From: mtaranto@shearson.com (Mark Taranto)
Subject: Re: A note on Modal Logic that has nothing to do with Icky Sex
Organization: Yale CS Mail/News Gateway
Date: Fri, 18 Dec 1992 15:41:25 GMT


ObBook:  The best treatment of Possible Worlds I've seen is Voltaire's
         CANDIDE.  For those interested in formal modal logical systems
         there are several textbooks, including one by Hughes & Cresswell.
 
 
zeleny@husc10.harvard.edu (Michael Zeleny) writes:
 
> mtaranto@shearson.com (Mark Taranto) writes:
 
 
Category 1:  formal modal logical systems.
 
> If you want to make this into a meaningful criticism, you will have to
> be more elaborate.  As it stands, your statement is surely in error,
> as witnessed by any number of working logics of time and computation.
 
Where did I say that my musings were an attempt at meaningful criticism?
If people have found applications for formal modal logics, I am happy for
them.  I suspect that most of the applications can be done without
appealing to modal logic.  But I still see no applications of these
theories to how we really use the words "Possible" and "Necessary" in
language, nor would I be willing to base a moral theory on these quite
limited logics.
 
Category 2: Quantifying over possible worlds.
 
>> For those who wonder why I have a problem quantifying over possible worlds,
>> it is for the same reason that there are problems quantifying over the
>> set of all sets.  I see cardinality problems.
 
> This is known as Kaplan's Paradox, and its conclusive dismissal will
> be found on pages 104--8 of David Lewis' book _On the Plurality of
> Worlds_.  Note that Lewis' treatment is essentially independent of any
> assumption of modal realism.
 
I would categorize this treatment in Category 1.  Perhaps I was not clear
that I was talking about "All Possible Worlds" in a natural language sense,
not in the limited sense used by many modal logicians.  I thank you for
the reference, but as I've already spent more than a year of my life
reading papers in Modal Logic, I have no desire to read any more.
 
> Finally, logicians quantify over all sets all the time; that's what
> the notion of a proper class is for.
 
Yes, logicians do.  But the good ones are very careful about how they do it.
Unfortunately, too many of the papers which I read were written by logicians
who were not so careful.  Their results were, therefore, dubious.
 
> As Gene Ward Smith might say, not an argument.
 
But it is an opinion, and that is all that I offered.
 
 
 
 
 
Category 3.  Study the meaning of "Possible" and "Necessary" through the
             tools of linguistics and Philosophy of Language.
 
 
>> Often it comes down to "X is possible" means that "I am unaware that
>> X is inconsistent with what I know."
 
> Sounds like emotivism to me.  Too bad it got so discredited; it would
> be nice to have a license to go around, referring solely to your
> private beliefs.
 
I offered the "X is inconsistent with what I know" point as an example, not
as the only way that people use the words.  That some people do use the word
possible in that way is undeniable.  I am neither advocating its use, nor
condemning it -- simply stating that it is so.
 
On the other hand, I do believe that if we want to study how modal operators
are used in language, then the tools of studying natural languages are more
fruitful than the tools for studying formal modal logics.
 
Mark
 
 
 
I will be unable to continue this discussion.
After today, I can be reached at mtaranto@panix.com


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