lo & quantifiers

[Gerald Koenig <jlk@NETCOM.COM>]

la pycyn pa cusku:


        We also agree that _lo_ and its ilk are +veridical and
-definite.  I argue that, both because it is a description and to fill a
gap in the pattern, _lo_ and its ilk are +specific.  The +veridical is
then essential, for without a known referent (-definite), the referent
cannot be determined except through its properties.  I agree with Xorxes
that this means that the default quantifiers are wrong and that set me
wondering how those were set.  I have a memory of issuing a bunch of
obiter dicta on questions like that on the basis of 30 second
presentations of issues while I was in my Lojban oblivion phase.  If that
is the history, I'd like to say I have more information now and would
like to change my vote.

djer>
I would very much like to hear your current opinion on the default
quantifiers.  It would also be interesting if you could relate a bit of
the history of the evolution of predicate calculus and numerical
quantifiers into artificial language, as lojbab did.

Below are some excerpts from the sumti paper which I believe are up to
date, showing the latest version of things. I see it as the beta
test version, and not the Rosetta stone final edition.

djer

sumti paper>

7.3) (many deletions)

There are rules for each of the 11 descriptors specifying what the
implicit values for the inner and outer quantifiers are.  The following
table lists the implicit values:

                le      ro le su'o
                lo      su'o lo ro
                la      ro la su'o

                lei     pisu'o lei su'o
                loi     pisu'o lei ro
                lai     pisu'o lei su'o

                le'i    piro le'i su'o
                lo'i    piro lo'i ro
                la'i    piro la'i su'o

                le'e    ro le'e su'o
                lo'e    su'o lo'e ro

When examined for the first time, this table looks dreadfully arbitrary.
In fact, there are quite a few regularities in it.  First of all,
the la-series (that is, the descriptors "la", "lai", and "la'i") and the
le-series (that is, the descriptors "le", "lei", "le'i", and "le'e") always
have corresponding implicit quantifiers, so we may subsume the la-series
under the le-series for the rest of this discussion: "le-series cmavo" will
refer to both the le-series proper and to the la-series.

The rule for the inner quantifier is very simple: the lo-series cmavo
(namely, "lo", "loi", "lo'i", and "lo'e") all have an implicit inner
quantifier of "ro", whereas the le-series cmavo all have an implicit inner
quantifier of "su'o".

Why?  Because lo-series descriptors always refer to all of the things
which really fit into the x1 place of the selbri.  They are not restricted
by the speaker's intention.  Descriptors of the le-series, however, are
so restricted, and therefore talk about some number, definite or indefinite,
of objects -- but never less than one.  A descriptor which involves the
speaker's intent, as the le-series cmavo do, cannot refer to zero objects;
whereas it might be the case that a lo-series descriptor describes something
that doesn't really exist (like a purple rhinoceros).  So "ro" does not
exclude "no" (zero), but "su'o" does exclude "no" as a possible quantifier.

Understanding the implicit outer quantifier requires rules of greater
subtlety.  In the case of mass and set descriptors, a single rule suffices
for each:  reference to a mass is implicitly a reference to some part of the
mass; reference to a set is implicitly a reference to the whole set.
Masses and sets are inherently singular objects: it makes no sense to talk
about two distinct masses with the same components, or two distinct sets
with the same members.  Therefore, the largest possible outer quantifier for
either a set description or a mass description is "piro", the whole of it.


The case of outer quantifiers for individual descriptors (including "le",
"lo", "la", and the typical descriptors "le'e" and "lo'e") is special.
When we refer to specific individuals with "le", we mean to refer to all
of those we have in mind, so "ro" is appropriate as the implicit quantifier,
just as it is appropriate for "do".  Reference to non-specific individuals
with "lo", however, is typically to only some of the objects which can be
correctly described, and so "su'o" is the appropriate implicit quantifier,
just as for quotations.

>From the English-speaking point of view, the difference in structure between
the following example using "le":

7.4)    [ro] le ci gerku cu blabi
        [all-of] those-described-as three dogs are-white.
        The three dogs are white.

and the corresponding form with "lo":

7.5)    ci lo [ro] gerku cu blabi
        three-of those-which-are [all] dogs are-white
        Three dogs are white.

looks very peculiar.  Why is the number "ci" found as an inner quantifier
in Example 7.4 and as an outer quantifier in Example 7.5?  The number of
dogs is the same in either case.  The answer is that the "ci" in Example
7.4 is part of the specification: it tells us the actual number of dogs
in the group that the speaker has in mind.  In Example 7.5, however, the
dogs referred to by "... lo gerku" are all the dogs that exist: the outer
quantifier then restricts the number to three; which three, we cannot tell.
The implicit quantifiers are chosen to avoid claiming too much or too little:
in the case of "le", the implicit outer quantifier "ro" says that each of
the dogs in the restricted group is white; in the case of "lo", the implicit
inner quantifier simply says that three dogs, chosen from the group
of all the dogs there are, are white.

Using exact numbers as inner quantifiers in lo-series descriptions is
dangerous, because you are stating that exactly that many things exist
which really fit the description.  So examples like

7.7)    [su'o] lo ci gerku cu blabi
        [some-of] those-which-really-are three dogs are-white

are semantically anomalous; Example 7.7 claims that some dog (or dogs) is
white, but also that there are just three dogs in the universe!

(Actually, because "gerku" has an x2 place, namely the breed or variety
of dog, it claims that there are three dogs of the breed which is understood
from context.  This is almost as bad, because no breed of dog has as few
as three members.)

Nevertheless, inner quantifiers are permitted on "lo" descriptors for
consistency's sake, and may occasionally be useful.


8. Indefinite Descriptions

By a quirk of Lojban syntax, it is possible to omit the descriptor "lo"
from a description like that of Example 7.5; namely, one which has an
explicit outer quantifier but no explicit inner quantifier.  The following
example:

8.1)    ci gerku [ku] cu blabi
        Three dogs are white.

is exactly equivalent in meaning to Example 7.5.  Even though the descriptor
is not present, the elidable terminator "ku" may still be used.  The name
"indefinite description" for this syntactic form is historically based:
of course, it is no more and no less indefinite than its counterpart with
an explicit "lo".

Indefinite descriptions must fit this mold exactly: there is no way to
make one which does not have an explicit outer quantifier ("*gerku cu blabi"
is ungrammatical), or which has an explicit inner quantifier ("*reboi ci
gerku cu blabi" is also ungrammatical  -- "re ci gerku cu blabi" is fine,
but means "23 dogs are white").

Note: Example 6.3 contains an indefinite description, namely "su'o ci
cutci"; another version using an explicit "lo" would be:

8.2)    mi ponse su'o ci lo cutci
        I possess at-least three things-which-really-are shoes
        I own three (or more) shoes.


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