
> satisfy the "laws" or axioms of your "possible world" or database. I
> am quite happy to talk about surrogates in a database, and it
> simplifies my communications with database administrators and
> programmers.
A lot of modal contexts have nothing to do with databases or laws in any
obvious way. I could have worn a different shirt today. Do we really
want to understand this in terms of, say, consistency with some law?
Possible world semantics seems to me to be more illuminating in cases
like this. Again, a variety of semantic theories should be explored, as
befits the breadth and pervasiveness of modal phenomena.
> But when you use words like "possibilia" you confuse people, ...
Only if the word is not carefully defined.
> >Again, I say, the issue for knowledge engineering is not model
> >theory, but which system of modal logic (if any) we want to use. And
> >if use of FOL + S5 enables us more effectively to represent and share
> >information, who cares about the fact that it appears to commit us to
> >possibilia?
>
> This is an example where Dunn's semantics clarifies issues that are
> obscure in Kripke's version. The semantics for S5 (either Kripke's,
> Hintikka's, or Dunn's) implies that all possible worlds are accessible
> from one another.
<niggle>
Actually no. In models of S5 accessibility is an equivalence relation.
That does not imply that all worlds are mutually accessible.
</niggle>
> On the surface, that sounds good. Accessibility seems like something
> we want: it seems that it would facilitate knowledge sharing.
Only if you are wanting to think of worlds as databases or something of
the sort. That may be appropriate in some settings, but not in others.
And if you *do* think of them as databases, then maybe that in itself
would be reason to weaken the accessbility relation. Indeed, there is a
large literature on applications of possible world semantics in database
theory (and theoretical computer science generally), especially when the
"indices" of a model are understood as times. Gabbay's work in
particular springs to mind. I have lots of references for those who
might be interested.
> But when you look at Dunn's semantics, you get a better idea of the
> implications: every possible world must have exactly the same laws or
> axioms. And that would suggest that knowledge sharing is an
> impossible dream unless everybody adopts exactly the same axioms.
You've lost me. The mutual accessibility of worlds does not imply that
the same things must be true in them. And anyway knowledge sharing is
something that happens across the object languages in which the relevant
knowledge bases are expressed. I just don't see the connection you are
trying to draw with the semantics of modality.
> And this is where Dunn's semantics has a very serious application to
> knowledge engineering. It provides a semantic foundation for
> alternatives to modal logic, such as McCarthy's contexts, It also
> enables us to formulate the criteria for knowledge sharing between two
> different knowledge bases that are based on different axioms.
And there are possible world approaches to all of the same issues with
similarly effective solutions. Let a hundred flowers bloom, John. The
question for KE is what systems of modal logic we want to have
available to support representation and reasoning. In addition to their
metatheoretical role, different model theories enhance images and
intuitions that can help us decide which systems are particularly
appropriate for which applications. All are potentially useful, none is
obviously better than another.
-chris
--
Christopher Menzel # web: philebus.tamu.edu/~cmenzel
Philosophy, Texas A&M University # net: chris.menzel@tamu.edu
College Station, TX 77843-4237 # vox: (979) 845-8764