A Simpler Quantifier Logic (blog article)

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selpahi

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Oct 7, 2016, 8:09:59 AM10/7/16
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In this article I will take a closer look at the quantifier logic
currently present in (post-xorlo) Lojban. I will identify logical
problems as well as practical disadvantages. Finally, I will offer a
solution that addresses both.

Not only is the current system both impractical and unintuitive, its
introduction also left behind one major logical flaw as Lojban made the
move from singular logic to plural logic.

Read on to find out what singular logic and plural logic are, how they
are related to xorlo, and why the current situation is not tenable.

https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/

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Oct 7, 2016, 12:27:20 PM10/7/16
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Em sexta-feira, 7 de outubro de 2016 15:09:59 UTC+3, selpa'i escreveu:
In this article I will take a closer look at the quantifier logic
currently present in (post-xorlo) Lojban. I will identify logical
problems as well as practical disadvantages. Finally, I will offer a
solution that addresses both.

Not only is the current system both impractical and unintuitive, its
introduction also left behind one major logical flaw as Lojban made the
move from singular logic to plural logic.

Read on to find out what singular logic and plural logic are, how they
are related to xorlo, and why the current situation is not tenable.

https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/

One thing is that it says that under singular logic "nobody is gathering" is impossible but why not use {selcmi}. That's of course beside the point of the article. That section is clearly called "singular meets plural", which some readers might forget about, though.

Phrasing {na ku su’oi jbopre na ku remna} might make the reader think whether the scope is affected by plural quantifiers or not (since {su'oi} is in the middle but later it's asserted that plural {re} and {ci} aren't affected by scope).

Also it'd be nice to explain one mysterious particle of class LE one day since it's (for obvious reasons) absent from the proposal in this article.


And singular/plural looks like an obsession with Pythagorean number, which rule the world. 
E.g. such quantifier as "various" in "People talk to each other in various languages" is roughly {so'i} and precisely based on {vrici} and non-distributive (or sometimes is distributive) but is a quantifiers that quantifies other predicates. Such quantifiers are unfortunately often forgotten.

Remo Dentato

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Oct 7, 2016, 12:34:01 PM10/7/16
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I've not be able to fully grok the articles but I really like this series of "Simpler".
I really look forward to see the one on "Morphology".

Remo

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John E Clifford

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Oct 7, 2016, 1:01:07 PM10/7/16
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It's been a while since I paid much attention to attempts to patch up otherwise improve this inherently flawed system, but the simplified connective system seems actually have done some useful work in that direction.  It has been even longer since I thought about xorl0, but if asked I would have said that it had both plural terms and plural quantifiers (though I would not have been surprised to learn that people were not using them consistently nor well).  Still, it is nice to see it all spelled out again, except, of course, for the forced positional attribution of distribution or collectivity.  Some words just aren't fixed that way ("carry" from the classic case going back to JCB) and so we still need an occasional device to mark which is to be used in a particular case -- one that attaches to particular argument slots. 


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Jorge Llambías

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Oct 7, 2016, 6:37:20 PM10/7/16
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On Fri, Oct 7, 2016 at 9:10 AM, selpahi <sel...@gmx.de> wrote:

https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/

Nice. I agree with most of it, although I'm not too sure yet what I think about ro and su'o becoming ro'oi and su'oi.

Have you thought about "su'e"? Presumably it should pattern with "ru'o", not with "ro'oi", so the su'o/su'e symmetry would be broken if su'o becomes su'oi.

Would "no" become "no'oi" as well? 

We should also have explicit definitions for me'i, za'u, da'a, so'a, so'e, etc since they all admit more than one pluralification, but I'm guessing they would all follow the "ru'o" pattern as well.

mu'o mi'e xorxes

And Rosta

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Oct 7, 2016, 8:23:18 PM10/7/16
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For me, this is Lojban's most valuable contribution to the world: the discovery of the practical necessity of plural logic. (It was xorxes's discovery, but wouldn't have happened without Lojban.)

I think a clearer example of the need for ru'o is "weighs 20 kg" -- ro'oi rock weighs 20kg must be false if there's more than one rock; ro'oi pa rock weighs 20kg gets the distrib reading; so ru'o rock weigh 20kg is needed for the collective or not-necessarily-distributive.

