From: zeleny@husc10.harvard.edu (Michael Zeleny)
Newsgroups: rec.arts.books,sci.philosophy.tech
Subject: Re: A note on Modal Logic that has nothing to do with Ikky Sex
Date: 18 Dec 92 01:48:52 GMT
Article-I.D.: husc3.1992Dec17.204853.18644
Organization: The Phallogocentric Cabal

In article <1992Dec17.222000.13099@u.washington.edu>
joechip@hardy.u.washington.edu (Erich Vandenloos) writes:

>Michael Zeleny says:

MZ:
>>Also note that Russell's reasoning does
>>not in any way vitiate the possibility that the collection of all
>>possible worlds is a set, given a reasonable approach to semantics.

EV:
>Could you elaborate a little on "a reasonable approach to semantics?

I think that it is well understood that there are only two reasonable
approaches to semantics, namely Russell's ramified type theory and
Tarski's linguistic hierarchy; moreover, in a fundamental sense, the
former is a special case of the latter (vide Church's classic 1976 JSL
article).  I write this in full cognizance of alternatives like
Kripke's theory of truth, and situation semantics, -- both of these
just seem to push the fundamental difficulty into metalanguage.

But this is mere background.  Consider Kaplan's paradox, as reported by
Lewis.  (I have a dim recollection of Kaplan's disquisition in a 1986
seminar, but my memory is tainted by a bad case of modal skepticism,
which I managed to overcome in the interim.)  We have a set of possible
worlds M, which gives rise to 2^{card(M)} (>card(M)) distinct
propositions.  Presumably (*), for each such proposition S \in P(M),
a.k.a. a set of possible worlds, there possibly exists an individual p,
and a time t, such that the content of the thought of p at t would be
specifiable by a sentence s expressing S.  This possibility then would
allegedly (**) correspond to a possible situation, unaccounted for by
the set M, for reasons of cardinality.

(I am valiantly resisting the temptation to curtail the discussion by
making an obscure allusion to Tarski.  Here goes my effort at clarity.)

Now, Lewis rejects the presumption (*), on the grounds that "Most sets
of worlds, in fact all but an infinitesmal minority of them, are not
eligible contents of thought."  This is a tenable view for a modal
realist, who is beholden to the metaphysical absoluteness of M, but on a
stipulative conception of modality, it is simply unnecessary.  For
suppose that M is stipulated as partially constitutive of the semantics
for the language L.  Then we could accept the presumption (*), without
thereby committing ourselves to the conclusion that the sentence s must
belong to the object language L, rather than its strict superset, the
meta-language mL.  On this, easily justifiable view, the allegation (**)
may be regarded as a _non sequitur_.  In other words, there simply can
be no theory of *all* possible situations, independently of a particular
choice of a language of possibility.

>Mark Taranto says:

MT:
>>>I mentioned that there is a third way to deal with modal operators.  This is
>>>through Linguistics and the Philosophy of Language.  When we say "X is
>>>possible" or "X is necessarily true" what do we really mean?  Part of the
>>>problem is that we don't mean the same things.
>>>
>>>Often it comes down to "X is possible" means that "I am unaware that
>>>X is inconsistent with what I know."
>>>
>>>I believe that this is a more fruitful avenue of study.

MZ:
>>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.

EV:
>It must be nice, too, to think you have a license to go around talking about
>possible worlds.

I find it no more problematic than talking about sets.  It gets a lot
easier if you regard it as no more than a convenient way to account for
counterfactuals and other instances of "subjunctive reasoning".

To me, Taranto's comment simply reeks of bullshit obscurantism.

cordially,
mikhail zeleny@husc.harvard.edu
"Le cul des femmes est monotone comme l'esprit des hommes."