Individuals and xorlo

[Dan Rosén]

Dear selmriste,

It seems that using xorlo prevents explicitly talking about indivduals, such as
/one elephant/, a seemingly simple concept. Let's start with an inner quantifier:

    lo pa xanto = zo'e noi ke'a xanto gi'e zilkancu li pa lo xanto,

However, the latter {lo xanto} in zilkancu3 can denote about a group of
elephants, so {lo pa xanto} can indeed be many elephants.  Outer quantifiers
will not help, as they will only range over the inner object.

Using zo'e directly is obviously fruitless since xorlo seems to influence how
both zo'e, and how noi work: together they remove our abilities to explicitly
talk about individuals. This make me assume that it also affects the
da-family, so {pa xanto} is also out of the question.

Finally, any brivla will not help us here as the dreaded lo-zo'e-noi-trinity
will always be able to sneak in a group where we want an individual. For
instance in {lo pa kantu be lo pa xanto}, or {lo xantyka'u}, we still might end
up with a onesome of elephants.

Why was it decided to make it like this?  It seems that a monolingual jbopre
would not /really/ be able to differentiate an elephant from its flock.
(But perhaps not if we were talking about sheep, but I digress)

Hopefully I have misunderstood everything. If this is so, please enlighten me.

ki'e mi'e la danr

[Felipe Gonçalves Assis]

Here is a way if recovering the concept of an individual elephant just from the concepts of elephants and parthood:
A xanto pamei is something that is xanto and that can't be divided in two things such that each one is xanto.

I would express a counting unit with a property:
{lo pa xanto cu zilkancu li pa lo ka xanto}

mu'o
mi'e .asiz.

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[Jorge Llambías]

On Mon, Feb 3, 2014 at 8:36 PM, Dan Rosén <lur...@gmail.com> wrote:

It seems that using xorlo prevents explicitly talking about indivduals, such as
/one elephant/, a seemingly simple concept. Let's start with an inner quantifier:

    lo pa xanto = zo'e noi ke'a xanto gi'e zilkancu li pa lo xanto,

However, the latter {lo xanto} in zilkancu3 can denote about a group of
elephants, so {lo pa xanto} can indeed be many elephants.  Outer quantifiers
will not help, as they will only range over the inner object.

"lo pa xanto" can only be a single elephant: the elephant in front of you, the African elephant, the elephant being digested by a boa constrictor in Saint-Exupery's drawing, etc. but it always has to be one. It cannot be a group of elephants in front of you, all African elephants, the millions of elephants being digested by boa constrictors in the millions of reproductions of that picture, etc.

Sometimes you can make the same claims about the African elephant that you can make about all African elephants, or about the elephant inside the boa and about all the elephants inside all those boas, or even perhaps about the elephant in front of you and a group of elephants in front of you, but that doesn't mean that linguistically they are the same object.

mu'o mi'e xorxes 

[Jorge Llambías]

On Mon, Feb 3, 2014 at 9:14 PM, Felipe Gonçalves Assis <felipe...@gmail.com> wrote:

Here is a way if recovering the concept of an individual elephant just from the concepts of elephants and parthood:
A xanto pamei is something that is xanto and that can't be divided in two things such that each one is xanto.

That may (perhaps) work for xanto, but it won't work for djacu. or even worse, for kurfa. 

[Felipe Gonçalves Assis]

I was pretty sure I was missing something, yes.

With {djacu}, that doesn't create any issues in defining what can be {lo pa djacu}, but with {kurfa}, that means that the concept of kurfa pamei precedes that of kurfa, right? I guess this is what troubles danr.

[Dan Rosén]

Thank you xorxes and .asiz

"lo pa xanto" can only be a single elephant: the elephant in front of you, the African elephant, the elephant being digested by a boa constrictor in Saint-Exupery's drawing, etc. but it always has to be one. It cannot be a group of elephants in front of you, all African elephants, the millions of elephants being digested by boa constrictors in the millions of reproductions of that picture, etc.

I'm using the expansions suggested in http://www.lojban.org/tiki/BPFK+Section:+gadri, where

    lo pa xanto = zo'e noi ke'a xanto gi'e zilkancu li pa lo xanto,

but {lo xanto} can be plural, so this removes the effect of the zilkancu part. Is it that I misunderstand this equation, or is it just false?

.asiz suggested:

    {lo pa xanto cu zilkancu li pa lo ka xanto},

This might have been better, but the other examples do not use a ka-abstraction in zilkancu3, so zilkancu1 in {zilkancu li pa lo ka xanto}, would seem to be to be a property, not an elephant.

[Felipe Gonçalves Assis]

On 4 February 2014 16:31, Dan Rosén <lur...@gmail.com> wrote:

    lo pa xanto = zo'e noi ke'a xanto gi'e zilkancu li pa lo xanto,

but {lo xanto} can be plural, so this removes the effect of the zilkancu part. Is it that I misunderstand this equation, or is it just false?

I don't have much to say. I can't make sense of this equation, and disregard it.

Let me just note that making xanto singular wouldn't help me either: Which elephant in the world could possibly be a unit for counting elephants?

[Dan Rosén]

Let me just note that making xanto singular wouldn't help me either: Which elephant in the world could possibly be a unit for counting elephants?

Ha, good point! ki'e

[Jorge Llambías]

If you don't think that the elephant is a good unit for counting elephants, you could say "lo gradu be fi lo ka xanto", or, as you said, redefine "kancu" so that it takes a tergradu instead of a gradu in x4.

Do you have the same qualms with "lo mitre" or "lo snidu" to refer to units? What would you fill the x1 of gradu with?

[Jorge Llambías]

On Tue, Feb 4, 2014 at 3:31 PM, Dan Rosén <lur...@gmail.com> wrote:

I'm using the expansions suggested in http://www.lojban.org/tiki/BPFK+Section:+gadri, where

    lo pa xanto = zo'e noi ke'a xanto gi'e zilkancu li pa lo xanto,

but {lo xanto} can be plural, so this removes the effect of the zilkancu part. Is it that I misunderstand this equation, or is it just false?

I don't think it's quite right to say that "lo xanto" can be plural, because Lojban doesn't have grammatical number, so it can't strictly be singular or plural. But a natural translation of "lo xanto" in this context would indeed be plural in English, something like "is 1 counting in elephants".

[Felipe Gonçalves Assis]

On 4 February 2014 20:50, Jorge Llambías <jjlla...@gmail.com> wrote:

On Tue, Feb 4, 2014 at 6:25 PM, Felipe Gonçalves Assis <felipe...@gmail.com> wrote:

Let me just note that making xanto singular wouldn't help me either: Which elephant in the world could possibly be a unit for counting elephants?

If you don't think that the elephant is a good unit for counting elephants, you could say "lo gradu be fi lo ka xanto", or, as you said, redefine "kancu" so that it takes a tergradu instead of a gradu in x4.

I am sorry, maybe you can expand on your understanding of {gradu}?

The best I could come up with for using {gradu} is, e.g.,

  {ko'a gradu lo si'o mitre} <=> {ko'a mitre li pa}

  {gradu ko'e ko'i} <=> {ko'e ckilu ko'i}

with, e.g,

  {lo si'o mitre cu ckilu lo ka ma kau ni ce'u clani}

 

Do you have the same qualms with "lo mitre" or "lo snidu" to refer to units? What would you fill the x1 of gradu with?

As exposed, I would indeed fill the x1 of {gradu} with {lo mitre} and {lo snidu}, but to me these are references to things that are one meter and one second long, respectively. They are concrete stuff. A standard of measurement would be a se gradu or a ckilu.

[Jorge Llambías]

On Tue, Feb 4, 2014 at 8:24 PM, Felipe Gonçalves Assis <felipe...@gmail.com> wrote:

I am sorry, maybe you can expand on your understanding of {gradu}?

My personal "definition" of gradu is this:

...

milti

centi

decti 

gradu

dekto

xecto

kilto

...

same type of place structure for all of them. 

The best I could come up with for using {gradu} is, e.g.,

  {ko'a gradu lo si'o mitre} <=> {ko'a mitre li pa}

  {gradu ko'e ko'i} <=> {ko'e ckilu ko'i}

with, e.g,

  {lo si'o mitre cu ckilu lo ka ma kau ni ce'u clani}

I never really understood the connection of "si'o" with scales. 

[Felipe Gonçalves Assis]

On 4 February 2014 21:49, Jorge Llambías <jjlla...@gmail.com> wrote:

On Tue, Feb 4, 2014 at 8:24 PM, Felipe Gonçalves Assis <felipe...@gmail.com> wrote:

I am sorry, maybe you can expand on your understanding of {gradu}?

My personal "definition" of gradu is this:

...

milti

centi

decti 

gradu

dekto

xecto

kilto

...

same type of place structure for all of them. 

How would you contrast {gradu} and {dunli}?

 

The best I could come up with for using {gradu} is, e.g.,

  {ko'a gradu lo si'o mitre} <=> {ko'a mitre li pa}

  {gradu ko'e ko'i} <=> {ko'e ckilu ko'i}

with, e.g,

  {lo si'o mitre cu ckilu lo ka ma kau ni ce'u clani}

I never really understood the connection of "si'o" with scales. 

I am just using {si'o} as a generic relationship abstraction here. I guess it would be

{lo ka ce'u mitre ma kau}.

[Jorge Llambías]

On Tue, Feb 4, 2014 at 9:02 PM, Felipe Gonçalves Assis <felipe...@gmail.com> wrote:

How would you contrast {gradu} and {dunli}?

I think "mi dunli do lo ka ce'u citka ma kau" is normal, whereas "mi gradu do ..." is bizarre.

[Felipe Gonçalves Assis]

Sure! va'i {gradu} is about scales stricto sensu.

Well, as to how this affects the previous exchange, using your definition of {gradu}, I would say that a standard of measurement could be a ka gradu.

[Gleki Arxokuna]

Sorry for intruding. I need to explain this in simple words for a future lojban tutorial.

So 

{zo'e} denotes an individual/individuals.

{lo najgenja} = carrot/carrots

{ci lo najgenja cu grake li 60} = {ci zo'e noi najgenja cu grake li 60} - describes carrots. Three of carrots are 60 grams each.

Now I postulate an axiom that {[su'o] lo pa najgenja} describes one carrot (I'll avoid formulae here since i need it for a tutorial, not for a reference grammar).

{ro lo ci najgenja} describes each of the three carrots.

Two important conclusions:

1. {ro lo ci najgenja cu grake li 60} - one carrot is always 60 grams in weight.

2. {ro loi ci najgenja cu grake li 60} = {ro zo'e noi gunma lo ci najgenja cu grake li 60} - describes masses (again of carrots but carrots here are of less importance since carrots are hidden inside gunma2). Each mass of carrots (with three carrots in each mass) is 60 grams so each carrots weighs 20 grams on average.

Is my reasoning correct?

I remember someone saying that {lo} is more vague and might include masses as well but here {loi} and it's underlying {gunma} move carrots higher. Can we accept raising here? If yes then all this reasoning immediately breaks.

--

[selpa'i]

la .xorxes. cu cusku di'e

> {lo si'o mitre cu ckilu lo ka ma kau ni ce'u clani}
>
> I never really understood the connection of "si'o" with scales.