I do have one question, regarding the following:
"One last note about predicates not being defined clearly as distributive/non-distributive in xorlo; xorxes wanted lo to be absolutely non-committal with regards to distributivity, therefore, in his model, all predicates are left vague with regards to distributivity. In my proposed full plural logic, predicates are defined as distributive or non-distributive, so it is usually unnecessary to force distributivity via explicit universal quantification."
I take it that this is not held to be a necessary feature of full plural logic, but rather is held to be desirable so as to not have to force distributivity via quantification. And I take it also that by "predicates" you mean "argument places"? Each argument place is either distributive or collective? Would you not also want an "unspecified as regards distributivity"? And wouldn't this mean that where the xorxesian underspecification of distributivity would have one predicate with, say, three argument places, yours would have 2^3 or 3^3 predicates? This looks so untenable that I conclude I must be misunderstanding you.

--And.

Martin Bays

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Oct 8, 2016, 5:29:18 PM10/8/16
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* Friday, 2016-10-07 at 14:10 +0200 - selpahi <sel...@gmx.de>:

> https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/

Very nice.

One thing which might be worth mentioning: we shouldn't forget about
masses.

(Here, I mean 'masses' in the mereological sense: things which
can't be counted, as in "mass noun". I'm not talking about {gunma}.)

But working mereologically/{me}reologically, i.e. basing everything on
{me}, means we essentially get masses for free. e.g. {ru'o djacu poi
nenri lo kabri cu lenku} gets the expected meaning. And with your
proposed redefinition of numerical quantifiers, {za'u [no]} would work
as the existential quantifier.

.e'u nai ro pa me ro tadni poi sruri lo dinju cu ba se sruri za'u djacu
signature.asc

John E Clifford

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Oct 8, 2016, 5:45:15 PM10/8/16
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Well, mereology is strictly the logic of the part/whole relationship and turns out to be isomorphic to full-fledged plural quantification, so we get all that just by changing our spectacles.  (Indeed, set-theory and singular quantification raised as I was, I always thought of pq in mereological terms, with L-sets -- except occasionally, when I wanted an empty set, in terms of C-sets.)  We can reconstruct the goo and slice notion of mass but as derivative within the great semi-lattices the basic logic.  When the cop drives his Hummer into the protesters, he gets protester all over his wheels and windscreen, just "lo protester" (with a fairly strange node as referent). 



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selpahi

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Oct 9, 2016, 11:22:57 AM10/9/16
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On 08.10.2016 00:37, Jorge Llambías wrote:
> Have you thought about "su'e"? Presumably it should pattern with "ru'o",
> not with "ro'oi", so the su'o/su'e symmetry would be broken if su'o
> becomes su'oi.

What I really want is for the existential quantifier to become distinct
from the "at least n" operator. In my preferred version of cekitauj (the
cmavo swap dialects) the existential quantifier is spelled {su} and the
"at least" operator is spelled {su'o}. This split is not possible in
official Lojban, unfortunately, but it would keep the symmetry intact.

(There is also another problem it would deal with: for some reason some
people want {su'o} without a following number to be the same as {su'o
xo'e} rather than a guaranteed {su'o pa}. With a distinct {su} this
wouldn't be as much of a problem)

> Would "no" become "no'oi" as well?

Yes, I believe it must and should.

{no} should be {na ku su'oi} so that a claim like {no da jmaji} has the
proper strength.

> We should also have explicit definitions for me'i, za'u, da'a, so'a,
> so'e, etc since they all admit more than one pluralification, but I'm
> guessing they would all follow the "ru'o" pattern as well.

Yes.

{so'e jbopre cu banka'e lo .inglico} ("Most Lojbanists speak English")
cannot be expanded like a normal numerically quantified statement:

? su'oi da poi jbopre gi'e so'e mei cu banka'e lo .inglico
"Some xx that are Lojbanists and most in number speak English." [1]

Quantifiers like {so'e}, {so'a}, ..., so-called proportional
quantifiers, require there to be something they are proportional to. The
number of broda in e.g. {so'e broda cu brode} is compared to the number
of (all) broda that brode. "Out of all the Lojbanists, most of them
speak English."

So I would say that

ru'o da poi jbopre zo'u so'e de poi menre da cu banka'e lo .inglico
"All [the] Lojbanists taken together are such that most of them
speak English."

is a better (intermediate) expansion. (Getting rid of {so'e} entirely is
possible, but I'm too lazy to type it out. The proportion is >0.5)

But {me'i} and {za'u} can be considered prefixes. I had thought {me'i PA
da} would mean {su'oi da poi me'i PA mei}. A definition in terms of
{ru'o} would also be possible, but I'm not sure that it would be better.
It would mean allowing prefixes (like "<" and ">") to turn non-{ru'o}
numerical quantifiers into {ru'o}-type quantifiers, and this requires a
good justification.

~~~mi'e la solpa'i

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[1]: I don't think arguing that mei2 could save this expansion is all
that helpful.

selpahi

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Oct 9, 2016, 11:32:38 AM10/9/16
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The relationship between plural logic and mass nouns, specifically the
idea that mass nouns are just plurals, is something that I've been very
interested in recently. (and relatedly, the relationship between kinds
and plurals)

Chierchia (1998), for example, is a nice read.

I agree masses (mass nouns) should not be ignored, but I think the topic
of mass nouns is specific enough to be a topic unto itself, for a
different article, which maybe someone else would like to write? :)

