Re: Contexts and quantifiers in KIF

sowa <sowa@turing.pacss.binghamton.edu>
Date: Wed, 14 Apr 1993 09:19:44 -0700
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From: sowa <sowa@turing.pacss.binghamton.edu>
To: Multiple recipients of list <srkb-list@ISI.EDU>
Subject: Re: Contexts and quantifiers in KIF

Jim,

Some comments on your last note:

> I guess I am more of a realist about possible worlds (by whatever name).  I 
> certainly do not regard them as mere data structures, rather they are what 
> "could" be represented by those data structures.  
 
My basic point is that there is only one world, and that is the real live
concrete one we live in.  A possibility exists only as a model:  either a
mental model in some person's brain, a data structure in a computer system,
an abstract set-theoretic construction in a mathematical formalism, or a
physical analog that simulates the behavior of some other system.  The use
of the word "world" for any of these structures is a metaphor, and like all
metaphors it can help to clarify some points, but it can also cause serious
confusion if taken literally.  David Lewis, for example, is a smart man, but
I believe that he has spread around an enormous amount of confusion by not
distinguishing the literal and metaphorical uses of the word "world".

I have found that one of the easiest ways to clarify a philosophical problem
is to restate it in different terms that avoid some of the loaded connotations
of a misleading metaphor.  If you do a global change of the word "world" 
to almost any other term -- "model", "data structure", "set theoretic
construction", or "whatchamacallit" -- all of the formal properties of the
theories by Kripke, Montague, and others are preserved, but the misleading
connotations are eliminated.

> The "could" in that assertion on the interpretation of the modality used in 
> those data structures, or equivalently (as Kripke showed) on the interpretation 
> of the accessibility relationship among the worlds.  Some examples:

> 1.  I use the words 'not' and 'and' in such a way that for any sentence P 
> it is logically false that P and not P.  That means that there is no possible 
> world in which a sentence is both true and false.  This modality, i.e., 
> logical truth and falsity, is rather easy to write off as saying something 
> about words and not about worlds.  It represents decisions about our choices 
> for using language in ways we regard as consistent.

If you do a global change of "world" to "model" in the last section, I agree
with you.  I definitely agree that talk about possibility is more than a mere 
discussion about words.  But instead of saying that modal language is about 
alternative worlds, I say that it is about alternative models of the world.

> 2.  The sentence 'Bush was President' is true now in virtue of the fact that 
> the sentence 'Bush is President' was true previously, i.e., in virtue of the 
> fact that there was a time (we refer to "times" in normal English, but what 
> we seem to be talking about when we do so seems more like a world) at which 
> the person, here referred to as 'Bush', had the office, here described as 
> 'is President'.  Under the temporal interpretation of modalities, possible 
> worlds are no more mysterious than history or the future.  They are not data 
> structures; they are the past or future states of the world.  

I agree that the world existed for a long time and I hope that it will continue
to exist for a long time to come.  But a history is not a collection of states
of the world -- it is a collection of records or models of past states.  We can
never have more than one world at a time, we can never save any previous states
of the world, but we can have as many models of past or future states as we like.

This discussion reminds me of a tour guide in Greece who pointed to a child's
skull in a museum and said "This is the skull of Alexander the Great when he
was 12 years old."  A person has only one skull, and you can't preserve
multiple skulls at different stages of life.  In the same way, you can't
have a collection of multiple worlds at different times.

> 3.  There is a significant sense in which the following sentence is true:
> 'Bush could have been re-elected, although he was not.'  Here the 'could' 
> reflects not a logical possibility but a "causal" or "historical" one.  
> Much of our ability to learn from the past involves our understanding of 
> What would have happened instead if ....  Perhaps the most interesting use 
> of modal data structures is to describe precisely the causal consequences of 
> of roads not taken (what are all the differences that makes?).  The possible 
> worlds here are REAL to the extent that the modal statements (i.e., it COULD 
> have been ...) are TRUE.

I agree with everything in that paragraph execept the sentence "The possible
worlds here are REAL...."  That word "REAL", even when capitalized, has no
meaning other than a general term of approbation.  While you're doing a global
change of "possible world" to "model", I suggest that you also do a global change
of "REAL" to "supercalifragilisticexpialidocious."

> So before we write off possible worlds as mere data structures, let's look
> a little more closely at the reality represented by the true sentences in 
> those data structures.

There's nothing "mere" about data structures.  They're the only things we
can process on computers, and the possibilities of processing them in wild
and wondrous ways are almost unlimited.  And I'm not writing off possible
worlds.  I'm just saying that if you call them models, you'll have all the
formal power without the metaphysical confusion.

John