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Subject: Re: [lojban] A Simpler Quantifier Logic (blog article)
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Date: Mon, 10 Oct 2016 22:15:58 +0200
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On 10.10.2016 02:36, Jorge Llamb=C3=ADas wrote:
> I don't believe a distributive "citka" is all that useful. I want to be
> able to say "the children ate the whole cake" without having to
> introduce any roundabouts.

Of course. But I believe that a distributive {citka} does not prohibit this=
.

> It's also a simplification to say that there are only two kinds of
> distributivity (fully distributive and fully collective). Those are just
> the two extremes.

Yes. I'm not saying there are only two kinds of distributivity (I will=20
go into more detail below), but I'm saying that it's possible to group=20
predicates into one of only two categories and deal with intermediate=20
distributivity via other means.

>     Unspecified distributivity in an argument place is a form of
>     ambiguity at the definitional level of a predicate.
>
>
> No, it's just a form of vagueness, where you don't specify what you
> don't want or need to specify.

Let us look at some of the many possible meanings of a simple quantified=20
statement in English, say, "At least three people carried a chair":

1) At least three people are such that each of them carried a chair.
2) At least three people are such that each of them was involved in=20
carrying a chair.
3) Some people that are at least three moved a piano together.

Would you say that all of these describe the same relationship or=20
different relationships?

Or your "eating cake" example, would you say that each different reading=20
is a different meaning of "eat"?

The way I see it, each reading has at its core the same base predicate,=20
"x1 eats x2", which is a simple relation of one thing eating another=20
thing. Everything else is built on top of this basic meaning, but the=20
meaning of {citka} itself does not change in the process.

On the other hand, if you say {citka} means all sorts of things from the=20
get-go, then you start with ambiguity (or call it vagueness) and then=20
build additional vagueness on top as you create full statements. (Please=20
don't understand me as trying to get rid of fuzziness; no matter how=20
precise a definition is, there is always fuzziness, and there is nothing=20
wrong with that.)

I mentioned above that there are other means by which intermediate=20
distributivity can be achieved, and by which "the children ate the cake"=20
is acceptable even with a distributive "eat".

One such approach is one that we use in other areas of Lojban (or any=20
language) as well, and that is the idea of pragmatic slack. In certain=20
contexts and situations, sentences that are false when taken literally=20
can still be considered true at the level of detail that is currently=20
relevant. We don't care if really every single one of the things ate=20
cake, because it isn't relevant to our specific situation. Similarly, we=20
don't mind if someone says "I woke up at nine" when really they woke up=20
a few minutes after nine. Nevertheless, the meaning of "wake up at nine"=20
is not changed, nor is the meaning of "ate cake" changed.
(Lasersohn (1999) discusses this in great detail)

Another approach is to use the concept of a "cover" to account for=20
intermediate distributivity. A cover of a set is a set of subsets such=20
that each element of the original set is included in at least one of the=20
subsets. When a distributive claim is made, this is done via a universal=20
quantifier (which we do implicitly when the predicate place is=20
distributive), but instead of applying to 'all of the things', it only=20
quantifies universally over those of the things that are part of the=20
cover. The cover allows for certain individuals to drop out of the=20
picture. The predicate remains distributive with this approach, too.
(Schwarzschild (1996) and Brisson (1998) use this approach)

And additionally, when it is important, words like {kansi'u} exist (and=20
I have proposed that a bunch of similar words could exist that express=20
related forms of "doing something together", depending on the nature of=20
the togetherness (e.g. just being in the same place as some of them eat,=20
helping each other so that some of them eat, and so on). These are not=20
necessarily roundabout, and you would only use them when you think it=20
matters.

So all in all, you may say it doesn't matter which approach we use as=20
long as you

 > can say "the children took the chairs to the garden" when you don't=20
know or don't care about how the action was distributed among children=20
and chairs.

But it makes a difference to me, because in one case we throw our hands=20
in the air about the meaning of a predicate, and in the other case we=20
can decide what it means on a fundamental level.

>     There are other ways (for example, in the realm of pragmatics) to
>     deal with vague distributivity, outside of the definition of
>     argument places, and I prefer those ways.
>
>
> I'm not too sure how stringent you want to be with defining
> distributivity into all predicate places. For some places it's
> reasonable that it be part of the definition of the predicate ("pavmei"
> might be an example).

{pavmei} cannot be distributive. It is only true of things that are one=20
in number. {[su'oi] re da pavmei} is false. If you meant its=20
distributivity type must be non-distributive, then yes.

There are many predicates that only make sense non-distributively.

There are also many predicates that are fundamentally distributive, and=20
where making them non-distributive only adds vagueness.

> For other predicates, I don't see how forcing a
> fixed distributivity helps, since there are things that can just as well
> be done separately or together.

It helps pin down the fundamental meaning of a predicate.

But it makes me wonder. Is it really such a crazy idea for Lojban to=20
have different words for rather different kinds of carrying even though=20
English only has one? Let's not forget that Lojban is also a way to=20
experience new ways of thinking about situations. We split English words=20
into multiple distinct brivla all the time, why shouldn't we here? It=20
would be interesting.

~~~mi'e la solpa'i


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