Message-Id: <m0rBjij-00007EC@xiron.pc.helsinki.fi>
Date:         Sat, 26 Nov 1994 14:23:35 -0800
Reply-To:     "John E. Clifford" <pcliffje@CRL.COM>
Sender:       Lojban list <LOJBAN%CUVMB.bitnet@FINHUTC.hut.fi>
From:         "John E. Clifford" <pcliffje@CRL.COM>
Subject:      Ol Uncle Tom Cobleigh
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 13236
Lines: 194

        I used imperatives to make a point in the "any" thread of the
current tangle, then carelessly picked it up thinking it was in the
"opaque" thread.  Thank you, Xorxes, for setting me straight.
Imperatives, however odd they may be in other respects, are not opaque:
identity substitutions preserve satisfaction and quantifying in presents
no problems (unless, of course, the command takes one into an opaque
context, "Don't think about the Wizard of Oz" -- the person, not the
book).  Pulling quantifiers out does not work in general, but that is not
so much opacity as the problems of when and who gets to make choices. The
point of the example, that some references in opaque contexts work
outside, remains, though.  Sorry if I caused any confusion (more than
usual for me).
        I take my job here to proclaim the orthodoxy of formal logic, to
apply it to Lojban when possible and to defend it when necessary.
Happily, logical orthodoxy is as Episcopalian as I am (or as "big-tent"
Republican as I am not), embracing or at least tolerating a variety of
points of view over a broad spectrum of questions, tied together by a
commitment to a few basic practices.
        One of the realms of (usually) friendly disagreement is about the
range of the quantifiers.  The extreme positions here are that bound
variable range only over actually existing things in this world (the
extreme extreme would not even allow numbers and suchlike mathematical
entities) and that they range over the existents of all possible worlds
(and maybe even impossible ones). Lojban has officially (I think) taken
the view that quantifiers in a world range over the things that exist
(zaste) in that world.  McCawley* reminds us that ordinary languages are
more generous than that, though less than a rabid substitutionalist would
allow, and Lojban practice has tended to follow natural language practice
when no one hauls it back into line with theory.  As McCawley notes, we
tend to allow the characters of established fiction and even those loosely
related to them -- Ulysses and Sherlock Holmes and Data and even
Sherlock's mistress and my son are all in (having a name is a sufficient
condition in almost all of the expansionist logical views) and even,
occasionally, unnamed members of classes from such tales (unicorns, for
example, none of which has a name -- that I know of, anyhow).  We say such
paradoxical things (for a strict constructionist) as "There are
 mythical beasts" which we then instantiate, when challenged, with
"Unicorns".  And we surely allow that, if both Rembrandt and Picasso drew
pictures of Zeus, that there is something (even someone) that they both
drew pictures of -- even if they illustrated different events in the
tales, so the quantification is not over events in which Zeus appears.
And, of course, we quantify -- in English often but constantly in Lojban
-- over events that never obtain.  (I personally have no objection to
saying that events exist even if they never obtain, but even some
expansionists are not so liberal.)
        Even if we allow a richer range for variables than just the real
existents, we still need to bring our focus back to them from time to
time: for science if nowhere else but for many practical matters as well.
The laws of physics nor aerodynamics need not account for flying carpets
nor is even the reformed Scrooge a source for a loan. And many predicates
require that their various arguments have the same ontic status: we can
only hit what is in the world with us, for example.  We could, within an
expanded quantifier range, always haul back to the real with an
appropriate predicate, _zaste_ in Lojban, "real" or "exist" in English.
But in a logical language, it is often more convenient to use a different
quantifier for the two cases. And right now we seem to have two quantifier
sets floating around, one of which is already being used (pretty much
unofficially) for what bes and the other for what exists -- except that
the two concepts are not separated consistently.  Using _da_ alone and
with _poi_ (for predicates non-empty in this world) for the strong
quantifier ("there exists") and _lo_ for the weak ("there is" or "bes")
would solve a number of current controversies and a few old ones and head
off a few that have been long abrewing but have not yet -- or only just
now -- come on the scene: the problem with event descriptions as needed
for intensional predicates, for example.  I recommend that we change the
official line accordingly.
        All of which has almost NOTHING to do with opacity.
        What it does have to do with opacity is that it suggests a
principle for determining what terms are imported from outside into an
opaque context and, consequently, can be picked up by external (weak)
quantifiers. We could consider a range of answers, but the most likely one
in practice is one a little to the right of what counts as being in this
world, probably a name or a clear association with something whose being
in the world is not in doubt.  The safest cases -- after those explicitly
mentioned in the surrounding non-opaque context-- are all the _le_
descriptions (picked out by the clearly real speaker), deictic and
possessed descriptions (_lovi_ and _lodo_, etc. -- again because of their
association with real persons and places in the world) and proper names.
But we can adjust from this base as needs be.  Whether we want to let in
the established classes of nameless (unicorns, elves) or not or restrict
the names to established ones in some way, for example, are points usage
will decide -- as it has already voted, more or less clearly, for some
such expansion.  Notice that binding on the outside does not affect the
other properties that define an opaque context.  External identities need
not apply: Hesperus, Phosphorus and Venus can be quite different things
in the intensional realm and George Bush and the President of the United
States can be the same.  Nor does this allow fronting quantifiers -- even
weak ones -- from the opaque contexts to the outside: even if we confine
our list of possible suspects to externally identified people, the fact
that I know someone killed the Viscount does not mean that there is
someone I know to have killed the Viscount.  But still this move may have
some practical consequences for Lojban usage, again bringing theory into
conformity with practice. As I have noted, sumti from opaque context need
to be marked when the context is not apparent (sumti-raising, generally)
and externally established terms in opaque contexts also could use a mark,
at least optionally, when generalizing was in the offing.  And, as Xorxes
keeps insisting, for some terms, we want to just use them alone in reduced
opaque contexts.  So, with established terms we might allow that the
raising marker from its current use and the external establishment marker
from the opaque context cancel each other out, leaving just the bare term
(with some danger in other respects, but probably minor).  So we could say
_mi_sisku_lemi_cukta_.