~~~mi'e la solpa'i


selpahi

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Oct 9, 2016, 11:49:30 AM10/9/16
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On 08.10.2016 02:23, And Rosta wrote:
> I do have one question, regarding the following:
> "One last note about predicates not being defined clearly as
> distributive/non-distributive in xorlo; xorxes wanted lo to be
> absolutely non-committal with regards to distributivity, therefore, in
> his model, all predicates are left vague with regards to distributivity.
> In my proposed full plural logic, predicates are defined as distributive
> or non-distributive, so it is usually unnecessary to force
> distributivity via explicit universal quantification."
> I take it that this is not held to be a necessary feature of full plural
> logic, but rather is held to be desirable so as to not have to force
> distributivity via quantification. And I take it also that by
> "predicates" you mean "argument places"?

Yes. "Predicate" is a sloppy abbreviation, but it works as long as you
assume that the predicates under discussion are unary.

I don't think it's a *necessary* feature of all possible plural logics.
It is merely one that I currently favor.

> Each argument place is either
> distributive or collective? Would you not also want an "unspecified as
> regards distributivity"? And wouldn't this mean that where the xorxesian
> underspecification of distributivity would have one predicate with, say,
> three argument places, yours would have 2^3 or 3^3 predicates? This
> looks so untenable that I conclude I must be misunderstanding you.

This would indeed be untenable, but I do not believe that you need every
version of every predicate. For example, I believe that a distributive
{citka} is enough. Very often, a non-distributive version is either not
distinct from the distributive version, or includes some added meaning
of "doing it together while possibly some of them only watch" (things
like {kansi'u lo ka citka}). There is a lot more to be said here, but
I'd rather first hear any additional points from you.

Unspecified distributivity in an argument place is a form of ambiguity
at the definitional level of a predicate. It makes it very difficult to
ever answer "what does it mean to {broda}", because there are by
definition multiple potentially non-overlapping answers. (I cannot
possibly count the hours that went into discussing {bevri lo pipno} over
the years without ever getting to a conclusion. This sort of stuff is
hard to sort out!)