Me neither. I don't understand how it makes sense, as it's very
difficult to interact with a {si'o} systematically. I use {ka} instead,
sometimes with two {ce'u}, although I find the {ce'u ma kau} way just as
intuitive, for example in klani3:

lo vi rokci cu klani li mu lo ka ce'u ki'ogra ce'u/ma kau

which means the same as

lo vi rokci cu ki'ogra li mu

How to use {klani} with predicates that don't have an obvious
input-output pair is another question. Here, {kau} seems to be more
convenient as the output marker than a second {ce'u}, say:

mi klani li ci lo ka ce'u citka xo kau plise
"I measure three in how many apples I ate."

Probably the more difficult challenge is to find a situation where klani
is actually the more practical (or the only practical) option. Maybe {ni}:

li vo ni mi bajysru lo foldi [kei lo ka ce'u xo kau roi fasnu]
"Four is the quantity of my running around the the field, [measured
in how many times it happened]"

But then, that's still only a complicated way of saying:

mi vo roi bajysru lo foldi

So... the challenge stands.

Though maybe the advantage lies in the vagueness of klani3-less
{klani}-usage. I'm really not sure.

mi'e la selpa'i mu'o

[selpa'i]

la .xorxes. cu cusku di'e

If I may, Dan is asking why the unit {lo xanto} cannot be (implicitly)
{lo ci xanto}, in which case three elephants would be counted as one
counting off by threes. Using a property in zilkancu3 would probably be
clearer for that reason. As it stands, some people seem to think that
the zilkancu3 unit contains a context-dependent inner quantifier, thus
counting of by {xo'e mei}. I don't think that's the intended meaning, so
it should be stated clearly that we're dealing with singletons.

[selpa'i]

la .dan. cu cusku di'e

> Using zo'e directly is obviously fruitless since xorlo seems to
> influence how both zo'e, and how noi work: together they remove our abilities to
> explicitly talk about individuals.

I don't think {noi} changed at all. {zo'e} allows plural reference, but
that isn't new either.

> This make me assume that it also affects the
> da-family, so {pa xanto} is also out of the question.

This comes down to whether or not {da} allows for plural variables.
Since plural reference is so common in Lojban, it would make sense for
{da} to also allow plural variables, but singular variables also have
advantages.

Imagine {za'a lo ci xanto cu va cadzu} to set the context. Now, it all
depends on on {da}'s plurality what {da va cadzu} can mean. Clearly, we
just saw that {lo ci xanto} is a cadzu1, so it should be a possible
value for the {da}. The downside to this is that with plural variables,
the one X in {pa lo ci xanto} could be all three elephants (although a
distributive handling of {me}'s x1 could fix that, or in other words, by
saying that {mi'o na me mi'o}), whereas singular variables could only
pick out an individual elephant from {lo ci xanto}.

So singular variables are simpler and avoid certain problems, like the
{pa xanto} one. On the other hand, it would mean that we can't say {da
simxu lo ka prami} for "There are some X who love each other", and we'd
have to use more complicated mechanisms for that, like {da poi su'o mei
cu simxu lo ka prami} (which isn't *that* bad).

Personally I would be all but opposed to the idea of having plural
variables to along with the plural reference while keeping the
simplicity of singular quantification, but I probably can't have my cake
and eat it, too. I would not want two sets of quantifers, for eaxmple.
Another idea would be to have each selbri place decide if it's
distributive or not, but I'm not sure I like that very much. So the more
practical solution right now seems to be to stick with singular
variables, even though it breaks the {simxu} example above and can
sometimes be counter-intuitive in a language full of plural reference.

[John E Clifford]

It seems that the constantly evolving xorlo (now moving far from 'lo' -- and probably from xorxes as well) has gotten itself into yet another jam, presumably from trying to do too much again.  I suspect that what is needed is to go back to basics and get that clear once more and then move ahead cautiously.  So, the basic 'lo broda' is "the salient node of the upward semilattice of jest on the set assigned to 'broda'" (some set of brodas and broda parts -- whatever that may mean for a particular kind of thing as broda).  'lo', unlike 'loi' says nothing about how the set involved is connected to the predicates involved (collective or distributive).  Variables range over L-sets or are plural, depending on your mathematical theology.  Etc.  do we need to fill in all the details and, if not, which ones?

---

From: selpa'i <sel...@gmx.de>
To: loj...@googlegroups.com
Sent: Wednesday, February 5, 2014 10:49 AM
Subject: Re: [lojban] Individuals and xorlo

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[selpa'i]

la .pycyn. cu cusku di'e

> It seems that the constantly evolving xorlo (now moving far from 'lo' --
> and probably from xorxes as well)

I don't think so. It's just that some questions that often get asked
about xorlo are actually more general than xorlo. Nothing is changing
about xorlo either, it's just that when new people come around, they
find a mess of underdocumented and scattered definitions and need to ask
the same (or similar) questions each time again. This will only stop
once there is a more complete specification that one can point someone
to instead of having to re-open a discussion about xorlo.

> So, the basic 'lo broda' is "the salient node of
> the upward semilattice of jest on the set assigned to 'broda'" (some set
> of brodas and broda parts -- whatever that may mean for a particular
> kind of thing as broda). 'lo', unlike 'loi' says nothing about how the
> set involved is connected to the predicates involved (collective or
> distributive).

All that is well-known, although we tend to use different terminology.

> Variables range over L-sets or are plural, depending on
> your mathematical theology. Etc. do we need to fill in all the details
> and, if not, which ones?

We need to know if variables are plural or singular, that's all.
Currently, they are "defined" as singular, for some value of "defined"
that makes sense when there is no official body to define it.

The rules are simple enough, they just aren't layed out properly. (If
they were, we wouldn't be having this discussion.)

[guskant]

Le mercredi 5 février 2014 20:47:54 UTC+9, selpa'i a écrit :

la .xorxes. cu cusku di'e 
> On Tue, Feb 4, 2014 at 3:31 PM, Dan Rosén <lur...@gmail.com 
> <mailto:lur...@gmail.com>> wrote: 
> 
> 
>     I'm using the expansions suggested in 
>     http://www.lojban.org/tiki/BPFK+Section:+gadri, where 
> 
> 

>          lo pa xanto = zo'e noi ke'a xanto gi'e zilkancu li pa lo xanto, 
> 

>     but {lo xanto} can be plural, so this removes the effect of the 
>     zilkancu part. Is it that I misunderstand this equation, or is it 
>     just false? 
> 
> 
> I don't think it's quite right to say that "lo xanto" can be plural, 
> because Lojban doesn't have grammatical number, so it can't strictly be 
> singular or plural. But a natural translation of "lo xanto" in this 
> context would indeed be plural in English, something like "is 1 counting 
> in elephants". 

If I may, Dan is asking why the unit {lo xanto} cannot be (implicitly) 
{lo ci xanto}, in which case three elephants would be counted as one 
counting off by threes. Using a property in zilkancu3 would probably be 
clearer for that reason. As it stands, some people seem to think that 
the zilkancu3 unit contains a context-dependent inner quantifier, thus 
counting of by {xo'e mei}. I don't think that's the intended meaning, so 
it should be stated clearly that we're dealing with singletons. 

If you mean simply "one-some" of a mass with the word "singleton", I agree with you for English "explanation" of {lo PA broda}. As for Lojban "definition", I would rather support the current definition, and need a Lojban definition of {kancu}, which is used in the definition of {zilkancu}.

I suggest as follows:

{x1 kancu x2 x3 x4} =ca'e {gau x1 boi x2 se tcita x3 noi ke'a namcu gi'e x3 mei x4 noi ke'a gradu}

I'm not sure if this definition would be totally reasonable, but at least it mentions {x4 noi ke'a gradu}, consequently {x4 pa mei} because of definition of {gradu}={x1 pa mei gi'e ckaji x3 noi se ckilu x2}.

With this definition, {zilkancu}_3 is clearly defined as {pamei}_1, and no other explanation is necessary.

However, if you mean "individual" with the word "singleton", it is better not to state it, because any mass, no matter if it is used as collective or distributive, can be a unit "one-some" in some sense.

An individual is defined as follows (based on Plural Predication by Thomas McKay, 2006):

"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}

where RO and DA are not a singular quantifier {ro} and a singular variable {da} of Lojban, but a plural quantifier and a plural variable respectively.

If {zilkancu}_3 should be always an individual, {lo ckafi} is not an individual in many cases of universe of discourse, and it cannot be {zilkancu}_3.

However, {lo ckafi} can be naturally a unit:

{mi cpedu tu'a lo pa ckafi} = {mi cpedu tu'a zo'e noi ke'a ckafi gi'e zilkancu li pa lo ckafi}

This flexibility of {zilkancu}_3, the unit, is advantage of xorlo, and indispensable for keeping expressiveness of Lojban.

 

Le jeudi 6 février 2014 01:49:34 UTC+9, selpa'i a écrit :

So singular variables are simpler and avoid certain problems, like the
{pa xanto} one. On the other hand, it would mean that we can't say {da
simxu lo ka prami} for "There are some X who love each other", and we'd
have to use more complicated mechanisms for that, like {da poi su'o mei
cu simxu lo ka prami} (which isn't *that* bad).

No, because the domain of {da} of {da poi (ke'a) su'o (re) mei} spans distributively over plural {su'o (re) mei}_1. 

{da poi ke'a gunma cu simxu lo ka prami} treats the plural {simxu}_1 collectively,

just like a developed form of {su'o loi}={su'o da poi ke'a me lo gunma be lo}.

 

Le mercredi 5 février 2014 16:53:25 UTC+9, la gleki a écrit :

Sorry for intruding. I need to explain this in simple words for a future lojban tutorial.

So 

{zo'e} denotes an individual/individuals.

{lo najgenja} = carrot/carrots

{ci lo najgenja cu grake li 60} = {ci zo'e noi najgenja cu grake li 60} - describes carrots. Three of carrots are 60 grams each.

Now I postulate an axiom that {[su'o] lo pa najgenja} describes one carrot (I'll avoid formulae here since i need it for a tutorial, not for a reference grammar).

{ro lo ci najgenja} describes each of the three carrots.

Two important conclusions:

1. {ro lo ci najgenja cu grake li 60} - one carrot is always 60 grams in weight.

2. {ro loi ci najgenja cu grake li 60} = {ro zo'e noi gunma lo ci najgenja cu grake li 60} - describes masses (again of carrots but carrots here are of less importance since carrots are hidden inside gunma2). Each mass of carrots (with three carrots in each mass) is 60 grams so each carrots weighs 20 grams on average.

 

Is my reasoning correct?

Yes, it is correct.

 

I remember someone saying that {lo} is more vague and might include masses as well but here {loi} and it's underlying {gunma} move carrots higher. Can we accept raising here? If yes then all this reasoning immediately breaks.

{lo} can be a mass, but it does not say if the mass satisfies the predicate collectively or/and distributively.

On the other hand, {loi}={lo gunma be lo} says that the mass satisfies the predicate collectively.

When an outer PA is attached to the sumti, the implicit {da} spans distributively over the domain:

{ro lo ci najgenja}={ro da poi me lo ci najgenja}

{ro loi ci najgenja}={ro da poi me lo gunma be lo ci najgenja}

You see, the domain of {ro lo ci najgenja} is each {najgenja}, and that of {ro loi ci najgenja} is each {gunma}.

 

[Jorge Llambías]

On Wed, Feb 5, 2014 at 8:47 AM, selpa'i <sel...@gmx.de> wrote:

         lo pa xanto = zo'e noi ke'a xanto gi'e zilkancu li pa lo xanto,

If I may, Dan is asking why the unit {lo xanto} cannot be (implicitly) {lo ci xanto}, in which case three elephants would be counted as one counting off by threes. Using a property in zilkancu3 would probably be clearer for that reason.

