Re: Contexts and quantifiers in KIF

sowa <sowa@turing.pacss.binghamton.edu>
Reply-To: cg@cs.umn.edu
Date: Sun, 11 Apr 93 09:42:35 EDT
From: sowa <sowa@turing.pacss.binghamton.edu>
Message-id: <9304111342.AA05969@turing.pacss.binghamton.edu>
To: cg@cs.umn.edu, sowa@turing.pacss.binghamton.edu
Subject: Re: Contexts and quantifiers in KIF
Cc: interlingua@ISI.EDU, jfulton@atc.boeing.com, srkb@isi.edu

Chris,

Yes, I'm sorry that I used the distinction finite vs. infinite.
The partiality vs. totality distinction is much better for
distinguishing the B&P situations from the Kripke & Montague
possible worlds.

Those references you cited for situation theory are indeed more
up to date introductions to situation semantics, but the old B&P
book is still a good introduction to the motivation for the approach.

As for "infinite sets", I primarily use that term in a deprecatory
sense as something that should be avoided.  I believe that the 19th
century mathematicians were correct in insisting that the term
"infinity" be used only as a limiting case and that one should never
speak of an infinite set as a completed whole.  Georg Cantor was a
brilliant mathematician, and as an undergraduate, I was wowed and
amazed by his wonderful constructions.  But as an adult, I put away
such childish fantasies, and I now agree with Wittgenstein that
the whole subject matter of transfinite sets and cardinals is a
"swamp of confusions."

As for "possible worlds", my primary objection is to the word "world".
If you want to call them models, data structures, or abstract constructions,
then that's fine.  But calling them "worlds" blurs a very important
distinction between the real world and all those data structures.
The worst confusion comes from saying that among all those "possible 
worlds", we select a w0, which we "identify" with the real world.
That kind of talk reminds me of the old joke,

  Q:  If we call a tail a leg, how many legs does a dog have?

  A:  Four.  Calling a tail a leg doesn't make it one.

It's OK to say that a particular model w0 will be mapped to
aspects of the real world, but the term "identify" is either a
misleading metaphor or it betrays a fundamental confusion on
the part of the person who uses it.

John