Quantifier exactness

[Ian Johnson]

The issue of quantifier exactness has come up a few times already. The most recent example was "context and precision" which was forked by aionys from another thread. You can look at that thread On IRC today, playing around with functions we stumbled upon a combination of a sentence and situation such that one stance on quantifier exactness makes the sentence false while the other makes it true. Here's the setup:

There are 4 people, mi, do, la alis, la bab; the latter two are grouped under {lo re prenu}.
I like la alis a little bit, but hate la bab.
You like la alis and la bab a lot.
Now consider
{mi zmadu do lo ni ce'u nelci pa lo re prenu}
(If the ni confuses you, pretend it's ka, as that part's not important here. We can talk about ka-ni elsewhere.)

If quantifiers are exact, this is true. {do nelci pa lo re prenu} is completely false (you like two of them, not one), while {mi nelci pa lo re prenu} is true, if only a little bit, so I do exceed you in that aspect. Note that the CLL says this is how the language works, but if you look at the previous discussions you'll find that this is clumsy fairly frequently.
If quantifiers are not exact, this is false or at least false-ish, since {ro da poi me lo re prenu zo'u do zmadu mi lo ni ce'u nelci da}.

I thought this example warranted discussion primarily because it does not arise because of annoying, semi-ontological issues related to the universe of discourse. Instead there's only two people being quantified over, but the two interpretations still differ with respect to this (relatively simple) sentence.

.i do ma jinvi

.i mi'e la latro'a mu'o

[Felipe Gonçalves Assis]

I don't understand what you mean by "inexact quantifers". Do you mean that {pa}
should be understood as {su'o}? I don't see why that is necessary, or why you
would need such a convoluted example to exemplify the different interpretations.

mu'o
mi'e .asiz.

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[Ian Johnson]

Not {su'o}, no. Instead it's more like "at least one, and probably about one." As for the example, trivial examples don't really help (since the issue could basically be left up in the air and trivial cases would still be resolvable in context), while universe-of-discourse-based examples seem pedantic at best.

mi'e la latro'a mu'o

[Ian Johnson]

...Actually, both of the above situations are the same. {ci prenu cu zvati lo zdani} when 5 are present is an "inexact quantifier", but it can be sneakily worked around by playing with the universe of discourse (i.e. we're excluding them from the discussion). There's no such workaround in the first example, because the quantifier range is explicit.

mi'e la latro'a mu'o

[la gleki]

On Sunday, January 6, 2013 10:59:58 PM UTC+4, Latro wrote:

The issue of quantifier exactness has come up a few times already. The most recent example was "context and precision" which was forked by aionys from another thread. You can look at that thread On IRC today,

if there is something important in those logs could you please copy them here? not everyone has access to full logs including english messages.

[Felipe Gonçalves Assis]

What is lacking here is the argument /for/ quantifier inexactness,
which goes against CLL.

On 7 January 2013 01:15, Ian Johnson <blindb...@gmail.com> wrote:
> ...Actually, both of the above situations are the same. {ci prenu cu zvati
> lo zdani} when 5 are present is an "inexact quantifier", but it can be
> sneakily worked around by playing with the universe of discourse (i.e. we're
> excluding them from the discussion). There's no such workaround in the first
> example, because the quantifier range is explicit.
>

The analysis of "There are three people in the house" has always been
{su'o ci prenu cu
zvati lo zdani}, as far as I know. The "probably just about three"
part comes naturally as a
pragmatic effect of scalar implicature: if more than three relevant
people are known to be
on the house, the speaker would have mentioned that.

[.arpis.]

On Mon, Jan 7, 2013 at 5:33 AM, Felipe Gonçalves Assis <felipe...@gmail.com> wrote:

What is lacking here is the argument /for/ quantifier inexactness,
which goes against CLL.

Much as I like quantifier exactness as a useful idiosyncrasy in lojban (and view adhering to the CLL) as a good default, I find the example given as an argument /against/ quantifier exactness (though not an entirely convincing one by itself), at least if I take latros's analysis at face value.

The sentence says to me "I, more than you, like one of the two people." Unless you can give me an intuition for a translation that preserves exact quantifier semantics (and just adding "exactly" to the previous statement doesn't do it), I'm going to be uneasy about them.
 

--
mu'o mi'e .arpis.

[v4hn]

On Mon, Jan 07, 2013 at 10:01:50AM -0500, .arpis. wrote:
> > >>> > {mi zmadu do lo ni ce'u nelci pa lo re prenu}
>

> The sentence says to me "I, more than you, like one of the two people."
> Unless you can give me an intuition for a translation that preserves exact
> quantifier semantics (and just adding "exactly" to the previous statement
> doesn't do it), I'm going to be uneasy about them.

To me this example sounds like these
childish debates on who like someone more.
"I like him more than you do."
or in this case:
"I like one of them more than you like one of them."

What's wrong with this translation?


v4hn

[Ian Johnson]

"I like him more than you do" is incorrect. Since the quantified variable is instantiated separately in each of the function applications, the original sentence under exact quantifiers means it's more like "It is more true that I like exactly one of them than it is true that you like exactly one of them." This re-instantiation is why the original example is counterintuitive. I'm not fully sure whether I would draw the same conclusion from your second translation; I think I might, though, since "one of them" is introduced twice (unlike arpis's previous translation, which only introduces it once and hence makes it seem like the referent is the same).

mi'e la latro'a mu'o

[v4hn]

On Mon, Jan 07, 2013 at 11:15:22AM -0500, Ian Johnson wrote:
> "I like him more than you do" is incorrect.