There are other ways (for example, in the realm of pragmatics) to deal
with vague distributivity, outside of the definition of argument places,
and I prefer those ways.

~~~mi'e la solpa'i





And Rosta

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Oct 9, 2016, 1:14:45 PM10/9/16
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On 9 Oct 2016 16:22, "selpahi" <sel...@gmx.de> wrote:
>  (Getting rid of {so'e} entirely is possible, but I'm too lazy to type it out. The proportion is >0.5)

"Most" works for proportions of groups of infinite cardinality, but does ">0.5"? Better is ">0.5 of any typical group of". I remember that we discussed this 15--20 years ago, but do not remember any outcome.

--And.

Jorge Llambías

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Oct 9, 2016, 8:08:38 PM10/9/16
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On Sun, Oct 9, 2016 at 12:23 PM, selpahi <sel...@gmx.de> wrote:

What I really want is for the existential quantifier to become distinct from the "at least n" operator. In my preferred version of cekitauj (the cmavo swap dialects) the existential quantifier is spelled {su} and the "at least" operator is spelled {su'o}. This split is not possible in official Lojban, unfortunately, but it would keep the symmetry intact.

That makes sense. One difference with the singular version is that plural "su'e" (and plural "me'i") will have existential import: "su'e re no tadni cu sruri lo dinju" with plural "su'ereno" would mean "there are some students, who are at most twenty, surrounding the building". 

How do we say the old singular "su'e mu broda cu brode" (which allows the possibility that "no broda cu brode") with the new system?
 

 
Would "no" become "no'oi" as well?

Yes, I believe it must and should.

And singular "no" is then "no pa", right?

 
{so'e jbopre cu banka'e lo .inglico} ("Most Lojbanists speak English") cannot be expanded like a normal numerically quantified statement:

   ? su'oi da poi jbopre gi'e so'e mei cu banka'e lo .inglico
     "Some xx that are Lojbanists and most in number speak English." [1]

Quantifiers like {so'e}, {so'a}, ..., so-called proportional quantifiers, require there to be something they are proportional to. The number of broda in e.g. {so'e broda cu brode} is compared to the number of (all) broda that brode. "Out of all the Lojbanists, most of them speak English."

So I would say that

   ru'o da poi jbopre zo'u so'e de poi menre da cu banka'e lo .inglico
   "All [the] Lojbanists taken together are such that most of them speak English."

is a better (intermediate) expansion. (Getting rid of {so'e} entirely is possible, but I'm too lazy to type it out. The proportion is >0.5)

I think the expansion should be:

 PA broda cu brode -> su'oi da poi PA mei lo broda cu brode

which I think would work for all the numeric quantifiers: [da'a][su'o|su'e|me'i|za'u|ji'i] n; so'V; du'e, mo'a, rau; and also for ru'o.

But {me'i} and {za'u} can be considered prefixes. I had thought {me'i PA da} would mean {su'oi da poi me'i PA mei}. A definition in terms of {ru'o} would also be possible, but I'm not sure that it would be better. It would mean allowing prefixes (like "<" and ">") to turn non-{ru'o} numerical quantifiers into {ru'o}-type quantifiers, and this requires a good justification.

What do you mean by non-ru'o numerical quantifiers? su'oi, ro'oi, no'oi, me'oi are non-ru'o, in the sense that they don't expand to a "su'oi da poi PA mei" form. (I don't even know what "PA mei" would mean for them.)

Jorge Llambías

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Oct 9, 2016, 8:36:21 PM10/9/16
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On Sun, Oct 9, 2016 at 12:49 PM, selpahi <sel...@gmx.de> wrote:
On 08.10.2016 02:23, And Rosta wrote:

Each argument place is either
distributive or collective? Would you not also want an "unspecified as
regards distributivity"? And wouldn't this mean that where the xorxesian
underspecification of distributivity would have one predicate with, say,
three argument places, yours would have 2^3 or 3^3 predicates? This
looks so untenable that I conclude I must be misunderstanding you.

This would indeed be untenable, but I do not believe that you need every version of every predicate. For example, I believe that a distributive {citka} is enough. Very often, a non-distributive version is either not distinct from the distributive version, or includes some added meaning of "doing it together while possibly some of them only watch" (things like {kansi'u lo ka citka}). There is a lot more to be said here, but I'd rather first hear any additional points from you.

I don't believe a distributive "citka" is all that useful. I want to be able to say "the children ate the whole cake" without having to introduce any roundabouts.

It's also a simplification to say that there are only two kinds of distributivity (fully distributive and fully collective). Those are just the two extremes. In many cases we can have partial distributivity. For example, I can say "the children took the chairs to the garden", when one of the children took one chair, another one took two, and two other children took one chair together. If you make "take" distributive, you make it hard to say something simple like "the children took the chairs to the garden" when you don't know or don't care about how the action was distributed among children and chairs. If you say you can use the collective version for that, then you can use it for everything, since in that case "non-distributive" doesn't really mean "all together at once". 
 
Unspecified distributivity in an argument place is a form of ambiguity at the definitional level of a predicate.

No, it's just a form of vagueness, where you don't specify what you don't want or need to specify.
 
It makes it very difficult to ever answer "what does it mean to {broda}", because there are by definition multiple potentially non-overlapping answers.