 But "lo ka ce'u xanto" is a property of "lo ci xanto" as well as of "lo xanto", so I'm not sure it adds anything in that respect. "ka" does help people who don't like generic references, but I'm not sure it does anything more than "lo xanto" to specify the size of the unit. How would it help to say that you are counting by things that have the property "lo ka ce'u xanto" if among those things there's lo ci xanto as well as lo pa xanto?

As it stands, some people seem to think that the zilkancu3 unit contains a context-dependent inner quantifier, thus counting of by {xo'e mei}. I don't think that's the intended meaning, so it should be stated clearly that we're dealing with singletons.

 

An important point of xorlo is that it gets rid of implicit quantifiers, but yes.  

[selpa'i]

la .guskant. cu cusku di'e

> Le mercredi 5 février 2014 20:47:54 UTC+9, selpa'i a écrit :
> If I may, Dan is asking why the unit {lo xanto} cannot be (implicitly)
> {lo ci xanto}, in which case three elephants would be counted as one
> counting off by threes. Using a property in zilkancu3 would probably be
> clearer for that reason. As it stands, some people seem to think that
> the zilkancu3 unit contains a context-dependent inner quantifier, thus
> counting of by {xo'e mei}. I don't think that's the intended
> meaning, so
> it should be stated clearly that we're dealing with singletons.
>
>
> If you mean simply "one-some" of a mass with the word "singleton", I
> agree with you for English "explanation" of {lo PA broda}. As for Lojban
> "definition", I would rather support the current definition, and need a
> Lojban definition of {kancu}, which is used in the definition of {zilkancu}.

Right, I'm not proposing to change the definition. I only explained the
reason for Dan's confusion. Making zilkancu (or kancu) clearer, would
solve the problem, but it would also help to explicitly state (in
English, for beginners) that in {lo PA broda}, we don't count by context
dependent units. Counting off by {lo broda} is intended to mean that {lo
ci broda} contains three individuals that each {broda}. This is what the
current definitions tries to say. It just wasn't clear enough for Dan or
la latro'a.

> However, if you mean "individual" with the word "singleton", it is
> better not to state it, because any mass, no matter if it is used as
> collective or distributive, can be a unit "one-some" in some sense.

Once you have a mass, then that mass is a new individual altogether. But
a sumti like {mi'o} or {mi jo'u do} is not a mass, it's just two
individuals together.

> An individual is defined as follows (based on Plural Predication by
> Thomas McKay, 2006):
>
> "SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
> where RO and DA are not a singular quantifier {ro} and a singular
> variable {da} of Lojban, but a plural quantifier and a plural variable
> respectively.

Yes, that is exactly the definition of "individual" I am using.

> If {zilkancu}_3 should be always an individual, {lo ckafi} is not an
> individual in many cases of universe of discourse, and it cannot be
> {zilkancu}_3.

{lo ckafi} is an amount of coffee. If I have two separate amounts of
coffee, then I can count them together {lo re ckafi}.

I would still call {lo ckafi} an individual. Using a property in
zilkancu3 has been suggested, so we either count by {lo ckafi} or {lo ka
ckafi}. The thing that makes {lo pa ckafi} different from {lo pa prenu}
is that splitting {lo pa ckafi} will result in two new {lo ckafi},
whereas splitting a person will just... kill it.

> However, {lo ckafi} can be naturally a unit:
> {mi cpedu tu'a lo pa ckafi} = {mi cpedu tu'a zo'e noi ke'a ckafi gi'e
> zilkancu li pa lo ckafi}

Certainly.

> This flexibility of {zilkancu}_3, the unit, is advantage of xorlo, and
> indispensable for keeping expressiveness of Lojban.

I don't think anyone is trying to remove flexible units.

[selpa'i]

la .xorxes. cu cusku di'e

> Using a property in zilkancu3
> would probably be clearer for that reason.
>
>
> But "lo ka ce'u xanto" is a property of "lo ci xanto" as well as of
> "lo xanto", so I'm not sure it adds anything in that respect. "ka" does
> help people who don't like generic references,

Personally, I don't mind generic references.

> but I'm not sure it does
> anything more than "lo xanto" to specify the size of the unit. How would
> it help to say that you are counting by things that have the property
> "lo ka ce'u xanto" if among those things there's lo ci xanto as well as
> lo pa xanto?

You're right, it doesn't help at all, because {lo ci xanto cu xanto}.
"to be an elephant" is a distributive predicate, but Lojban doesn't put
that job on the selbri. We could try:

lo ci xanto cu xanto gi'e zilkancu li ci lo ka ro xo kau ce'u xanto

And now I'd rather go back to {lo xanto} as the unit. :)

[MorphemeAddict]

It seems to me that if you allow "pa xanto" or "pa lo xanto" to mean anything other than "one elephant" without relying on context, there's going to be a problem. 

stevo

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[Jonathan Jones]

On Wed, Feb 5, 2014 at 12:05 PM, selpa'i <sel...@gmx.de> wrote:

la .pycyn. cu cusku di'e

<snip>

underdocumented and scattered definitions.... [M]ore complete specification that one can point someone to instead of having to re-open a discussion about xorlo.

The official definitions of cmavo are organized by selma'o on the BPFK Sections page. This page should allow adding such relevant information. I would suggest either the general Notes or Issues, or specific Notes for the gadri itself.

I would assume these pages also exist on the MediaWiki, but you'd have to ask the maintainer, Gleki, where they are.

<snip>

Variables range over L-sets or are plural, depending on
your mathematical theology.  Etc.  do we need to fill in all the details
and, if not, which ones?

We need to know if variables are plural or singular, that's all. Currently, they are "defined" as singular, for some value of "defined" that makes sense when there is no official body to define it.

Sets in general can be any number and are neither singular nor plural. It is possible to have 0-sets, 1-sets, or even ∞-sets. A specific set will be either singular, plural, or neither depending entirely on how many members it has in it. In Lojban the precise set being referenced (, i.e., the members of the set {la.djan.} are all entities who have "John" or its variant spellings as the name by which they are called), can usually be inferred from context (, i.e., those named "John" who are relevant to the context of the current discussion, which in this case is John Clifford and myself.)

In the case of {lo ve kalcu}, I would say that the set would always, or at least nearly always be a 1-set, and would typically be the 1-set [1], although I can imagine counting by multiples, such as in {kancu li cire to du li ci te'a mu toi me'o li mu li re}.

 

<snip>

--
mu'o mi'e .aionys.

.i.e'ucai ko cmima lo pilno be denpa bu .i doi.luk. mi patfu do zo'o
(Come to the Dot Side! Luke, I am your father. :D )

[Jonathan Jones]

sa du li re te'a mu toi li mu me'o pi'i re

[guskant]

Le jeudi 6 février 2014 05:28:08 UTC+9, selpa'i a écrit :

la .guskant. cu cusku di'e
> Le mercredi 5 février 2014 20:47:54 UTC+9, selpa'i a écrit :
>     If I may, Dan is asking why the unit {lo xanto} cannot be (implicitly)
>     {lo ci xanto}, in which case three elephants would be counted as one
>     counting off by threes. Using a property in zilkancu3 would probably be
>     clearer for that reason. As it stands, some people seem to think that
>     the zilkancu3 unit contains a context-dependent inner quantifier, thus
>     counting of by {xo'e mei}. I don't think that's the intended
>     meaning, so
>     it should be stated clearly that we're dealing with singletons.
>
>
> If you mean simply "one-some" of a mass with the word "singleton", I
> agree with you for English "explanation" of {lo PA broda}. As for Lojban
> "definition", I would rather support the current definition, and need a
> Lojban definition of {kancu}, which is used in the definition of {zilkancu}.

Right, I'm not proposing to change the definition. I only explained the
reason for Dan's confusion. Making zilkancu (or kancu) clearer, would
solve the problem, but it would also help to explicitly state (in
English, for beginners) that in {lo PA broda}, we don't count by context
dependent units. Counting off by {lo broda} is intended to mean that {lo
ci broda} contains three individuals that each {broda}. This is what the
current definitions tries to say. It just wasn't clear enough for Dan or
la latro'a.

That's nice. 

Although it will become out of topic, I have another suggestion related to the BPFK page of gadri.

"Any term without an explicit outer quantifier is a constant" should be changed to 

"Any term without an explicit outer quantifier can be a constant",

because an usual predicate logic has an axiom on a constant c that "F(c) {inaja} there is at least one (individual) x such that F(x)";

this means that the sentence "any term without an explicit outer quantifier is a constant" automatically implicates an outer quantifier {su'o},

and it contradicts to xorlo itself that there are no default quantifiers.

Most general term, without quantifier, with no universe of discourse yet defined, should be called "free variable".

Once a context is given, it defines an universe of discourse, then each free variable in a sentence becomes a bound plural variable OR a constant (not always a constant), then the truth value of the sentence is specified; if a term denotes an individual, it can become a bound singular variable, then an outer quantifier of Lojban is also available for the term.

The whole procedure depends on the context, and the language itself should not define that a term is a constant.

 

> However, if you mean "individual" with the word "singleton", it is
> better not to state it, because any mass, no matter if it is used as
> collective or distributive, can be a unit "one-some" in some sense.

Once you have a mass, then that mass is a new individual altogether. But
a sumti like {mi'o} or {mi jo'u do} is not a mass, it's just two
individuals together.

I use the term "mass" as something in a domain of plural variable, saying nothing about collectivity/distributivity.

I know BPFK and you use the term "mass" only for "collective mass", but I think this usage is confusing for beginners, because:

1. CLL uses the term "mass" more generally, not always for collective mass;

2. the English word "mass" is too vague to be used as a technical term that involving collectivity;

3. it is useful to define "mass" as follows:

"mass" =ca'e "something in a domain of plural variable";

"collective mass" =ca'e "mass that satisfies the predicate collectively";

"distributive mass" =ca'e "mass that satisfies the predicate distributively".

If you suggest another short term for "something in a domain of plural variable, saying nothing about collectivity/distributivity", I would abandon my usage of "mass" in this meaning.

 

> An individual is defined as follows (based on Plural Predication by
> Thomas McKay, 2006):
>
> "SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
> where RO and DA are not a singular quantifier {ro} and a singular
> variable {da} of Lojban, but a plural quantifier and a plural variable
> respectively.

Yes, that is exactly the definition of "individual" I am using.

> If {zilkancu}_3 should be always an individual, {lo ckafi} is not an
> individual in many cases of universe of discourse, and it cannot be
> {zilkancu}_3.

{lo ckafi} is an amount of coffee. If I have two separate amounts of
coffee, then I can count them together {lo re ckafi}.

I would still call {lo ckafi} an individual. Using a property in
zilkancu3 has been suggested, so we either count by {lo ckafi} or {lo ka
ckafi}. The thing that makes {lo pa ckafi} different from {lo pa prenu}
is that splitting {lo pa ckafi} will result in two new {lo ckafi},
whereas splitting a person will just... kill it.

Yes, but whether {lo ckafi}, {lo prenu} etc. are individual or not depends on epistemology, and the epistemology depends on the universe of discourse, on the context.

It is not defined by Lojban.

 

[Gleki Arxokuna]

On Thu, Feb 6, 2014 at 3:35 AM, Jonathan Jones <eye...@gmail.com> wrote:

I would assume these pages also exist on the MediaWiki, but you'd have to ask the maintainer, Gleki, where they are.

