Subject: Re: [lojban] More about quantifiers

From: [email-masked]
Date: Sun, 10 Mar 2002 15:35:48 EST

In a message dated 3/10/2002 11:32:29 AM Central Standard Time, 
[email-masked] writes:

> O- ganai da broda gi me'irode zo'u ganai de broda gi de brode
> O+ [ge da broda gi] me'irode zo'u ganai de broda gi de brode
> 

These don't seem quite right at first glance (it's hard to get existential 
import with conditionals), but a run-through shows that it does work, such is 
the power of {me'iro}.

These cases aside, I have to agree with this list, since I gave the same one 
yesterday. I should note, though, in case, the idiosyncrasies of this 
quantification system is given any as an argument for a particular position, 
that there are equally tidy ways to do everything in terms of {lo ro broda} 
and of a set involving the Aristotelian A+E-I+ O-. At least the first of 
these also has a priority position in Lojban equal to (or even greater than) 
prenex quantifiers. All the DeMorgan ("inversion") rules for any of these 
can be matched in any of the others, with about the same number of mucky 
cases and the same kind of muck. Presumably the trick is to hit on one and 
find some short forms for the mucky cases, forms that minimimize 1) the 
changes from Lojban in practice already and 2) involve the least complex 
transformations at the negation breaks (and perhaps 3) do least violence to 
existing Lojban semantics). The first two may already be incompatible, since 
the simple transformations are the ones in use and they were made without an 
conscious attention to import, leading to the apparent lack of systematic 
connection between form and function here.

<There is no possible misinterpretation of those. Also these
are common ground:

roda = noda naku = naku me'iroda = naku su'oda naku
noda = roda naku = naku su'oda = naku me'iroda naku
su'oda = me'iroda naku = naku noda = naku roda naku
me'iroda = su'oda naku = naku roda = naku noda naku>

Remembering, of course, to change the tags in front from {ge da broda} to 
{ganai da broda} and conversely, since negation changes import along with 
quantity and quality. 

<Now we have to decide whether {ro da poi broda cu brode} will
mean {ro da zo'u ganai da broda gi da brode}
or {ge da broda gi ro de zo'u ganai de broda gi de brode}.>

Cowan (starting this off all unawares):
<The question is about universal statements and how to map them.
Traditionally, "All swans are white" (used by Aristotle, but now known
to be empirically false) was read as having existential import, as
you say.

Modernists mapped this to "For all X, if X is a swan then X is white"
which does not have existential import about swans (it has existential
import about X, but that is no problem unless we are considering a
purely empty universe, which can be dismissed). It merely says that
*if* there are any swans then they are white.

This clash can be resolved in one of two ways: decide that "All swans
are white" has no existential import either, or decide that "For all X
etc." is not a fully adequate mapping of "All swans etc."
Lojban takes the second view, since both forms can be expressed:
one using number + predicate directly (= "All swans"), the other
using a bound variable and a relative clause ("All X such that").>

I took this to mean that this issue was settled with importing forms getting 
{lo broda} and the free forms {da poi broda}. I was so delighted to see the 
issue dealt with at all in a definitive manner that I did not mind that this 
was not what I took to be the optimal settlement. It was, however, an 
accurate report of usage, as far as the clear cases went (there are no end of 
unclear cases, of course, because by and large what we talk about does exist, 
so the import distinction is not apparent). 
To incorporate {da poi broda} on the importing side is nicer from the point 
of view of logic (it gives real restricted quantifiers of the familiar sort) 
and forces people who want to talk about non-existent or uncertainly existing 
things to take an appropriate amount of effort to do so (the basic forms for 
-s). That is, it throws the weight of quantifer theory onto the + side 
wjhere it usually belongs. But, of course, it mucks inversion again, by 
bringing in the - cases rather than the + ones, which are usually what one 
really intends (existence rarely being an issue). 
So the issue is not just to find out what to take {ro da poi} to mean, but to 
find a system that covers all the cses simply and economically -- yet does 
not do (too much) violence to established usage and semantics.

<Obviously it is much simpler to use the first, because then
we have:

A- [ganai da broda gi] rode poi broda cu brode
A+ ge da broda gi rode poi broda cu brode
E- [ganai da broda gi] rode poi broda cu naku brode
E+ ge da broda gi rode poi broda cu naku brode
I- ganai da broda ginai rode poi broda cu naku brode
I+ [ge da broda gi] naku rode poi broda cu naku brode
O- ganai da broda ginai rode poi broda cu brode
O+ [ge da broda gi] naku rode poi broda cu brode

If you make the other choice, you will have a lot of
trouble to make the conversion for all of them. Probably
it can't even be done. The same argument can be made writing
everything in terms of {su'o}, or in terms of {no}, or
in terms of {me'iro}. We can now use the same conversion
table to write each one back with its cannonical quantifier:>

Of course we can do anything with another system we can do with this one, 
though some forms may be messier -- and other simpler. 
But, to my confusion, you now seem to be arguing that {ro da poi} be - and I 
thought you were saying it should be +; where did I go astray or you change 
your mind? I had it as - in the system I presented, to which I thought you 
objected. 

<If we follow the same process by writing everything in terms
of each of the quantifiers, and taking {Q broda cu brode} to
be short for {Q da poi broda cu brode} we get the forms:

A- [ganai da broda gi] ro broda cu brode
A+ ge da broda gi ro broda cu brode
E- [ganai da broda gi] no broda cu brode
E+ ge da broda gi no broda cu brode
I- ganai da broda gi su'o broda cu brode
I+ [ge da broda gi] su'o broda cu brode
O- ganai da broda gi me'iro broda cu brode
O+ [ge da broda gi] me'iro broda cu brode>

This move makes sense in Lojban if {ro da poi} is A+, but not if it is A-, 
since {ro broda} has existential import in Lojban (see Cowan again, as well 
as all the other evidence that has come along in this exchange.

<So far we have said nothing about inner quantifiers, and indeed we
don't need to say anything about them. We know that {Q broda}
can also be written as {Q lo ro broda}, but that doesn't change
anything in what we've done.

All we have had to define so far is {ro da poi broda cu brode} as
{ro da zo'u ganai da broda gi da brode} and {Q broda} as
{Q da poi broda}. I don't think you can get a simpler system.>

And it is just for this reason that taking {ro broda} as A- doesn't work, 
since the internal quantifier {ro} still has existential import.

<It seems to me that the system I presented is the most Lojbanic
if we accept the common ground forms as fundamental. If we don't
start from those, we get into particular people's intuitions
about what "all" means and so forth, and I see no point in
going that way. It's highly subjective and the forms and
relationships obtained are much more complex.>

Well, aside from going against a fistful of basic bits of Lojban philosophy 
and semantics and leaving a bunvch of messy loose ends (unreduced final 
expressions for example, which at least could be improved on in the orignal 
system), I don't see that it has that much to offer over my system (which is 
probably not a final version yet, though no one has commented on it from a 
Lojban -- as opposed to Llamban) point of view). I personally believe that 
having to make a significant change, rather than just a trivial one to shift 
from + to - or back is useful, as is having all of one import be of the same 
form. In any case, the system I presented is the nearest thing we have so 
far to a Lojban syste, with all Lojban's quirks intact. And, note, half of 
the forms are as simple as xorxes' and the other half are much simpler.