That's true with or without distributivity. Very few predicates can be defined so precisely that they won't admit of multiple potentially non-overlapping definitions.

(I cannot possibly count the hours that went into discussing {bevri lo pipno} over the years without ever getting to a conclusion. This sort of stuff is hard to sort out!)

But don't we already know what it means? At least to the extent that we can use it without creating any kind of confusion? Why wouldn't a definition similar to "support and move (someone or something) from one place to another." work?

There are other ways (for example, in the realm of pragmatics) to deal with vague distributivity, outside of the definition of argument places, and I prefer those ways.

I'm not too sure how stringent you want to be with defining distributivity into all predicate places. For some places it's reasonable that it be part of the definition of the predicate ("pavmei" might be an example). For other predicates, I don't see how forcing a fixed distributivity helps, since there are things that can just as well be done separately or together.

And Rosta

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Oct 10, 2016, 9:16:54 AM10/10/16
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On 9 Oct 2016 16:49, "selpahi" <sel...@gmx.de> wrote:
>
> On 08.10.2016 02:23, And Rosta wrote:
>>
>> Each argument place is either
>> distributive or collective? Would you not also want an "unspecified as
>> regards distributivity"? And wouldn't this mean that where the xorxesian
>> underspecification of distributivity would have one predicate with, say,
>> three argument places, yours would have 2^3 or 3^3 predicates? This
>> looks so untenable that I conclude I must be misunderstanding you.
>
>
> This would indeed be untenable, but I do not believe that you need every version of every predicate. For example, I believe that a distributive {citka} is enough. Very often, a non-distributive version is either not distinct from the distributive version, or includes some added meaning of "doing it together while possibly some of them only watch" (things like {kansi'u lo ka citka}). There is a lot more to be said here, but I'd rather first hear any additional points from you.

My view is the same as xorxes's (thanks to my long ago having been persuaded by his insights on this point, as on so many others). "The guests have eaten all the sausages" is not (fully) distributive and judgements of whether a given predicate, such as "eat all the sausages", can be fully collective, or fully distributive, or intermediate, are more a matter of pragmatics than of formal semasiology.

So I think the better way to handle this linguistically is to have ways to explicitly encode full collectivity ("plurality X but not necessarily any subplurality of X" = ru'o) and full distributivity ("every single X but not necessarily any plurality of them" = ro('oi) pa), without fretting about their truth-conditions with any given predicate.

--And.

selpahi

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Oct 10, 2016, 2:45:38 PM10/10/16
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On 10.10.2016 02:08, Jorge Llambías wrote:
> On Sun, Oct 9, 2016 at 12:23 PM, selpahi <sel...@gmx.de
> <mailto:sel...@gmx.de>> wrote:
>
>
> What I really want is for the existential quantifier to become
> distinct from the "at least n" operator. In my preferred version of
> cekitauj (the cmavo swap dialects) the existential quantifier is
> spelled {su} and the "at least" operator is spelled {su'o}. This
> split is not possible in official Lojban, unfortunately, but it
> would keep the symmetry intact.
>
>
> That makes sense. One difference with the singular version is that
> plural "su'e" (and plural "me'i") will have existential import: "su'e re
> no tadni cu sruri lo dinju" with plural "su'ereno" would mean "there are
> some students, who are at most twenty, surrounding the building".
>
> How do we say the old singular "su'e mu broda cu brode" (which allows
> the possibility that "no broda cu brode") with the new system?

How about {na ku za'u mu broda cu brode}?

(And when existential import isn't a problem, {ru'o broda cu su'e mu
mei} (or {lo broda cu su'e mu mei}) are options).

> Would "no" become "no'oi" as well?
>
> Yes, I believe it must and should.
>
>
> And singular "no" is then "no pa", right?

Yes, I would say so.

> So I would say that
>
> ru'o da poi jbopre zo'u so'e de poi menre da cu banka'e lo .inglico
> "All [the] Lojbanists taken together are such that most of them
> speak English."
>
> is a better (intermediate) expansion. (Getting rid of {so'e}
> entirely is possible, but I'm too lazy to type it out. The
> proportion is >0.5)
>
>
> I think the expansion should be:
>
> PA broda cu brode -> su'oi da poi PA mei lo broda cu brode
>
> which I think would work for all the numeric quantifiers:
> [da'a][su'o|su'e|me'i|za'u|ji'i] n; so'V; du'e, mo'a, rau; and also for
> ru'o.

This seems to be pretty much the same as the {ru'o} expansion.

But I think it's only equivalent if you subscribe to {lo}'s maximality.
(It wouldn't be the first expansion that presupposes maximality even
though we never decided that {lo} must have maximality)

So, I take it, you do subscribe to maximality? (I do)

> But {me'i} and {za'u} can be considered prefixes. I had thought
> {me'i PA da} would mean {su'oi da poi me'i PA mei}. A definition in
> terms of {ru'o} would also be possible, but I'm not sure that it
> would be better. It would mean allowing prefixes (like "<" and ">")
> to turn non-{ru'o} numerical quantifiers into {ru'o}-type
> quantifiers, and this requires a good justification.
>
>
> What do you mean by non-ru'o numerical quantifiers? su'oi, ro'oi, no'oi,
> me'oi are non-ru'o, in the sense that they don't expand to a "su'oi da
> poi PA mei" form. (I don't even know what "PA mei" would mean for them.)

Sorry if I wasn't clear. I meant "non-{ru'o}" in a {noi} way. All
numerical quantifiers are of the non-{ru'o} type. Your prefixes turn
them into {ru'o} types.