Probably at the same place: http://mw.lojban.org/index.php?title=BPFK_Section:_gadri

However, maintainer is supposed to maintain a wiki in a working state. Why asking the maintainer of Wikipedia where this or that information exists?

However, since it's not an official wiki the question for now is only to have the mediawiki in sync with the official wiki. BPFK sections are the most important part so it's better to always read the tiki.

[selpa'i]

la .guskant. cu cusku di'e

> Once you have a mass, then that mass is a new individual altogether.
> But
> a sumti like {mi'o} or {mi jo'u do} is not a mass, it's just two
> individuals together.
>
> I use the term "mass" as something in a domain of plural variable,
> saying nothing about collectivity/distributivity.
> I know BPFK and you use the term "mass" only for "collective mass", but
> I think this usage is confusing for beginners, because:
>
> 1. CLL uses the term "mass" more generally, not always for collective mass;
> 2. the English word "mass" is too vague to be used as a technical term
> that involving collectivity;
> 3. it is useful to define "mass" as follows:
> "mass" =ca'e "something in a domain of plural variable";
> "collective mass" =ca'e "mass that satisfies the predicate collectively";
> "distributive mass" =ca'e "mass that satisfies the predicate
> distributively".

The term "mass" is confusing exactly because it has been used to mean so
many different things. I would avoid the term myself. However, whenever
I say mass, I mean {gunma}.

{lo gunma} is an individual, too. The referent of {lo gunma} is the
"mass", not its members, which is the whole point of {gunma}. I also
think that {gunma}'s semantics aren't very clear. We still don't have a
definite answer on what properties a {gunma} has, how those properties
are related to its members, and whether it can attain new properties,
and which ones. For me, a {gunma} is a whole new entity, and it can be
the value of a singular variable. There is also no question of
distributivity with {gunma}, as it is just one thing (unless you have
multiple {gunma}, in which case {lo PA gunma} is the same as any other
{lo PA broda}, not specifying distributivity).

> If you suggest another short term for "something in a domain of plural
> variable, saying nothing about collectivity/distributivity", I would
> abandon my usage of "mass" in this meaning.

A term that I've been using, but which doesn't seem to be very
wide-spread (yet?), is "individual-collection". Anything that can be
expressed as {X jo'u Y jo'u Z ...} is an individual collection and is
identical to a {lo broda} with those {jo'u}-connected referents.

> Yes, but whether {lo ckafi}, {lo prenu} etc. are individual or not
> depends on epistemology, and the epistemology depends on the universe of
> discourse, on the context.
> It is not defined by Lojban.

The way I see it, any {lo broda} is an individual (or an
individual-collection). It doesn't matter what {broda} is. What kind of
individuals there are in {lo broda} depends on {broda}, but they are
still always individuals. There is no difference between {lo ckafi} and
{lo prenu} in terms of individualness.

[Jorge Llambías]

On Thu, Feb 6, 2014 at 1:34 AM, guskant <gusni...@gmail.com> wrote:

Although it will become out of topic, I have another suggestion related to the BPFK page of gadri.

"Any term without an explicit outer quantifier is a constant" should be changed to 

"Any term without an explicit outer quantifier can be a constant",

because an usual predicate logic has an axiom on a constant c that "F(c) {inaja} there is at least one (individual) x such that F(x)";

That applies to singular constants, whereas unquantified terms need not be singular, but the version with plural quantifiers will still be valid.

 

this means that the sentence "any term without an explicit outer quantifier is a constant" automatically implicates an outer quantifier {su'o},

It shouldn't implicate that. "F{c} -> Ex F(x)" does not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...". Similarly xorlo says that "lo broda" is not just shorthand for "su'o lo broda".

 

and it contradicts to xorlo itself that there are no default quantifiers.

Not just no default quantifiers. No implicit hidden quantifiers at all, The point is that "lo broda" is not a quantification of the bridi it appears in, the way "su'o lo broda" is.

[Jorge Llambías]

On Thu, Feb 6, 2014 at 8:33 AM, selpa'i <sel...@gmx.de> wrote:

la .guskant. cu cusku di'e

If you suggest another short term for "something in a domain of plural
variable, saying nothing about collectivity/distributivity", I would
abandon my usage of "mass" in this meaning.

A term that I've been using, but which doesn't seem to be very wide-spread (yet?), is "individual-collection". Anything that can be expressed as {X jo'u Y jo'u Z ...} is an individual collection and is identical to a {lo broda} with those {jo'u}-connected referents.

The problem with that, with whatever term is chosen in the metalanguage to talk about the language, is that the term eventually leaks into the language, and then collections become individuals too. That happened to "mass" very quickly, probably from the start, compounded with the problem that it was used for a lot of other things and not just for plural reference. I prefer to say that the domain of plural variables is just individuals, not something else, but that variables don't need to take one value at a time.

[selpa'i]

la .xorxes. cu cusku di'e

> On Thu, Feb 6, 2014 at 8:33 AM, selpa'i <sel...@gmx.de
> <mailto:sel...@gmx.de>> wrote:
>
> la .guskant. cu cusku di'e
>
>
> If you suggest another short term for "something in a domain of
> plural
> variable, saying nothing about collectivity/distributivity", I would
> abandon my usage of "mass" in this meaning.
>
>
> A term that I've been using, but which doesn't seem to be very
> wide-spread (yet?), is "individual-collection". Anything that can be
> expressed as {X jo'u Y jo'u Z ...} is an individual collection and
> is identical to a {lo broda} with those {jo'u}-connected referents.
>
>
> The problem with that, with whatever term is chosen in the metalanguage
> to talk about the language, is that the term eventually leaks into the
> language, and then collections become individuals too.

That is indeed a possible danger, I agree. But of course we need to be
able to talk about it *somehow* (both in English and in Lojban),
although I will grant that it is logic/linguistics jargon and thus of
lower priority than everyday life vocabulary, which Lojban is still
lacking to a great extent.

> I prefer to say that the domain of plural variables is
> just individuals, not something else, but that variables don't need to
> take one value at a time.

I agree 100% with that.

[jacfold...@gmail.com]

Do you still mean 

"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}

with the term "individual"?

If so, keeping {lo broda} to be individual requires attentiveness on the universe of discourse, and reduces the flexibility of the language.

Let me give an example.

lo prenu cu jmaji gi'e jukpa gi'e citka

I want to mean with this sentence that this {lo prenu} consists of at least two persons {by} and {cy}, and satisfies {jmaji} collectively {je} non-distributively, {jukpa} collectively {ja} distributively, {citka} non-collectively {je} distributively. This {lo} cannot be replaced by {loi} because I want it to satisfy a selbri non-collectively.

For this {lo prenu}, {by me lo prenu} is true, but {lo prenu me by} is false, so this {lo prenu} is not individual.

It is still possible that you don't include {by} and {cy} in your universe of discourse and say that {lo prenu} is individual, but it is your epistemology, and not defined by the language.

 

[guskant]

Do you still mean 

"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}

[guskant]

Le vendredi 7 février 2014 06:22:09 UTC+9, xorxes a écrit :

On Thu, Feb 6, 2014 at 1:34 AM, guskant <gusni...@gmail.com> wrote:

Although it will become out of topic, I have another suggestion related to the BPFK page of gadri.

"Any term without an explicit outer quantifier is a constant" should be changed to 

"Any term without an explicit outer quantifier can be a constant",

because an usual predicate logic has an axiom on a constant c that "F(c) {inaja} there is at least one (individual) x such that F(x)";

That applies to singular constants, whereas unquantified terms need not be singular, but the version with plural quantifiers will still be valid.

Actually, there is no explicit plural qiantifier in Lojban, though implicitly there are.

Even Thomas McKay does not adopt plural constant. For individual constant c, there are two axioms:

- [for all Y: Y {me} c] c {me} Y ;

- F(c) {inaja} there is X such that F(X) .

Even in the plural logic, F(c) implies a quantifier.

If you use the term "constant" as of the version with plural quantifiers, you should mention it in the gadri page, and also you should explain how Lojban treats plural quantifiers. Otherwise I don't understand how a constant implies no implicit quantifier.

 

 

this means that the sentence "any term without an explicit outer quantifier is a constant" automatically implicates an outer quantifier {su'o},

It shouldn't implicate that. "F{c} -> Ex F(x)" does not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...". Similarly xorlo says that "lo broda" is not just shorthand for "su'o lo broda".

 

I did not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...".

When F(c) is said, it says implicitly that "Ex F(x)" is true.

 

and it contradicts to xorlo itself that there are no default quantifiers.

Not just no default quantifiers. No implicit hidden quantifiers at all, The point is that "lo broda" is not a quantification of the bridi it appears in, the way "su'o lo broda" is.

I agree to that point, and I consider that F(c) implies implicit hidden quantifiers, and conclude that it contradicts xorlo.

 

[guskant]

Le vendredi 7 février 2014 10:54:57 UTC+9, guskant a écrit :

 

For this {lo prenu}, {by me lo prenu} is true, but {lo prenu me by} is false, so this {lo prenu} is not individual.

Sorry, I forgot {cu} :

"For this {lo prenu}, {by me lo prenu} is true, but {lo prenu cu me by} is false, so this {lo prenu} is not individual."

[selpa'i]

la .guskant. cu cusku di'e

> The way I see it, any {lo broda} is an individual (or an
> individual-collection). It doesn't matter what {broda} is. What kind of
> individuals there are in {lo broda} depends on {broda}, but they are
> still always individuals. There is no difference between {lo ckafi} and
> {lo prenu} in terms of individualness.
>
>
>
> Do you still mean
> "SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
> with the term "individual"?
>
> If so, keeping {lo broda} to be individual requires attentiveness on the
> universe of discourse, and reduces the flexibility of the language.

Note that I said "is an individual or an individual-collection". That
is, {lo broda} can refer to one individual or to multiple individuals,
but we are always dealing in terms of individuals. It doesn't mean that
{lo broda} must be singular, it only means that whether or not it is
plural, the only referents it has are individuals.

> Let me give an example.
>
> lo prenu cu jmaji gi'e jukpa gi'e citka
>
> I want to mean with this sentence that this {lo prenu} consists of at
> least two persons {by} and {cy}, and satisfies {jmaji} collectively {je}
> non-distributively, {jukpa} collectively {ja} distributively, {citka}
> non-collectively {je} distributively. This {lo} cannot be replaced by
> {loi} because I want it to satisfy a selbri non-collectively.
>
> For this {lo prenu}, {by me lo prenu} is true, but {lo prenu me by} is
> false, so this {lo prenu} is not individual.

Correct, because this {lo prenu} has two referents, both of which are
individuals. {lo prenu} itself is not an individual, but its referents
are individuals.

Your example sentence is perfectly fine.

[Jorge Llambías]

On Thu, Feb 6, 2014 at 10:58 PM, guskant <gusni...@gmail.com> wrote:

If you use the term "constant" as of the version with plural quantifiers, you should mention it in the gadri page, and also you should explain how Lojban treats plural quantifiers. Otherwise I don't understand how a constant implies no implicit quantifier.

There's a pretty long explanation of what I meant by constant there already, I think it's clear that a plural constant is meant:

• Any term without an explicit outer quantifier is a constant, i.e. not a quantified term. This means that it refers to one or more individuals, and changing the order in which the constant term appears with respect to a negation or with respect to a quantified term will not change the meaning of the sentence. A constant is something that always keeps the same referent or referents. For example {lo broda} always refers to brodas. 

