Re: logical issues (lambda,ka, man-dogs, etc.)

[Jorge Llambias <jorge@PHYAST.PITT.EDU>]

Having done my homework, I can now comment :)

>         The talk of types, which is already beginning to appear in the
> discussion of lambda, makes little sense in Lo??an, since the langugae is
> basically reductive, taking all types as individuals

I agree with that. Lojban does have propositions, but they are treated
as individuals. {da} can be a proposition as well as a dog.

McCawley's talk of "sorts" is also interesting. What he calls "sets" are
our masses, of course, not our sets. He gives the example of "the boys
carried the piano upstairs" as an example of "set argument", but I'm sure
he doesn't mean it in the mathematical sense, as in "the boys carried the
piano upstairs and have cardinality three". He surely means {lei nanla cu
bevri le pipno le gaploi}.

Also interesting are his "kinds": individual, stage, and generic.
"Generic" I think corresponds to Lojban's {lo'e}, but Lojban makes
no distinction between his "individuals" and "stages": {mi se cmene
zo xorxes} and {mi klama le zarci} use the same {mi}, even though the
first is mi the individual and the second is only a stage of mi the
individual.

>         McCawley gives a nice test to demonstrate that restricted
> quantifiers have existential import inherently, not just as a conversational
> implicature, a matter that has been of some moment here from time to
> time.

He gives a nice test but he doesn't arrive at a definite conclusion.
The test is whether the natural answer to questions with a vacuous universal
is "yes" or "no".

He gives the example:

        Do all unicorns drive Chevrolets?

and he ranks the possible answers:

        *Yes, indeed there are no unicorns.
        ?No, indeed there are no unicorns.
        *Yes, but there are no unicorns.

The "no" answer would indicate existential import, and "yes" would
indicate no import. He marks the two "yes" answers as incorrect (*)
and the "no" as uncertain (?).

This is of course just one example, and it cannot demonstrate that
"all" always has existential import. It can at most show that it does
in this example. I wonder how he would evaluate this other one:

        Will all who come get to see the baby?

        Yes, indeed noone will come.
        No, indeed noone will come.
        Yes, but noone will come.

I find the last answer to be the one that makes most sense, but then
I'm not a native English speaker. But is it necessary to be a native
English speaker to see whether the universal quantifier has existential
import "inherently"? I don't think so. Indeed, in Spanish it is easy
to see that it doesn't have to. The difference between:

        Todos los que vengan vera'n al bebe.
        All who come will see the baby.
and:
        Todos los que vendra'n vera'n al bebe.
        All who will come will see the baby.

is that the first one does not imply that at least someone will
come while the second one does. The existential implicature is given
by the tense used, and not at all by the quantifier!

My biggest problem with the unicorn example is that it is so
unlikely. If one talks about unicorns it is because there are
unicorns. I picture a unicorn driving a Chevrolet and I know
that it is not true that they all do that. But what about more
reasonable things:

     All even prime numbers greater than three are multiples of 27.
     Yes, indeed there are no even prime numbers greater than three.

Is that really bad English?

>         McCawley's mapping of lambdas onto English is not going to fit
> perfectly with the hard cases in Lojban, because Lojban treats a number of
> items in different clusterings from the way English does (events and
> propositions apparently together, for example -- but, as noted, the
> logicians are not too good on those anyhow).

McCawley doesn't even mention the kind of thing that we need lambdas for.
He only uses them to explain the "deep structure" of English sentences
that use the equivalent to {go'i} and {no'a}, but he gives no example
of a property being an argument in a relationship with things that
have the property.

Jorge