~~~mi'e la solpa'i


Jorge Llambías

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Oct 10, 2016, 4:04:07 PM10/10/16
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On Mon, Oct 10, 2016 at 3:45 PM, selpahi <sel...@gmx.de> wrote:
On 10.10.2016 02:08, Jorge Llambías wrote:

        Would "no" become "no'oi" as well?

    Yes, I believe it must and should.

And singular "no" is then "no pa", right?

Yes, I would say so.

I don't know if it's a good idea to use the same word for the digit "0" and the (plural) quantifier "~E". 

It could be confusing that "no pa no" is "no ten" rather than "010".
 

I think the expansion should be:

 PA broda cu brode -> su'oi da poi PA mei lo broda cu brode

which I think would work for all the numeric quantifiers:
[da'a][su'o|su'e|me'i|za'u|ji'i] n; so'V; du'e, mo'a, rau; and also for
ru'o.

This seems to be pretty much the same as the {ru'o} expansion.

But I think it's only equivalent if you subscribe to {lo}'s maximality. (It wouldn't be the first expansion that presupposes maximality even though we never decided that {lo} must have maximality)

So, I take it, you do subscribe to maximality? (I do)

I subscribe to a version of it where generic is maximal. I think for example that "ro (pa) lo smani pu citka lo badna" makes perfect sense for "each (one) of the monkeys ate bananas".

In any case, the definition could be changed to "su'oi da poi PA mei ru'o broda cu brode" if that's an issue.
  
    But {me'i} and {za'u} can be considered prefixes. I had thought
    {me'i PA da} would mean {su'oi da poi me'i PA mei}. A definition in
    terms of {ru'o} would also be possible, but I'm not sure that it
    would be better. It would mean allowing prefixes (like "<" and ">")
    to turn non-{ru'o} numerical quantifiers into {ru'o}-type
    quantifiers, and this requires a good justification.

What do you mean by non-ru'o numerical quantifiers? su'oi, ro'oi, no'oi,
me'oi are non-ru'o, in the sense that they don't expand to a "su'oi da
poi PA mei" form. (I don't even know what "PA mei" would mean for them.)

Sorry if I wasn't clear. I meant "non-{ru'o}" in a {noi} way. All numerical quantifiers are of the non-{ru'o} type. Your prefixes turn them into {ru'o} types.

I meant that all numerical quantifiers work with the same expansion whether or not they contain the prefixes da'a/su'o/su'e/me'i/za'u/ji'i. They are all ru'o-types.

selpahi

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Oct 10, 2016, 4:15:38 PM10/10/16
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On 10.10.2016 02:36, Jorge Llambías wrote:
> I don't believe a distributive "citka" is all that useful. I want to be
> able to say "the children ate the whole cake" without having to
> introduce any roundabouts.

Of course. But I believe that a distributive {citka} does not prohibit this.

> It's also a simplification to say that there are only two kinds of
> distributivity (fully distributive and fully collective). Those are just
> the two extremes.

Yes. I'm not saying there are only two kinds of distributivity (I will
go into more detail below), but I'm saying that it's possible to group
predicates into one of only two categories and deal with intermediate
distributivity via other means.

> Unspecified distributivity in an argument place is a form of
> ambiguity at the definitional level of a predicate.
>
>
> No, it's just a form of vagueness, where you don't specify what you
> don't want or need to specify.

Let us look at some of the many possible meanings of a simple quantified
statement in English, say, "At least three people carried a chair":

1) At least three people are such that each of them carried a chair.
2) At least three people are such that each of them was involved in
carrying a chair.
3) Some people that are at least three moved a piano together.

Would you say that all of these describe the same relationship or
different relationships?

Or your "eating cake" example, would you say that each different reading
is a different meaning of "eat"?

The way I see it, each reading has at its core the same base predicate,
"x1 eats x2", which is a simple relation of one thing eating another
thing. Everything else is built on top of this basic meaning, but the
meaning of {citka} itself does not change in the process.

On the other hand, if you say {citka} means all sorts of things from the
get-go, then you start with ambiguity (or call it vagueness) and then
build additional vagueness on top as you create full statements. (Please
don't understand me as trying to get rid of fuzziness; no matter how
precise a definition is, there is always fuzziness, and there is nothing
wrong with that.)

I mentioned above that there are other means by which intermediate
distributivity can be achieved, and by which "the children ate the cake"
is acceptable even with a distributive "eat".

One such approach is one that we use in other areas of Lojban (or any
language) as well, and that is the idea of pragmatic slack. In certain
contexts and situations, sentences that are false when taken literally
can still be considered true at the level of detail that is currently
relevant. We don't care if really every single one of the things ate
cake, because it isn't relevant to our specific situation. Similarly, we
don't mind if someone says "I woke up at nine" when really they woke up
a few minutes after nine. Nevertheless, the meaning of "wake up at nine"
is not changed, nor is the meaning of "ate cake" changed.
(Lasersohn (1999) discusses this in great detail)

Another approach is to use the concept of a "cover" to account for
intermediate distributivity. A cover of a set is a set of subsets such
that each element of the original set is included in at least one of the
subsets. When a distributive claim is made, this is done via a universal
quantifier (which we do implicitly when the predicate place is
distributive), but instead of applying to 'all of the things', it only
quantifies universally over those of the things that are part of the
cover. The cover allows for certain individuals to drop out of the
picture. The predicate remains distributive with this approach, too.
(Schwarzschild (1996) and Brisson (1998) use this approach)

And additionally, when it is important, words like {kansi'u} exist (and
I have proposed that a bunch of similar words could exist that express
related forms of "doing something together", depending on the nature of
the togetherness (e.g. just being in the same place as some of them eat,
helping each other so that some of them eat, and so on). These are not
necessarily roundabout, and you would only use them when you think it
matters.