        That does imply that all of the opaque-making terms have been
brought together into a common format.  As I have said, I think that that
format should be one requiring an event description in the place.  Objects
then come in as raised sumti from such descriptions.  The objections to
this proposal seem to be that it leaves vague descriptions when the object
only appears, that it does not fits some cases -- representations and
_sisku_, and that some event descriptions are not opaque -- "I saw someone
playing pool," for example.  To the vagueness case, it seems to me
sufficient to point out that the notion wanted is already vague: "I need a
box" does not say what I need the box for nor does it say in what relation
I need to stand to the box: possession? use of? will bare existence and
propinquity do?  It depends on what I need the box for, probably, and if
it does, we can figure it out in Lojban as well as we can in English. And
Lojban even has a way of saying "a vague event involving _lo_tanxe_".  On
the other side, I would argue that all the representations are not merely
representations of some object but of that object in context, doing
something, being something, i.e., as satisfying some predicate and so in
an event.  We never get a picture of Zeus plain , for example, but only of
him reigning or raping or....  Of course, there are painting that don't
represent anything, but then the raising problem hardly arises.  As for
_sisku_ (and its presumed ilk, though no one ever offers another one), I
suggest they have absorbed their event description into their own deep
structure -- moving it from syntax to semantics -- so that, although they
only take object sumti, those object sumti are to be marked as raised
nonetheless.  As for my person seen playing pool, I still do not believe
that this is an event description, even though I am still unsure of how
to represent it adequately.
        Short notes:
        Opaque contexts screw up connectives as well as quantifiers.  "I
want coffee or tea" need not entail "I want coffee or I want tea", I may
be undecided between the two (and another's report of my state of mind
will be equally indecisive). Lojban has several different constructions
for the English and at least some of them make the failure of the
inference apparent (sorry I can't lex them.  Is there a current cmavo list
somewhere in the bowels of Yale?  My list lacks many used a lot here and
seems to be wrong about some it does have, to the point that I do not
trust it.)
        Fiction is opaque because real identities cannot necessarily be
exchanged within it: Hesperus and Venus, for example.  But it is global
and so may have its own opacities -- and indeed its own fictions (The
Ocean of Stories or the Thousand and One Nights) -- within it.  And of
course, quantifiers do not work and weak ones need some help (but the
story itself may be justification enough).
        Chassell's suggestion to think subjunctively does not help me
understand or verify a sentence which means different things depending on
whether it is true or false.  Subjunctive reasoning gives hypothetical
conclusions and I want to know what the sentence means and/or whether it
is true.  Suppose I reason that if the sentence is true than it means that
situation s obtains but situation s does not obtain.  So, if the sentence
were true, it would be false since it describes the world as it is not.
Thus, the sentence is false.  If it is false it means that situation z
obtains -- and, since it is false, situation z ought not obtain.  But what
if situation z does obtain.  The sentence is then true, if it means what
it means when it is false, but it is not false on that meaning.  But it
is false on the meaning it has when it is true.  So, what does it mean and
is it true?
        I oppose the lambda suggestion.  The annotation suggested is
inadequate to do the fancy things that lambdas do: it cannot be used -- as
it stand now -- to abstract complex sentences into predicates, since it
does not adequate distinguish scopes.  But I see no reason to correct this
problem, since Lojban is already adequately (and then some) equipped to
deal with abstracted sentences as arguments of higher order predicates
(one main use of lambda) and has no need for the substitution-in-context
procedure ( lambda conversion) which is the other major use -- in the
metalanguage, not in the language in use.  We can use our own abstractions
instead, if we really have to show the relation of interest, but mainly we
can just write out the resulting sentence.
        The correct thing to say about the second rabbit you see when you
are using massifiers is not "another bit of Rabbit" or "another
manifestation of Rabbit" but "Rabbit again".  For good Trobrianders
(assuming that they were not pulling Malinowski's leg -- a dangerous
assumption I would say, based on my time among the Korwa) it is all the
same guy.  Take all the references in English or Lojban to individual
rabbits or groups of them of any size and replace them all with the same
single expression, "Rabbit,"  and you will get it about right.  Actually,
one use of lambda that might be of help here is pulling out what
properties of individual rabbits applies to Rabbit, for, for example, if
some particular rabbit never gets to Chicago but another one does, Rabbit
has, of course, been to Chicago but also (not been to Chicago), which is
not the denial of the first (Rabbit is real and therefore not self
contradictory).
        *McCawley, James D., Everything that Linguists have Always Wanted
to Know about Logic but were ashamed to ask, UChicago, 1981 (I think there
is a revised edition) is a great place to read up on the logic that gets
into linguistics: e.g., opaque contexts, lambda calculus.  It is a bit
quirky however (the stuff on opaque contexts goes off on a tangent that
misses a major point) so it needs to be checked off against a
logicians' view of linguistics.  I recommend Logic, Language, and Meaning
by L.T.F. Gamut, the name of massification of a set of Dutch logicians and
linguists, especially vol 2., Intensional Logic and Logical Grammar.
UChicago 1991.
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