As for plural quantifiers, I once proposed "su'oi", "ro'oi", "no'oi" and "me'oi". 

this means that the sentence "any term without an explicit outer quantifier is a constant" automatically implicates an outer quantifier {su'o},

It shouldn't implicate that. "F{c} -> Ex F(x)" does not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...". Similarly xorlo says that "lo broda" is not just shorthand for "su'o lo broda".

 

I did not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...".

When F(c) is said, it says implicitly that "Ex F(x)" is true.

If c is singular, yes. That's not what I mean by implicit hidden quantifier though. All I mean is that saying "lo broda" is not just another way of saying "su'o lo broda" nor "[some quantifier] lo broda". 

 

and it contradicts to xorlo itself that there are no default quantifiers.

Not just no default quantifiers. No implicit hidden quantifiers at all, The point is that "lo broda" is not a quantification of the bridi it appears in, the way "su'o lo broda" is.

I agree to that point, and I consider that F(c) implies implicit hidden quantifiers, and conclude that it contradicts xorlo.

Sorry, I don't understand what you mean by that. 

[guskant]

Le vendredi 7 février 2014 20:56:57 UTC+9, selpa'i a écrit :

la .guskant. cu cusku di'e
>     The way I see it, any {lo broda} is an individual (or an
>     individual-collection). It doesn't matter what {broda} is. What kind of
>     individuals there are in {lo broda} depends on {broda}, but they are
>     still always individuals. There is no difference between {lo ckafi} and
>     {lo prenu} in terms of individualness.
>
>
>
> Do you still mean
> "SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
> with the term "individual"?
>
> If so, keeping {lo broda} to be individual requires attentiveness on the
> universe of discourse, and reduces the flexibility of the language.

Note that I said "is an individual or an individual-collection". That
is, {lo broda} can refer to one individual or to multiple individuals,
but we are always dealing in terms of individuals. It doesn't mean that
{lo broda} must be singular, it only means that whether or not it is
plural, the only referents it has are individuals.

OK, now I understand what you meant.

However, I don't agree to calling {lo broda} "an individual" or "a collection of individual" for two reasons.

1. There is no guarantee that "something in a domain of plural variable, saying nothing about collectivity/distributivity (SDPV)" is always "an individual" or "a collection of individual". An individual is only a special case of SDPV. Lojban should not force a speaker to have an individual of {lo sidbo}, for example, in the universe of discourse. Regarding SDPV as "an individual" or "a collection of individual" is atomism, and should not be forced by the language.

2. Calling {lo broda} "an individual" or "a collection of individual" may let a beginner think of set theory. In order to make clear that the concept of SDPV is completely different from that of a set, such a risk should be avoided.

 

[guskant]

Le samedi 8 février 2014 05:54:27 UTC+9, xorxes a écrit :

On Thu, Feb 6, 2014 at 10:58 PM, guskant <gusni...@gmail.com> wrote:

If you use the term "constant" as of the version with plural quantifiers, you should mention it in the gadri page, and also you should explain how Lojban treats plural quantifiers. Otherwise I don't understand how a constant implies no implicit quantifier.

There's a pretty long explanation of what I meant by constant there already, I think it's clear that a plural constant is meant:

• Any term without an explicit outer quantifier is a constant, i.e. not a quantified term. This means that it refers to one or more individuals, and changing the order in which the constant term appears with respect to a negation or with respect to a quantified term will not change the meaning of the sentence. A constant is something that always keeps the same referent or referents. For example {lo broda} always refers to brodas. 

It is still unclear which logical axioms are applied to a plural constant.

I now understand that your term "constant" is neither of classical predicate logic, nor of Thomas McKay. However, I don't understand how is it applied in logic of Lojban. I need axioms for the term "constant".

 

As for plural quantifiers, I once proposed "su'oi", "ro'oi", "no'oi" and "me'oi". 

I know, but they were finally abandoned.

 

this means that the sentence "any term without an explicit outer quantifier is a constant" automatically implicates an outer quantifier {su'o},

It shouldn't implicate that. "F{c} -> Ex F(x)" does not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...". Similarly xorlo says that "lo broda" is not just shorthand for "su'o lo broda".

 

I did not mean that "F(c)" and "Ex F(x)" have the same meaning, nor that "c" is just a shorthand for "Ex ...x...".

When F(c) is said, it says implicitly that "Ex F(x)" is true.

If c is singular, yes. That's not what I mean by implicit hidden quantifier though. All I mean is that saying "lo broda" is not just another way of saying "su'o lo broda" nor "[some quantifier] lo broda". 

 

and it contradicts to xorlo itself that there are no default quantifiers.

Not just no default quantifiers. No implicit hidden quantifiers at all, The point is that "lo broda" is not a quantification of the bridi it appears in, the way "su'o lo broda" is.

I agree to that point, and I consider that F(c) implies implicit hidden quantifiers, and conclude that it contradicts xorlo.

Sorry, I don't understand what you mean by that. 

Because I did think that c is always singular, saying {lo broda} implies saying {su'o da poi ke'a broda}. It is not {su'o lo broda}, but another quantified term is implied. 

My problem is, for example, how {lo no broda} can be meaningful if {lo broda} implies {su'o da poi ke'a broda}. 

To solve this problem, I need axioms for "plural constant".

 

[selpa'i]

la .guskant. cu cusku di'e
> Le vendredi 7 février 2014 20:56:57 UTC+9, selpa'i a écrit :
> Note that I said "is an individual or an individual-collection". That
> is, {lo broda} can refer to one individual or to multiple individuals,
> but we are always dealing in terms of individuals. It doesn't mean that
> {lo broda} must be singular, it only means that whether or not it is
> plural, the only referents it has are individuals.
>
>
>
> OK, now I understand what you meant.
> However, I don't agree to calling {lo broda} "an individual" or "a
> collection of individual" for two reasons.
>
> 1. There is no guarantee that "something in a domain of plural variable,
> saying nothing about collectivity/distributivity (SDPV)" is always "an
> individual" or "a collection of individual".

What else is a possible referent? Can you name anything that isn't an
individual (or more than one individual)? Are we using different senses
of the word?

> An individual is only a
> special case of SDPV. Lojban should not force a speaker to have an
> individual of {lo sidbo}, for example, in the universe of discourse.

I don't understand this point.

> Regarding SDPV as "an individual" or "a collection of individual" is
> atomism, and should not be forced by the language.

I'm not sure what is being forced here. I cannot think of anything that
is in the DPV that is not an individual.

> 2. Calling {lo broda} "an individual" or "a collection of individual"
> may let a beginner think of set theory. In order to make clear that the
> concept of SDPV is completely different from that of a set, such a risk
> should be avoided.

Does "collection" really remind you of set-theory? That's certainly not
the direction I was going for with the term. Maybe having no term at all
is better. We could just go back to saying "one or more individuals".

[Jorge Llambías]

On Fri, Feb 7, 2014 at 9:03 PM, guskant <gusni...@gmail.com> wrote:

My problem is, for example, how {lo no broda} can be meaningful if {lo broda} implies {su'o da poi ke'a broda}. 

To solve this problem, I need axioms for "plural constant".

"lo no broda" is not very meaningful, except perhaps as a joke or if you want to be whimsical or paradoxical. 

BTW, "lo broda cu brode" does not imply "su'o da poi broda cu brode", as you already pointed out, but it does imply "su'oi da poi broda cu brode". In other words "students are surrounding the building" does not necessarily imply that at least one student is surrounding the building, but it does imply that some student or students are surrounding the building.

[Robert LeChevalier]

On 2/6/2014 8:58 PM, guskant wrote:
>
>
> Le vendredi 7 février 2014 06:22:09 UTC+9, xorxes a écrit :
>
>

> On Thu, Feb 6, 2014 at 1:34 AM, guskant <gusni...@gmail.com> wrote:
>
>
> Although it will become out of topic, I have another suggestion
> related to the BPFK page of gadri.
>
> "Any term without an explicit outer quantifier is a constant"
> should be changed to
> "Any term without an explicit outer quantifier can be a constant",
> because an usual predicate logic has an axiom on a constant c
> that "F(c) {inaja} there is at least one (individual) x such
> that F(x)";
>
>
> That applies to singular constants, whereas unquantified terms need
> not be singular, but the version with plural quantifiers will still
> be valid.
>
>
>

> Actually, there is no explicit plural qiantifier in Lojban, though
> implicitly there are.

su'ore is the plural quantifier

lojbab

[Bob LeChevalier, President and Founder - LLG]

On 2/7/2014 6:56 AM, selpa'i wrote:
> la .guskant. cu cusku di'e

>> The way I see it, any {lo broda} is an individual (or an
>> individual-collection). It doesn't matter what {broda} is. What
>> kind of
>> individuals there are in {lo broda} depends on {broda}, but they are
>> still always individuals. There is no difference between {lo
>> ckafi} and
>> {lo prenu} in terms of individualness.
>>
>>
>>
>> Do you still mean
>> "SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
>> with the term "individual"?
>>
>> If so, keeping {lo broda} to be individual requires attentiveness on the
>> universe of discourse, and reduces the flexibility of the language.
>

> Note that I said "is an individual or an individual-collection". That
> is, {lo broda} can refer to one individual or to multiple individuals,
> but we are always dealing in terms of individuals. It doesn't mean that
> {lo broda} must be singular, it only means that whether or not it is
> plural, the only referents it has are individuals.

Nora hasn't the time to read and consider this thread in depth, but she
wonders whether the cmavo lu'a (and its relatives) doesn't resolve this
issue. At least it was intended that these words would resolve
ambiguity between individuals and the mass(es) comprised of them.

lojbab

[Jonathan Jones]

On Sat, Feb 8, 2014 at 4:02 AM, Bob LeChevalier, President and Founder - LLG <loj...@lojban.org> wrote:

Nora hasn't the time to read and consider this thread in depth, but she wonders whether the cmavo lu'a (and its relatives) doesn't resolve this issue.  At least it was intended that these words would resolve ambiguity between individuals and the mass(es) comprised of them.

lojbab

Do either of {lu'a soi'u no'o broda} = broda[no'o] = "The typical example of a single thing which [is|does|<etc.>] broda.", and if not, what is? I that specific meaning is what they're looking for.

{to lu le pamoi gadri .e le remoi gadri cu simxu lo ka kakne lo pamoi gadri li'u smuni za'e zo soi'u noi simsa zo soi toi}

[guskant]

SDPV is first given, and then "individual" is defined using it. When a universe of discourse is given, there is no need that SDPV is finally separated into individual pieces. Having SDPV without individual pieces in the universe of discourse should be permitted. I will discuss it also in the next post as response to la xorxes.

 

> 2. Calling {lo broda} "an individual" or "a collection of individual"
> may let a beginner think of set theory. In order to make clear that the
> concept of SDPV is completely different from that of a set, such a risk
> should be avoided.

Does "collection" really remind you of set-theory? That's certainly not
the direction I was going for with the term. Maybe having no term at all
is better. We could just go back to saying "one or more individuals".

Yes, and I will discuss it also in the next post.

 

[guskant]

Le samedi 8 février 2014 09:28:10 UTC+9, xorxes a écrit :

On Fri, Feb 7, 2014 at 9:03 PM, guskant <gusni...@gmail.com> wrote:

My problem is, for example, how {lo no broda} can be meaningful if {lo broda} implies {su'o da poi ke'a broda}. 

To solve this problem, I need axioms for "plural constant".

"lo no broda" is not very meaningful, except perhaps as a joke or if you want to be whimsical or paradoxical. 