So all in all, you may say it doesn't matter which approach we use as
long as you

> can say "the children took the chairs to the garden" when you don't
know or don't care about how the action was distributed among children
and chairs.

But it makes a difference to me, because in one case we throw our hands
in the air about the meaning of a predicate, and in the other case we
can decide what it means on a fundamental level.

> There are other ways (for example, in the realm of pragmatics) to
> deal with vague distributivity, outside of the definition of
> argument places, and I prefer those ways.
>
>
> I'm not too sure how stringent you want to be with defining
> distributivity into all predicate places. For some places it's
> reasonable that it be part of the definition of the predicate ("pavmei"
> might be an example).

{pavmei} cannot be distributive. It is only true of things that are one
in number. {[su'oi] re da pavmei} is false. If you meant its
distributivity type must be non-distributive, then yes.

There are many predicates that only make sense non-distributively.

There are also many predicates that are fundamentally distributive, and
where making them non-distributive only adds vagueness.

> For other predicates, I don't see how forcing a
> fixed distributivity helps, since there are things that can just as well
> be done separately or together.

It helps pin down the fundamental meaning of a predicate.

But it makes me wonder. Is it really such a crazy idea for Lojban to
have different words for rather different kinds of carrying even though
English only has one? Let's not forget that Lojban is also a way to
experience new ways of thinking about situations. We split English words
into multiple distinct brivla all the time, why shouldn't we here? It
would be interesting.

Jorge Llambías

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Oct 10, 2016, 5:16:03 PM10/10/16
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On Mon, Oct 10, 2016 at 5:15 PM, selpahi <sel...@gmx.de> wrote:
On 10.10.2016 02:36, Jorge Llambías wrote:
I don't believe a distributive "citka" is all that useful. I want to be
able to say "the children ate the whole cake" without having to
introduce any roundabouts.

Of course. But I believe that a distributive {citka} does not prohibit this.

A place is distributive when "ko'a broda" necessarily entails "ro (pa) ko'a broda".

"lo verba pu citka pi ro lo titnanba" should not entail "ro (pa) lo verba pu citka pi ro lo titnanba", but if citka1 was distributive, it would.
 


Let us look at some of the many possible meanings of a simple quantified statement in English, say, "At least three people carried a chair":

1) At least three people are such that each of them carried a chair.
2) At least three people are such that each of them was involved in carrying a chair.
3) Some people that are at least three moved a piano together.

Would you say that all of these describe the same relationship or different relationships?

They are all different situations, all describable by the original sentence, which is not as specific as the more specific (1), (2) and (3). 
 
Or your "eating cake" example, would you say that each different reading is a different meaning of "eat"?

No, that's my point, "eat" can describe many different situations, which you can distinguish by adding more words.
 

I mentioned above that there are other means by which intermediate distributivity can be achieved, and by which "the children ate the cake" is acceptable even with a distributive "eat".

One such approach is one that we use in other areas of Lojban (or any language) as well, and that is the idea of pragmatic slack. In certain contexts and situations, sentences that are false when taken literally can still be considered true at the level of detail that is currently relevant. We don't care if really every single one of the things ate cake, because it isn't relevant to our specific situation.

But that's not the issue here. Even if every single one of them ate cake, it is false that any one of them ate the whole cake, let alone each one of them. Distributivity would require that every one of them ate the *whole* cake.

Similarly, we don't mind if someone says "I woke up at nine" when really they woke up a few minutes after nine. Nevertheless, the meaning of "wake up at nine" is not changed, nor is the meaning of "ate cake" changed.
(Lasersohn (1999) discusses this in great detail)

I'm not talking about "eat cake", I'm talking about "eat the whole cake". I have no problem with saying that "eat cake" is distributive. But "eat the whole cake" is not even close to being distributive.

 
And additionally, when it is important, words like {kansi'u} exist (and I have proposed that a bunch of similar words could exist that express related forms of "doing something together", depending on the nature of the togetherness (e.g. just being in the same place as some of them eat, helping each other so that some of them eat, and so on). These are not necessarily roundabout, and you would only use them when you think it matters.

Definitely.  

So all in all, you may say it doesn't matter which approach we use as long as you

> can say "the children took the chairs to the garden" when you don't know or don't care about how the action was distributed among children and chairs.

