Subject: Re: [lojban] Tidying notes on {goi}

From: [email-masked]
Date: Fri, 27 Jul 2001 09:20:25 EDT

In a message dated 7/26/2001 6:02:41 PM Central Daylight Time, 
[email-masked] writes:

> >among those selected by the first quantifier,
> 
> What? Quantifiers don't select anything. {su'o da poi prenu cu prami}
> is a statement about the set of all persons.
> 

Well, yes and no -- and I suspect that it is this that is at the heart of a 
part of this problem. On the "yes" side, your sentence strictly staes that 
the set of persons intersects the set of lovers (every quantifier is a 
second-order relation between classes). On the "no" side, the members of 
that intersection can now function linguistically (even if not logically-- 
but I would say logically, too) as designated individuals -- the standard 
English "a boy"~"the boy" alternation (logic "some x" "eta x" or "alpha x", 
not "iota x").    

<I don't think we can have one rule for {ro} and a different rule
for {su'o}, as it would cause all sorts of inconsistencies>

Same rule, different results. the class selected by {ro} is the whole class, 
so you can use that class again to define the class on which the second 
quantifier works. with other initial quantifiers, the class for the second 
quantifier is already restricted.

<Consider this for example:

    su'o da poi prenu ku'o naku zo'u da prami su'o da

which is logically equivalent to:

    naku ro da poi prenu zo'u da prami su'o da>

Hmmm! Negation presents a problem here and I need to work out what happens.  
I suspect that, as usual, prenex forms decide what the "previous quantifier" 
actually is.

<This is also more or less what happens in natlangs in any case:
"No student took that class. They hate the teacher." "They"
obviously refers to all the students, not to "no student".
In Lojban that might go something like {no da poi tadni cu cilre
fo ko'a i ro da xebni le ctuca}.>

Now, this is an interesting case! We have, of course, several responses: 
"Natural language is so illogical," "In the logically pure form this is just 
a case of the sort we have already described" and probably others. In any 
case, this need not count against the present rule, but might lead to 
rethinking it.

<{su'o lo prenu} may refer to a different prenu every time it
is used. I don't understand how you could have a double binding
in this case.>

But {lo prenu} is not a variable (there is something odd about that sentence 
in context). 

<>I am unsure what that would mean for the {goi} case; probably gobbledygook
>unless la alphas was the same entity as la betas.

In {da goi la alfas} la alfas cannot have a previous referent.
If it does, then it is gobbledygook.>

Under which set of rules? Why can this not (under the present rules) not 
just be the namely rider on {da}, "there is an x, namely Alpha?"

<>Yes {da'o} clears the xy assignment and the subsequent {da} is a new
>quantifier, not now restricted to xy.

That's what I thought. You will have to correct you demonstration
then, as you leave xy dangling unassigned in the middle of it:>

Ummm! I thought that was your example; it isn't mine (who else was in this 
discussion?)

<What happens if The Book is in contradiction with Logic? Which one
wins?>

As Lojbab says, during the freeeze, the book does. But I am not yet 
convinced that this is such a case. It does raise an issue, much discussed 
in the 70's, about the difference between identifying and relational uses of 
quantifiers. That proved almost insoluble in formal logic, but can in fact 
be solved easily in langauges meant for use. I am not sure that lojban has 
done this very well and that may be the heart of issue here. Lojban does 
certainly have a number of work-arounds that cover the problem, but does not 
face it square on.