Sure, I didn't mean that to be a translation.
It's just an example of the kind of debate I was talking about.

> Since the quantified variable is instantiated separately in each
> of the function applications, the original sentence under exact quantifiers
> means it's more like

> > > > >>> > {mi zmadu do lo ni ce'u nelci pa lo re prenu}

> "It is more true that I like exactly one of them than it is true
> that you like exactly one of them."

I still don't get why you guys introduce the "is more true"
here. I can't see how this is in the original sentence!

"I like one of them more than you like one of them."

is something completely different from your translation,
so if my translation is wrong, then how would it be correct by the way?

> This re-instantiation is why the original example is
> counterintuitive. I'm not fully sure whether I would draw the same
> conclusion from your second translation;

Which conclusion? Do you think it works out, or don't you think so?

> I think I might, though, since
> "one of them" is introduced twice (unlike arpis's previous translation,
> which only introduces it once and hence makes it seem like the referent is
> the same).

v4hn

[Felipe Gonçalves Assis]

On 7 January 2013 12:01, .arpis. <rpglover...@gmail.com> wrote:
>
> On Mon, Jan 7, 2013 at 5:33 AM, Felipe Gonçalves Assis
> <felipe...@gmail.com> wrote:
>>
>> What is lacking here is the argument /for/ quantifier inexactness,
>> which goes against CLL.
>
>
> Much as I like quantifier exactness as a useful idiosyncrasy in lojban (and
> view adhering to the CLL) as a good default, I find the example given as an
> argument /against/ quantifier exactness (though not an entirely convincing
> one by itself), at least if I take latros's analysis at face value.
>

I don't see how the example is an argument. It is just that, an example.

> The sentence says to me "I, more than you, like one of the two people."
> Unless you can give me an intuition for a translation that preserves exact
> quantifier semantics (and just adding "exactly" to the previous statement
> doesn't do it), I'm going to be uneasy about them.
>

"I, more than you, like one of the two people."

{da poi me lo re prenu zo'u mi zmadu do lo ni ce'u nelci da} or
{mi zmadu do lo ni ce'u nelci lo [su'o/pa] me lo re prenu}

The odd thing with the original example is the quantification within
the ni-clause.

[.arpis.]

I meant a translation of the original statement into English. .u'u that I wasn't clear.

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[Felipe Gonçalves Assis]

On 7 January 2013 14:55, .arpis. <rpglover...@gmail.com> wrote:
> I meant a translation of the original statement into English. .u'u that I
> wasn't clear.
>

That is the point. I have never seen in any other linguistic
expression an object
like lo ni mi nelci PA da, as far as I can tell. This is why, in the
attempted translation,
the normally ambiguous scope of the natural language quantifier is
forced to long.
I have no intuition about lo ni mi nelci PA da, although I agree with
the axioms that
justify latro'a's reasoning.

[John E Clifford]

Ordinarily, the scope of a quantifier in an abstraction is restricted to that abstraction and moving it outside is a logical no-no (as though the UD of one world were the same for all).  Now {ni} is a strange abstraction and may be have differently, but until that case gets made we have to say  we must take it internally.   So, we have the case that my liking for A is 3 (on a 5-point scale) and for B is 0 (bottom), while you give both A and B 4 (top).  So, in fact, I don't like either of them more than you do.  Notice that, in this case at least, moving the quantifier outside doesn't change the result.  I suspect this is a problem with the example, but I don't want to fadge up a new one. 

---

From: Felipe Gonçalves Assis <felipe...@gmail.com>
To: loj...@googlegroups.com
Sent: Tuesday, January 8, 2013 5:46 PM
Subject: Re: [lojban] Quantifier exactness

On 7 January 2013 14:55, .arpis. <rpglover64+jbo...@gmail.com> wrote:
> I meant a translation of the original statement into English. .u'u that I
> wasn't clear.
>

That is the point. I have never seen in any other linguistic
expression an object
like lo ni mi nelci PA da, as far as I can tell. This is why, in the
attempted translation,
the normally ambiguous scope of the natural language quantifier is
forced to long.
I have no intuition about lo ni mi nelci PA da, although I agree with
the axioms that
justify latro'a's reasoning.

mu'o
mi'e .asiz.

>
> On Mon, Jan 7, 2013 at 11:54 AM, Felipe Gonçalves Assis
> <felipe...@gmail.com> wrote:
>>

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>
>
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[.arpis.]

If, however, you take 0, 1, and 2 (on the same scale) as {na'e nelci}, then {da poi co'e zo'u mi nelci da} but {na ku da poi co'e zo'u do nelci da} (it is the case that I like exactly one of them, but it is not the case that you like exactly one of them), so exact quantifiers being scoped within abstraction make the statement true; exact quantifiers that take bridi scope make the statement false.

I found an English statement that has the right intuition: "For you more than for me, there exists exactly one of the two whom we like."

Since the way to express it in English requires explicitly scoping quantifiers (like one of aziz's examples), I think the weirdness lies in unintuitive quantifier scoping and not in quantifier exactness (as aziz mentioned).

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