But it makes a difference to me, because in one case we throw our hands in the air about the meaning of a predicate, and in the other case we can decide what it means on a fundamental level.

I'm still not sure what you have in mind. If you tell me that citka1 is distributive, then "lo so'i verba pu citka pi ro lo titnanba" sounds like nonsense to me, because a distributive citka1 would entail "ro (pa) lo so'i verba pu citka pi ro lo titnanba".

 For some places it's
reasonable that it be part of the definition of the predicate ("pavmei"
might be an example).

{pavmei} cannot be distributive. It is only true of things that are one in number. {[su'oi] re da pavmei} is false. If you meant its distributivity type must be non-distributive, then yes.

I assumed you were using "pavmei" to mean "x1 is/are individuals", as opposed to "pa mei", "x1 are one".

The first one would have to be distributive: "lo so'i prenu cu pavmei" would be true and it entails "ro pa lo so'i prenu cu pavmei": "the many people are individuals" entails "each one of the many people is an individual".

The second one is necessarily non-distributive (like all "PA mei" predicates). "lo so'i prenu cu pa mei" would mean that the many people are one, which would be false, since they are many. (We can leave for another day "the many people are one nation" and things like that.)
 

There are many predicates that only make sense non-distributively.

Yes. "simxu" to take a common example. 

There are also many predicates that are fundamentally distributive, and where making them non-distributive only adds vagueness.

My understanding of "pavmei" (meaning "individual") would be one of them, but maybe you were using "pavmei" to mean something else. I don't believe "citka" is a good example of fundamentally distributive, since it's easy to come up with clearly non-distributive examples, such as "they ate the whole cake". 

But it makes me wonder. Is it really such a crazy idea for Lojban to have different words for rather different kinds of carrying even though English only has one? Let's not forget that Lojban is also a way to experience new ways of thinking about situations. We split English words into multiple distinct brivla all the time, why shouldn't we here? It would be interesting.

I don't mind introducing overly specific predicates, as long as we don't lose the more general ones so that we can still say simple things in simple ways. 

Pierre Abbat

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Oct 23, 2016, 9:06:30 PM10/23/16
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On Monday, October 10, 2016 5:03:16 PM EDT Jorge Llambías wrote:
> On Mon, Oct 10, 2016 at 3:45 PM, selpahi <sel...@gmx.de> wrote:
> > On 10.10.2016 02:08, Jorge Llambías wrote:
> >> And singular "no" is then "no pa", right?
> >
> > Yes, I would say so.
>
> I don't know if it's a good idea to use the same word for the digit "0" and
> the (plural) quantifier "~E".
>
> It could be confusing that "no pa no" is "no ten" rather than "010".

"no pa" is equal to "pa". Do you mean "no boi pa"?

Pierre
--
li ze te'a ci vu'u ci bi'e te'a mu du
li ci su'i ze te'a mu bi'e vu'u ci

Jorge Llambías

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Oct 23, 2016, 9:18:57 PM10/23/16
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On Sun, Oct 23, 2016 at 10:06 PM, Pierre Abbat <ph...@bezitopo.org> wrote:
On Monday, October 10, 2016 5:03:16 PM EDT Jorge Llambías wrote:
> On Mon, Oct 10, 2016 at 3:45 PM, selpahi <sel...@gmx.de> wrote:
> > On 10.10.2016 02:08, Jorge Llambías wrote:
> >> And singular "no" is then "no pa", right?
> >
> > Yes, I would say so.
>
> I don't know if it's a good idea to use the same word for the digit "0" and
> the (plural) quantifier "~E".
>
> It could be confusing that "no pa no" is "no ten" rather than "010".

"no pa" is equal to "pa". Do you mean "no boi pa"?

No, I did mean "no'oi pa" which would become "no pa" if "no'oi" was replaced by "no".

Vincent Broman

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Jun 10, 2021, 8:14:18 PMJun 10
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After re-reading la selpahi's excellent article on plural quantification, I became curious how much of a problem there was with collective or non-distributive sumti places.
Does that just come up with jmaji, simxu, and a few others, or is it pervasive?
So I went thru the whole gimste and decided which places seemed non-distributive and found 143, listed in the attachment.
As I think PC pointed out, there were a good number of cases where usage might go either way depending on context.
All the "under conditions" places might qualify, except I don't understand the meaning of that, yet.

Any one take a similar look at what places distribute?

mihe la bremenli
gismu-non-distributive.txt

gleki.is...@gmail.com

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Jun 12, 2021, 9:03:37 AMJun 12
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tilju1 is non-distrubutive? why? because of this ambiguous notion of "mass" or what?
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