Subject: Re: [lojban] More about quantifiers

From: [email-masked]
Date: Thu, 14 Mar 2002 10:41:58 EST

In a message dated 3/13/2002 5:29:15 PM Central Standard Time, 
[email-masked] writes:

> So, in:
> 
> ro broda su'o brode cu brodi
> = no broda me'iro da poi brode cu brodi
> 
> What is the "actual quantification" of broda and brode?
> I can tell what the actual import is: - for broda and + for brode
> in my system, ++ in yours. But what is the "actual
> quantification"?

I forget what my system is supposed by you to be. But in any case, I don't 
quite follow the identity you propose: Change {ro} into {no...naku}, change 
{su'o} into {me'iro ... naku} and then have the two {naku}s cancel out 
without also converting the {me'iro} back into a {su'o}? That doesn't look 
right. I assume that the {naku} goes directly in front of whatever is 
predicate to a given subject, so the one from getting {no} will be directly 
in front of {su'o}. Time to go back to ultimate forms and check how this 
does work, since I am pushing my intuitions a bit hard at the moment. In any 
case, {broda} is universal, negative, and importing and {brode} appears to be 
particular negative and free. But again I'm not sure that is right, as it 
seems to change what the original sentence says.

<><Which one is the traditional system?>
>
>All + with the assumption that all classes mentioned as subject are 
>non-null
>(and maybe a few less certain things as well).

That sounds exactly like (A-,E-,I+,O+) with the assumption
that all classes mentioned as subject are non-null. Indeed,
with that assumption we can drop the +/- distinction, as it
becomes irrelevant.>

It is any system with the +/- distinction dropped; that's what it has to 
recommend it. That, and the fact that it is the way to get all the 
conversions that one could desirte. And that it fits the needs of 99.9% 
cases of actual use (and the other per mill is cheaply gotten). 

<But for "not every" to be equivalent to "some not",
"every" and "some" must have opposite import.>

As they do in his system, since it is just standard logic, where universal 
appear to be - and paticulars to be +. 
Or in the cases where non-nullity is assumed.

<Do you agree or disagree that in Lojban these are equivalent:

1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode>

Where I am at the moment, I diagree: the first is +, the second is - FOR 
{BRODA}, though + for {da}.

<2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode>

It just occurs to be to ask what "=||=" means; I have taken it as 
bi-entailment, but it might be nonidentity, which would change my answer. 
Continuing with my original assumption, though, I agree with this one.

<>Every universal quantifier (in a non-empty universe) entails every instance
>of its matrix, every matrix with a free term entails its particular 
>closure
>on that term:
>AxFx therefore Fa therefore ExFx. That is about as thorough a working out 
>as
>I can think of.

Assuming a non-empty universe (and you are assuming it by bringing
up a), I have no problem with that.>

Well, not assuming a non-empty universe makes problems for a language, since 
no only would there be nothing to talk about, there would be nothing to say 
and no one to say it.
But, that being the case, "all" implies "some," which is all that I have 
claimed from the beginning.

<But of course that does not mean that
{ro da zo'u ganai da broda gi da brode} entails
{su'o da zo'u ge da broda gi da brode}. It does not.>

Of course not, and no one I know of has ever claimed that it did, so what is 
the point of bringing it up?

<So, if, as I believe, these hold:

1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode

2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode

then we cannot say that {ro da poi broda cu brode} entails {su'o
da poi broda cu brode}. You may not like 1. and 2. as definitions,
but they seem to me fairly standard. At least they are presented
as valid in the page I found (from a random search I did for
"restricted quantification")..>

Well, if they did hold, we could not say that, but, since they don't -- you 
left out the {ge de broda gi} clause on the first one (or the universal 
non-nullity of subject terms) -- we can. Every A entails its corresponding 
(same import) I -- this fails because you are shifting import or failing to 
take account of the fact that import has been neutralized because lo'i broda 
is non-null (as always in Lojban as now constituted, byt we can get rid of 
that problem by allowing {lo ro ni'u broda} and - quantifiers on things as 
well). 
I still need to read a bit more of this book, but it seems that he is using 
what I would call a non-standard definition of restricted quantification, 
using it only as a symtactic category, a different way of writing the usual 
system, without a different semantics attached. The equations you cite are 
strong evidence for this, as is the context in which all the examples I have 
seen so far occur.