[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: [lojban] A Simpler Quantifier Logic (blog article)
On 10.10.2016 02:36, Jorge Llambías 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
go into more detail below), but I'm saying that it's possible to group
predicates into one of only two categories and deal with intermediate
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
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
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
different relationships?
Or your "eating cake" example, would you say that each different reading
is a different meaning of "eat"?
The way I see it, each reading has at its core the same base predicate,
"x1 eats x2", which is a simple relation of one thing eating another
thing. Everything else is built on top of this basic meaning, but the
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
get-go, then you start with ambiguity (or call it vagueness) and then
build additional vagueness on top as you create full statements. (Please
don't understand me as trying to get rid of fuzziness; no matter how
precise a definition is, there is always fuzziness, and there is nothing
wrong with that.)
I mentioned above that there are other means by which intermediate
distributivity can be achieved, and by which "the children ate the cake"
is acceptable even with a distributive "eat".
One such approach is one that we use in other areas of Lojban (or any
language) as well, and that is the idea of pragmatic slack. In certain
contexts and situations, sentences that are false when taken literally
can still be considered true at the level of detail that is currently
relevant. We don't care if really every single one of the things ate
cake, because it isn't relevant to our specific situation. Similarly, we
don't mind if someone says "I woke up at nine" when really they woke up
a few minutes after nine. Nevertheless, the meaning of "wake up at nine"
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
intermediate distributivity. A cover of a set is a set of subsets such
that each element of the original set is included in at least one of the
subsets. When a distributive claim is made, this is done via a universal
quantifier (which we do implicitly when the predicate place is
distributive), but instead of applying to 'all of the things', it only
quantifies universally over those of the things that are part of the
cover. The cover allows for certain individuals to drop out of the
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
I have proposed that a bunch of similar words could exist that express
related forms of "doing something together", depending on the nature of
the togetherness (e.g. just being in the same place as some of them eat,
helping each other so that some of them eat, and so on). These are not
necessarily roundabout, and you would only use them when you think it
matters.
So all in all, you may say it doesn't matter which approach we use as
long as you
> can say "the children took the chairs to the garden" when you don't
know or don't care about how the action was distributed among children
and chairs.
But it makes a difference to me, because in one case we throw our hands
in the air about the meaning of a predicate, and in the other case we
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
in number. {[su'oi] re da pavmei} is false. If you meant its
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
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
have different words for rather different kinds of carrying even though
English only has one? Let's not forget that Lojban is also a way to
experience new ways of thinking about situations. We split English words
into multiple distinct brivla all the time, why shouldn't we here? It
would be interesting.
~~~mi'e la solpa'i
---
Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft.
https://www.avast.com/antivirus
--
You received this message because you are subscribed to the Google Groups "lojban" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lojban+unsubscribe@googlegroups.com.
To post to this group, send email to lojban@googlegroups.com.
Visit this group at https://groups.google.com/group/lojban.
For more options, visit https://groups.google.com/d/optout.