As long as PA of {lo PA broda} is defined as zilkancu_2, {lo no broda} should be meaningful.

From that definition, I guess that PA should be a member of a countable set, a rational number.

There is no other information about this PA, then it is natural that {lo no broda} is meaningful.

Also from a practical point of view, it is better to give {lo no broda} some reasonable meaning:

- lo xo prenu cu jmaji gi'e jukpa gi'e citka

 - no

Such a conversation is quite natural, and cannot be replaced by an outer quantifier in a simple way because it involves collectivity and distributivity. It should not be excluded from the language.

 

BTW, "lo broda cu brode" does not imply "su'o da poi broda cu brode", as you already pointed out, but it does imply "su'oi da poi broda cu brode". In other words "students are surrounding the building" does not necessarily imply that at least one student is surrounding the building, but it does imply that some student or students are surrounding the building.

Yes, such a description is indeed what I need on the page of gadri.

I guess finally one axiom related to plural constant C of Lojban:

- F(C) {inaja} there is X such that F(X),

where X is plural variable.

I became now aware of the reason why I was not aware of the fact that the constant of Lojban is not of classical predicate logic, nor of Thomas McKay, but plural constant.

I tried to understand the page of gadri based on plural logic, mainly of Thomas McKay.

I believe this principle was relevant, but undefined technical terms used in the gadri page are very misleading.

I supposed first that the term "individual" should be defined as follows:

"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}

where RO DA is quantified plural variable.

This supposition was not bad. 

However, I saw on the gadri page "An individual can be anything, including a group,..." Now I began to be misled.

I thought: "An individual can be a group, then it contradicts my first supposition." 

(Now I know "a group" meant {lo gunma}, not "something in a domain of plural variable"; but I was not aware of it at that time.)

I abandoned my supposition, and supposed that the "individual" must be something another.

Then I saw "Any term without an explicit outer quantifier is a constant, i.e. not a quantified term. This means that it refers to one or more individuals..." 

I have already abandoned my first correct supposition, and believed that this sentence meant a constant refers to one or more "something other than individual of plural logic". I did not conclude that it meant "plural constant", because Thomas McKay did not adopt it. I thought of the possibility of "plural constant", but I did not guess how a plural constant would be treated in logical axioms of Lojban, and finally abandoned the interpretation that it meant "plural constant".

To avoid such misleading, I now suggest adding the following information on the gadri page:

- definition of "individual",  that is,

"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}

where RO DA is quantified plural variable. {ro'oi da} instead of {RO DA} may be better if you give a definition for it.

- "constant" of Lojban is not necessarily a singular constant, but a plural constant.

- logical axioms for plural constant.

Moreover, calling something in a domain of plural variable "one or more individuals" is misleading for me.

The term for "something in a domain of plural variable" should be first given; after that "individual" is defined using it. The concept "individual" is only a special case of "something in a domain of plural variable" as defined above. This is not my particular way of thinking, but general way of plural logic.

Something that is broda is not always "one or more individuals" defined above: when a universe of discourse is given, there is no need that {lo broda} in the universe of discourse is finally separated into individual pieces that are members of the universe of discourse. An expression reasonable for me would be: say "{lo broda} is something that is {broda}" first, give a definition for "individual", and then "{lo broda} can be one or more individuals".

By the way, based on the fact that {lo broda} is plural constant, another problem occurs.

{lo broda} is defined as {zo'e}, and {zo'e} is defined as unspecific value.

When {lo broda} is a plural constant, it is a specific value, and contradicts the definition of {zo'e}. 

My understanding is that {zo'e} is essentially a free variable, and a plural constant is implicitly substituted when a universe of discourse is given. If it is correct, such a description should be included on the gadri or zo'e page. If it is incorrect, some reasonable explanation is necessary.

 

[guskant]

That is a singular quantifier. I did not mean it by "plural quantifier". I meant that of plural logic.

 

[selpa'i]

la .guskant. cu cusku di'e

> Moreover, calling something in a domain of plural variable "one or more
> individuals" is misleading for me.
> The term for "something in a domain of plural variable" should be first
> given; after that "individual" is defined using it. The concept
> "individual" is only a special case of "something in a domain of plural
> variable" as defined above.

What would be another case of SDPV that is not an individual? I can't
really make sense of your argument, because for me there are only
individuals and nothing else (DPV or not).

> Something that is broda is not always "one or more individuals" defined
> above: when a universe of discourse is given, there is no need that {lo
> broda} in the universe of discourse is finally separated into individual
> pieces that are members of the universe of discourse.

Please give an example where that does not happen.

[Jorge Llambías]

On Sat, Feb 8, 2014 at 12:29 PM, guskant <gusni...@gmail.com> wrote:

As long as PA of {lo PA broda} is defined as zilkancu_2, {lo no broda} should be meaningful.

From that definition, I guess that PA should be a member of a countable set, a rational number.

There is no other information about this PA, then it is natural that {lo no broda} is meaningful.

I think the definition works well for natural numbers (i.e. positive integers), anything else is iffy. Even things like "lo pa pi mu broda" I find questionable, if not outright wrong.

  

Also from a practical point of view, it is better to give {lo no broda} some reasonable meaning:

- lo xo prenu cu jmaji gi'e jukpa gi'e citka

 - no

Such a conversation is quite natural, and cannot be replaced by an outer quantifier in a simple way because it involves collectivity and distributivity. It should not be excluded from the language.

I agree that "lo no prenu" in such a context will be naturally interpreted as "no'oi prenu" (the plural "no"). But I doubt that it can be consistently worked into the system. For one thing, you open the door to things that look like referring terms but don't actually refer to anything. (We already have some of those, like "zi'o", but at least they are now confined to KOhA.)

Moreover, calling something in a domain of plural variable "one or more individuals" is misleading for me.

The term for "something in a domain of plural variable" should be first given; after that "individual" is defined using it. The concept "individual" is only a special case of "something in a domain of plural variable" as defined above. This is not my particular way of thinking, but general way of plural logic.

The problem with doing what you suggest, is that whatever term you choose for that in the metalanguage will inevitably find its way into the language at some point, and then in the language it will refer to individuals (as it does refer to meta-individuals in the metalanguage) and you have to start all over with something else. I think "one or more individuals" is healthier. But if you prefer some other terminology there's nothing stopping you from writing up definitions with your preferred point of view.

 

By the way, based on the fact that {lo broda} is plural constant, another problem occurs.

{lo broda} is defined as {zo'e}, and {zo'e} is defined as unspecific value.

It's defined as "elliptical/unspecified". It has a value or values, they are just not given explicitly. 

 

When {lo broda} is a plural constant, it is a specific value, and contradicts the definition of {zo'e}. 

My understanding is that {zo'e} is essentially a free variable, and a plural constant is implicitly substituted when a universe of discourse is given. If it is correct, such a description should be included on the gadri or zo'e page. If it is incorrect, some reasonable explanation is necessary.

An expression with a free variable doesn't have a truth value, it's not a complete proposition. An expression with "zo'e" is a complete proposition, so zo'e can't be a free variable. "ke'a" and "ce'u" are free variables since the bridi they appear in are incomplete and don't have a truth value by themselves.

[John E Clifford]

There several logical systems which are formally indistinguishable but which differ in metalanguage and informal chat.  They also extend in different ways when they are built into something like Lojban,  Mixing the different metalanguages or the different chat or the different extentions makes for results that are even more paradoxical than already happens in any one of the systems. For present purposes, lets just consider two relatively typical systems, plural quantification ala McKay and mereology ala Lesniewski (there are other plural quantifications and other part-whole theories). Plural quantification (and plural reference, which goes with it in McKay, though need not) starts with a domain of  individuals but then specifies reference and evaluation not as functions but as relations,  Thus, "term A refers to" is a predicate which may be true of several thing simultaneously and similarly "variable X evaluates as".  Mereology begins with wholes and introduces individuals, if at all, only as wholes which are their only parts.  The mereological metalanguage is normal, using functions rather than relations.  Talking about sets in either system is a bit misleading. In plural reference, there is no entity (in terms of the system) between  individuals and the role they play, so no sets.  In mereology, there is no separate type between individuals and what plays the role, so no (special class of ) individuals.  In fairness to terminology, the wholes of mereology are sometimes called sets or some such thing, but are definitely not the same as the usual, Cantorian, sets.  Similarly, in nontechnical discussions in English, it is almost impossible to talk about several things simultaneously with out introducing some collective expression: "plurality" or "bunch" (my favorite) or ... . The fundamental internal relation in the two systems are "among" for plural reference (a relation between some individuals simultaneously and some individuals simultaneously) and "is part of" in mereology (between two wholes).  A moment's thought will show these are going to behave exactly the same, if you understand the system (if you don't see they behave the same, then we need to go back to the two systems in more detail).  All this being the case, it turns out that, for  informal discussions, at least, it is most efficient to use one of those handy English expressions to talk about the system without specifying which version you are using.  But, since there is a temptation to take these terms literally, it is probably best to avoid freighted expressions like "set" or "group" or "mass" (this is why I like the unfreighted "bunch").  But the problems with literality are obviously different in the two cases: in one you call into existence some intermediate type, in the other you call into existence some fundamental individuals.  Lojban seems to split the difference, talking as though there were things of the intermediate type (you can't actually says some plural reference sorts of things in grammatical Lojban "A, B among A,B, C," for example) but sometimes talking as though there were ultimate individuals (counting what is in lo broda, for example).  But at other times (or, perhaps, with some predicate but not others) it goes with indefinitely extensible partness (as when 'lo gerku' can refer to dabs of stuff on my bumper from running into a pack of dogs).  I think any effort to resolve this kind of tension in general, rather than on each particular occasion, is going to fail, since we clearly want and need both approaches.  So the quest for THE meaning of a Lojban expression -- other than its formal role -- seems a not very promising task.  One of the nice things about that pedantic definition of 'lo broda', "the salient node of the upward semi-lattice ..." is that covers just about every kind of case. 

---

From: guskant <gusni...@gmail.com>
To: loj...@googlegroups.com
Sent: Saturday, February 8, 2014 9:34 AM
Subject: Re: [lojban] Individuals and xorlo

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[guskant]

Suppose a universe of discourse is given, where {lo linji} is in a domain of plural variable.

In this universe of discourse, {lo linji xi no} can be separated into shorter {lo linji xi pany}:

lo linji xi pano cu me lo linji xi no

i

lo linji xi papa cu me lo linji xi no

i

...

Repeat the separation also for {lo linji xi pany}.

After infinite times of separation, {lo linji} is finally separated into {lo mokca} which is individual:

RO DA poi ke'a me lo mokca zo'u lo mokca me DA

but for any shorter {lo linji}:

naku lo linji me lo mokca

Therefore, any {lo linji} does not satisfy 

RO DA poi ke'a me lo linji zo'u lo linji me DA

{lo linji} in this universe of discourse is not an individual.

Please note that another universe of discourse can be given so that {lo linji} is one or more individuals, but the selection of universe of discourse depends on the epistemology of context, and cannot defined by the language.

 

[guskant]

Le dimanche 9 février 2014 01:44:47 UTC+9, xorxes a écrit :

On Sat, Feb 8, 2014 at 12:29 PM, guskant <gusni...@gmail.com> wrote:

As long as PA of {lo PA broda} is defined as zilkancu_2, {lo no broda} should be meaningful.

From that definition, I guess that PA should be a member of a countable set, a rational number.

There is no other information about this PA, then it is natural that {lo no broda} is meaningful.

