Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import, and all that stuff

From: [email-masked]
Date: Sat, 9 Mar 2002 04:34:32 EST

In a message dated 3/8/2002 7:01:09 PM Central Standard Time, 
[email-masked] writes:

> I'll be glad to look at it once it's been honed. Meanwhile
> I'm happy with what I got.
> 

Well, I hope you will rejoin Lojban some day. In the meantime, have fun. 
But would you mind awfully not clogging the Lojban list with it?

<: how do you say that things that
>don't exist don't exist.

In (my dialect of) Lojban, one way is:

ro na zasti naku zasti

another way:

ro da poi na zasti ku'o naku zasti

I gather you approve of the second but not of the first.>

The first turns out that the first one is OK, too, since it denies that 
something that does not exist exists and the denial of any contradiction is a 
tautolgy. The relation between {zasti} or "exists" and quantification has a 
long and turbulent history, though most of which they have been recognized as 
not being the same (without being too clear about what either one is).

<>Happily, in a logical language it is pretty easy:
>{noda broda} (shorter too).

I have no problem with that to say that there are no broda.>

Well, if you want to do on then {no da poi na zasti cu zasti} Not shorter, 
but still systematic. Again, saved by being a tautology of sorts. Can you 
do anything interesting with all this?

<>But in your language, {su'o lo broda na zasti}
>seems to be true when lo'i broda is empty.

Correct. "It is not the case that at least one broda exists.">

What about {su'o broda cu zasti}? Presumably false, but also I-, so it ought 
to be true. The problem is that there are just too many non-standard 
features here to keep track of -- I hope you will someday explain what the 
system is here as everytime I try to work with one that looks right, it turns 
out to be wrong somehow.

<I know. One refers to a set, the other to its elements.
That's in my dialect. In real Lojban one refers to a set,
the other to its elements if it has any and it is nonsense if
it doesn't. Real Lojban is a bit more complicated than my
dialect. Unnecessarily so, in my opinion.>

Well, I suppose human langauges 
are inconvenient from a variety of points of view and Lojban is designed to 
be a human language, so it shares some of their foibles. (I know that you are 
going to say that that is not how it works in your language, but I will 
suspect that either that is true -- for whatever that says about you -- or 
that you have been brainwashed -- as many people seem to have been -- by 
logicians of some sort.)

<>Insofar as I can make coherent sense of your system, it seems that every
>quantifier is attached to a {(lo) broda}, thus specifying that the range of
>the quantifier is simply that set (which, however, you allow to be empty).

Yes. That's the same as in real Lojban, except that real Lojban
for some reason does not allow the set to be empty, right?>

No. The set can be empty, but then the reference to its members has to be 
treated in whatever way is appropriate for expressions that don't have a 
referent. I'm not sure what the Lojban rule is about that, if there is one. 
I am at a loss to know what the members of the empty set are and how a 
quantifier can range over them (note, this is not the same as the range of a 
function, though that is problematic with the empty set as well). 

<>Historically, universals true about empty sets have been pulled off by
>quantifying over another set (everything) and introducing the empty set
>conditionally. The truth then comes from the conditional reference, not 
>from
>the quantifier.

Ok. This of course is also possible in my variety of Lojban.>

Well, except for calling it Lojban (it presumably is a Loglan), this is not 
too surprising. I suppose it would be superfluous to do so, since you 
already ahve forms for all those critters. And, of couse, you can talk about 
the empty universe (a dubious advantage).

<>-- calling it false
>makes at least as much sense).

It would break the whole system though. Most of the relationships
between quantifiers would not hold in the case of empty sets. What
would be gained?>

Well, a closer approach to human intuitions and linguistic practice, 
conformity with logic which we are supposed to take as a guide. Breaking the 
system is hardly something that would bother me.

<Ok, I can live with that complaint. I'm not uncomfortable with
breaking official rules as long as I think it is justified (i.e.,
in this case a much simpler and elegant set of rules). What I would
not like is if there is an actual inconsistency, but so far at least
none has shown up.>

Since we don't quite know what the Lojban rules are, it is hard to say 
whether yours are simpler or more elegant and, of course, it is not obvious 
that simplicity and elegance in a small part should trump accuracy or 
coherence in the larger language situation. But it may be interesting to see 
whether Llamban can eventually develop into a full-scale competitor to Lojban 
(maybe the beginning of LoCCan3 -- a good place to take this discussion, by 
the way).