I think the definition works well for natural numbers (i.e. positive integers), anything else is iffy. Even things like "lo pa pi mu broda" I find questionable, if not outright wrong.

  

Also from a practical point of view, it is better to give {lo no broda} some reasonable meaning:

- lo xo prenu cu jmaji gi'e jukpa gi'e citka

 - no

Such a conversation is quite natural, and cannot be replaced by an outer quantifier in a simple way because it involves collectivity and distributivity. It should not be excluded from the language.

I agree that "lo no prenu" in such a context will be naturally interpreted as "no'oi prenu" (the plural "no"). But I doubt that it can be consistently worked into the system. For one thing, you open the door to things that look like referring terms but don't actually refer to anything. (We already have some of those, like "zi'o", but at least they are now confined to KOhA.)

Why don't you define 

{lo no broda} =ca'e {zi'o noi ke'a broda}

only for the case that PA=no?

Under the condition that there is no official plural quantifier in Lojban, the inclusion of {lo no broda} is necessary for keeping the expressiveness of Lojban equal to that of plural quantification.

 

Moreover, calling something in a domain of plural variable "one or more individuals" is misleading for me.

The term for "something in a domain of plural variable" should be first given; after that "individual" is defined using it. The concept "individual" is only a special case of "something in a domain of plural variable" as defined above. This is not my particular way of thinking, but general way of plural logic.

The problem with doing what you suggest, is that whatever term you choose for that in the metalanguage will inevitably find its way into the language at some point, and then in the language it will refer to individuals (as it does refer to meta-individuals in the metalanguage) and you have to start all over with something else. I think "one or more individuals" is healthier. But if you prefer some other terminology there's nothing stopping you from writing up definitions with your preferred point of view.

 

I would call {lo broda} "Something that is/are broda": I think it's enough for the most general value that is "something in a domain of plural variable", and no other description on the sumti is sufficient to describe the most general plural constant.

Using technical terms without definition is source of misleading.

Based on this simple definition, we can define "individual", "sumti that satisfies a selbri collectively" and "a set", then the readers will understand the whole aspect of gadri.

I'm not sure if it is permitted to edit the BPFK page of green line, but if you don't mind, I will try to modify the description of gadri page so that everyone will understand gadri correctly.

 

By the way, based on the fact that {lo broda} is plural constant, another problem occurs.

{lo broda} is defined as {zo'e}, and {zo'e} is defined as unspecific value.

It's defined as "elliptical/unspecified". It has a value or values, they are just not given explicitly. 

 

When {lo broda} is a plural constant, it is a specific value, and contradicts the definition of {zo'e}. 

My understanding is that {zo'e} is essentially a free variable, and a plural constant is implicitly substituted when a universe of discourse is given. If it is correct, such a description should be included on the gadri or zo'e page. If it is incorrect, some reasonable explanation is necessary.

An expression with a free variable doesn't have a truth value, it's not a complete proposition. An expression with "zo'e" is a complete proposition, so zo'e can't be a free variable. "ke'a" and "ce'u" are free variables since the bridi they appear in are incomplete and don't have a truth value by themselves.

OK, now I understand that open sentences are essentially not required in Lojban.

 

[selpa'i]

la .guskant. cu cusku di'e

> Suppose a universe of discourse is given, where {lo linji} is in a
> domain of plural variable.
> In this universe of discourse, {lo linji xi no} can be separated into
> shorter {lo linji xi pany}:
>
> lo linji xi pano cu me lo linji xi no
> i
> lo linji xi papa cu me lo linji xi no
> i
> ...

That sounds like {pagbu} to me, although all those lines should be the
same line mathematically, as they are all infinitely long. If you mean
line segments, then I really would use {pagbu}.

> Repeat the separation also for {lo linji xi pany}.
> After infinite times of separation, {lo linji} is finally separated into
> {lo mokca} which is individual:
>
> RO DA poi ke'a me lo mokca zo'u lo mokca me DA

And you can also have a {lo mokca} that refers to more than one individual.

In any case, the fact that {lo mokca} is individual does not entail that
{lo linji} does not refer to individuals.

Splitting an object and coming up with two entirely new sumti to
describe each of the two resulting parts is not the same as saying that
those two parts were {me lo <object>} all along. In other words, if I
have a single expanse of water, then {lo djacu} is an individual, even
if I have the ability to part the water (by filling it in two separate
containers for instance) and ending up with two new {lo djacu}. The
original {lo djacu} was still an individual. Splitting the water creates
new objects in the universe of discourse, because the situation changes.

> but for any shorter {lo linji}:
>
> naku lo linji me lo mokca

I would say that, since lines are not points:

no da poi linji ku'o su'o de poi mokca zo'u: da me de

No line is ever among something that is a point. And the reverse is also
true: No point is among a line. Points are parts of lines, but they
don't share the same referent(s).

> Therefore, any {lo linji} does not satisfy
> RO DA poi ke'a me lo linji zo'u lo linji me DA
>
> {lo linji} in this universe of discourse is not an individual.

It sounds to me like you are taking "individual" to mean "atomic,
non-separable thing". But individual just means that it can be
distinguished from other things as a referent.

The moment you say {lo linji} that sumti refers to something(s), and
that something is one or more individuals. How else could it be {lo broda}?

Even if you end up with a single {lo mokca} in the end, at no point does
{lo mokca cu me lo linji}, but {lo mokca cu pagbu lo linji}.

So I still cannot see at what point there was anything besides individuals.

[Gleki Arxokuna]

Sorry for intruding once again. How would you express "2/3 of my sisters like Ricky Martin" (implying that the rest don't like)? {fi'u} from L4B doesn't seem like a solution to me.

[Jorge Llambías]

On Sun, Feb 9, 2014 at 8:05 AM, guskant <gusni...@gmail.com> wrote:

Why don't you define 

{lo no broda} =ca'e {zi'o noi ke'a broda}

only for the case that PA=no?

Under the condition that there is no official plural quantifier in Lojban, the inclusion of {lo no broda} is necessary for keeping the expressiveness of Lojban equal to that of plural quantification.

If "zi'o" did what you wanted, then official Lojban would already have that expressiveness, wouldn't it?

But "zi'o" doesn't work for what you want. "zi'o sruri lo dinju" is true when some students are surrounding the building. "zi'o" doesn't say that nothing satisfies the predicate. "zi'o" changes the predicate to a new predicate that doesn't have that place. It's hard to describe what exactly the new predicate resulting from "zi'o poi tadni cu sruri" means, but it does not mean "x2 is not surrounded by students".

 

I would call {lo broda} "Something that is/are broda": I think it's enough for the most general value that is "something in a domain of plural variable", and no other description on the sumti is sufficient to describe the most general plural constant.

Using technical terms without definition is source of misleading.

One problem with using "something" is that it looks very much like a quantifier. Another problem for me (perhaps not so much for others) is that being a singular word, it seems to be talking about one thing. You sort of get around that a bit with the plural verb, "something that are broda", but that is ungrammatical English. You say "the most general value", but the whole point of plural logic is that a variable takes _values_, not _a value_.

Based on this simple definition, we can define "individual", "sumti that satisfies a selbri collectively" and "a set", then the readers will understand the whole aspect of gadri.

If by "a set" you mean, for example, "lo selcmi", then it is an individual as well. Everything is an individual in this context, there is nothing that is not an individual. 

 

I'm not sure if it is permitted to edit the BPFK page of green line, but if you don't mind, I will try to modify the description of gadri page so that everyone will understand gadri correctly.

The page doesn't appear to be locked, but I don't think it's a good idea to edit it. It's better if you create a new page with your take on things. 

[guskant]

Le dimanche 9 février 2014 21:39:10 UTC+9, selpa'i a écrit :

la .guskant. cu cusku di'e
> Suppose a universe of discourse is given, where {lo linji} is in a
> domain of plural variable.
> In this universe of discourse, {lo linji xi no} can be separated into
> shorter {lo linji xi pany}:
>
> lo linji xi pano cu me lo linji xi no
> i
> lo linji xi papa cu me lo linji xi no
> i
> ...

That sounds like {pagbu} to me, although all those lines should be the
same line mathematically, as they are all infinitely long. If you mean
line segments, then I really would use {pagbu}.

The definition of {linji} does not say that a line segment is not {linji}:

linji: x_1 se cimde pa da gi'e se cmima x_2 noi mokca

In any case, the selbri used here is not important.

Simply, in that universe of discourse, {lo linji} are recognized like that.

 

> Repeat the separation also for {lo linji xi pany}.
> After infinite times of separation, {lo linji} is finally separated into
> {lo mokca} which is individual:
>
> RO DA poi ke'a me lo mokca zo'u lo mokca me DA

And you can also have a {lo mokca} that refers to more than one individual.

In any case, the fact that {lo mokca} is individual does not entail that
{lo linji} does not refer to individuals.

Splitting an object and coming up with two entirely new sumti to
describe each of the two resulting parts is not the same as saying that
those two parts were {me lo <object>} all along. In other words, if I
have a single expanse of water, then {lo djacu} is an individual, even
if I have the ability to part the water (by filling it in two separate
containers for instance) and ending up with two new {lo djacu}. The
original {lo djacu} was still an individual. Splitting the water creates
new objects in the universe of discourse, because the situation changes.

> but for any shorter {lo linji}:
>
> naku lo linji me lo mokca

I would say that, since lines are not points:

    no da poi linji ku'o su'o de poi mokca zo'u: da me de

No line is ever among something that is a point. And the reverse is also
true: No point is among a line. Points are parts of lines, but they
don't share the same referent(s).

I don't care about that point.

Actually, I didn't need {lo mokca} in order to say that any {lo linji} are not one or more individuals.

I mentioned {lo mokca} only for clarifying the structure of {lo linji}, but it was really unnecessary.

Only I need to say is that {lo linji xi ny me lo linji xi my} continues infinitely in that universe of discourse.

In other words, this is an infinite instance of {lo re prenu cu me lo mu prenu}.

 

> Therefore, any {lo linji} does not satisfy
> RO DA poi ke'a me lo linji zo'u lo linji me DA
>
> {lo linji} in this universe of discourse is not an individual.

It sounds to me like you are taking "individual" to mean "atomic,
non-separable thing". But individual just means that it can be
distinguished from other things as a referent.

No, What you think individual is actually

X me Y ije Y me X

which is a definition of "X are the same thing as Y" of plural logic.

It does not mean individual.

 

[selpa'i]

la .guskant. cu cusku di'e

> Actually, I didn't need {lo mokca} in order to say that any {lo linji}
> are not one or more individuals.
> I mentioned {lo mokca} only for clarifying the structure of {lo linji},
> but it was really unnecessary.
> Only I need to say is that {lo linji xi ny me lo linji xi my} continues
> infinitely in that universe of discourse.
>
> In other words, this is an infinite instance of {lo re prenu cu me lo mu
> prenu}.

I'm not sure I follow.

Let's say the original single line segment L looks like this:

|-----------------------------------------------| <- {lo linji}
L

You seem to be saying that L is not an individual because we can turn it
into multiple smaller line segments A, B, C, like this:

|---------------| |---------------| |---------------|
A B C

Further, you seem to be saying that A, B, and C are all among L. You
also seem to be saying that each of A, B, C are not individuals either,
because we can further split them, like this:

|-------|-------| |-------|-------| |-------|-------|
M N O P Q R

And that M and N are among A, and so on.

Is this what you are saying?

I would say that the only line segment that is among L is L itself. A is
not among L, nor are B or C, let alone M, N, O, ...

A, B and C are *part* of L. M is *part* of A.

If you introduce new objects, then you are creating a new universe of
discourse each time, so the original singular {lo linji} is no longer
relevant. It seems like your {me} is jumping across domains.

Would you say that {lo sakta cu me lo najnimryjisra}? For me it would be
a very definite No.

[guskant]

Yes.

 

I would say that the only line segment that is among L is L itself. A is
not among L, nor are B or C, let alone M, N, O, ...

A, B and C are *part* of L. M is *part* of A.

Such a universe of discourse is of course natural and possible, but the universe of discourse given here is based on another epistemology that {lo linji xi ny cu me lo linji xi my} behaves just like {lo re prenu cu me lo mu prenu}. The only difference is that {lo linji xi my} consists of infinite {lo linji}, while {lo mu prenu} consists of finite {lo prenu}. Such a universe of discourse is also possible under the condition that you don't assert that

RO DA poi ke'a me lo linji zo'u lo linji me DA,

where RO DA is a quantified plural variable.

 

If you introduce new objects, then you are creating a new universe of
discourse each time, so the original singular {lo linji} is no longer
relevant. It seems like your {me} is jumping across domains.

 

I did not introduce new objects. those infinite number of {lo linji} were already prepared in the universe of discourse given first. 

For example, in the case of finite {lo ci prenu}, let us call the three persons p1, p2, p3. In the universe of discourse. The following sumti are all in the domain of plural variable that are prenu even if you don't mention the sumti:

p1

p2

p3

p1 jo'u p2

p2 jo'u p3

p3 jo'u p1

p1 jo'u p2 jo'u p3

Similarly, the infinite number of {lo linji} were in the domain of plural variable that are linji when the universe of discourse was given first.

Would you say that {lo sakta cu me lo najnimryjisra}? For me it would be
a very definite No.

No, but the current topic is not similar to that but to {lo re prenu cu me lo mu prenu}.

 

[guskant]

Le dimanche 9 février 2014 22:01:51 UTC+9, la gleki a écrit :

Sorry for intruding once again. How would you express "2/3 of my sisters like Ricky Martin" (implying that the rest don't like)? {fi'u} from L4B doesn't seem like a solution to me.

re fi'u ci loi mi mensi cu nelci rymy

says that correctly. Using the following definitions:

piPA sumti lo piPA si'e be pa me sumti

loi [PA] broda lo gunma be lo [PA] broda

{re fi'u ci loi mi mensi} can be expanded as follows:

lo re fi'u ci si'e be pa me lo gunma be lo mi mensi

It is exactly "2/3 of my sisters". The sentence above is meaningful if you have 3n sisters (n=1,2,...). Moreover, because Lojban numbers are used exclusively, it means also that 

naku zo'u pa fi'u ci loi mi mensi cu nelci rymy

[guskant]

Le dimanche 9 février 2014 22:12:31 UTC+9, xorxes a écrit :

On Sun, Feb 9, 2014 at 8:05 AM, guskant <gusni...@gmail.com> wrote:

Why don't you define 

{lo no broda} =ca'e {zi'o noi ke'a broda}

only for the case that PA=no?

Under the condition that there is no official plural quantifier in Lojban, the inclusion of {lo no broda} is necessary for keeping the expressiveness of Lojban equal to that of plural quantification.

If "zi'o" did what you wanted, then official Lojban would already have that expressiveness, wouldn't it?

But "zi'o" doesn't work for what you want. "zi'o sruri lo dinju" is true when some students are surrounding the building. "zi'o" doesn't say that nothing satisfies the predicate. "zi'o" changes the predicate to a new predicate that doesn't have that place. It's hard to describe what exactly the new predicate resulting from "zi'o poi tadni cu sruri" means, but it does not mean "x2 is not surrounded by students".

 

I see. However, under the conditions that:

- {lo broda} is defined as a plural constant, and 

- a logical axiom for a plural constant C is given as

F(C) {inaja} there is X such that F(X),

{lo no broda} is now excluded from the language.

In order to take it back and to give a reasonable meaning for it, we need an additional definition applied only to {lo no broda}.

How do you think the following suggestion?

{lo no broda} =ca'e {naku lo broda} 

only for the case that PA=no.

{naku lo broda} should be actually {naku lo su'oi broda} with a plural quantifier {su'oi} that you once proposed, but it is not necessary to mention it in the definition if the innner quantifiers are in general an implicit expression of plural quantifiers.

 

I would call {lo broda} "Something that is/are broda": I think it's enough for the most general value that is "something in a domain of plural variable", and no other description on the sumti is sufficient to describe the most general plural constant.

Using technical terms without definition is source of misleading.

One problem with using "something" is that it looks very much like a quantifier. Another problem for me (perhaps not so much for others) is that being a singular word, it seems to be talking about one thing. You sort of get around that a bit with the plural verb, "something that are broda", but that is ungrammatical English. You say "the most general value", but the whole point of plural logic is that a variable takes _values_, not _a value_.

Those problems are caused by the English language, and then I would better abandon using "something".

I would suggest instead:

{lo broda} =ca'e "what is/are broda" 

With this definition, it seems that the problems you remarked on will be avoided.

 

Based on this simple definition, we can define "individual", "sumti that satisfies a selbri collectively" and "a set", then the readers will understand the whole aspect of gadri.

If by "a set" you mean, for example, "lo selcmi", then it is an individual as well. Everything is an individual in this context, there is nothing that is not an individual. 

 

Of course a set is an individual. Once the terms "individual" and "set" are defined, it will be easy to explain that {lo selcmi} is one or more individuals:

{lo selcmi} is a set or sets.

a set is an individual: when {lo selcmi} refers to one set,

RO DA poi ke'a me lo selcmi zo'u lo selcmi me DA

If definition of terms are not given, "a set is an individual" cannot be explained.

 

I'm not sure if it is permitted to edit the BPFK page of green line, but if you don't mind, I will try to modify the description of gadri page so that everyone will understand gadri correctly.

The page doesn't appear to be locked, but I don't think it's a good idea to edit it. It's better if you create a new page with your take on things. 

OK, I will not touch the gadri page.

 

[selpa'i]

la .guskant. cu cusku di'e
> Le lundi 10 février 2014 00:55:01 UTC+9, selpa'i a écrit :
> Let's say the original single line segment L looks like this:
>
> |-----------------------------------------------| <- {lo linji}
> L
>
> You seem to be saying that L is not an individual because we can
> turn it
> into multiple smaller line segments A, B, C, like this:
>
> |---------------| |---------------| |---------------|
> A B C
>
> Further, you seem to be saying that A, B, and C are all among L. You
> also seem to be saying that each of A, B, C are not individuals either,
> because we can further split them, like this:
>
> |-------|-------| |-------|-------| |-------|-------|
> M N O P Q R
>
> And that M and N are among A, and so on.
>
> Is this what you are saying?
>
>
>
> Yes.

But how does that work? If the original {lo linji} (L) is an individual,
then only itself can be among itself. On the other hand, if it is *not*
an individual, then we cannot call it {lo linji} in the first place. You
could say that {lo linji} is more than one individual, and then the same
things that applied to the singular L would apply again for each of the
referents of the "more than one individual" L. At some point through the
taxonomy, you must arrive at an individual or individuals and then you
can't go further and say that even smaller things are among that
individual. Even the shortest line doesn't have {lo mokca} {me} it.

> For example, in the case of finite {lo ci prenu}, let us call the three
> persons p1, p2, p3. In the universe of discourse. The following sumti
> are all in the domain of plural variable that are prenu even if you
> don't mention the sumti:
> p1
> p2
> p3
> p1 jo'u p2
> p2 jo'u p3
> p3 jo'u p1
> p1 jo'u p2 jo'u p3

Yes.

But I don't quite see how this is the same case. If this is what you
were going for with the {linji} example, then it doesn't show anything
that qualifies as not being one or more individuals.

The 7 possible plural values for {prenu} above are all one or more
individuals. Listing infinitely many more would not change that.

> Similarly, the infinite number of {lo linji} were in the domain of
> plural variable that are linji when the universe of discourse was given
> first.

Infinity does not preclude individualness. If you have an infinite
number of "things", then you just have infinitely many individuals.

[guskant]

Le lundi 10 février 2014 21:38:06 UTC+9, selpa'i a écrit :

la .guskant. cu cusku di'e
> Le lundi 10 février 2014 00:55:01 UTC+9, selpa'i a écrit :
>     Let's say the original single line segment L looks like this:
>
>     |-----------------------------------------------|   <- {lo linji}
>                               L
>
>     You seem to be saying that L is not an individual because we can
>     turn it
>     into multiple smaller line segments A, B, C, like this:
>
>     |---------------| |---------------| |---------------|
>               A                 B                 C
>
>     Further, you seem to be saying that A, B, and C are all among L. You
>     also seem to be saying that each of A, B, C are not individuals either,
>     because we can further split them, like this:
>
>     |-------|-------| |-------|-------| |-------|-------|
>           M       N         O       P         Q       R
>
>     And that M and N are among A, and so on.
>
>     Is this what you are saying?
>
>
>
> Yes.

But how does that work? If the original {lo linji} (L) is an individual,
then only itself can be among itself. On the other hand, if it is *not*
an individual, then we cannot call it {lo linji} in the first place. You

The individuality is not an necessary condition for being {lo linji}. A special {lo linji} such that {RO DA poi ke'a me lo linji zo'u lo linji cu me DA} is an individual.

 

could say that {lo linji} is more than one individual, and then the same
things that applied to the singular L would apply again for each of the
referents of the "more than one individual" L. At some point through the
taxonomy, you must arrive at an individual or individuals and then you
can't go further and say that even smaller things are among that
individual. Even the shortest line doesn't have {lo mokca} {me} it.

There is no shortest line. That is the point for proving that any {lo linji} in this universe of discourse cannot be an individual.

 

> For example, in the case of finite {lo ci prenu}, let us call the three
> persons p1, p2, p3. In the universe of discourse. The following sumti
> are all in the domain of plural variable that are prenu even if you
> don't mention the sumti:
> p1
> p2
> p3
> p1 jo'u p2
> p2 jo'u p3
> p3 jo'u p1
> p1 jo'u p2 jo'u p3

Yes.

But I don't quite see how this is the same case. If this is what you
were going for with the {linji} example, then it doesn't show anything
that qualifies as not being one or more individuals.

The 7 possible plural values for {prenu} above are all one or more
individuals. Listing infinitely many more would not change that.

Not an infinite number of {lo linji} itself but an infinite number of procedures of affirming that {lo linji xi ny cu me lo linji xi my i ku'i naku lo linji xi my cu me lo linji xi ny} do prove that every {lo linji} is not one or more individuals.

 

> Similarly, the infinite number of {lo linji} were in the domain of
> plural variable that are linji when the universe of discourse was given
> first.

Infinity does not preclude individualness. If you have an infinite
number of "things", then you just have infinitely many individuals.

{lo linji} in that universe of discourse are not individuals but an infinite number of non-individuals, because every {lo linji xi my} has always another {lo linji xi ny} such that

{lo linji xi ny cu me lo linji xi my i ku'i naku lo linji xi my cu me lo linji xi ny}, and this proposition contradicts the condition for individual {RO DA poi ke'a me lo linji xi my zo'u lo linji xi my cu me DA}. Therefore, every {lo linji} is neither an individual nor individuals.

 

[John E Clifford]

This muddle has gotten out of hand.  At least the following words are being used in at least two senses, often in the same sentence:"individual", "line (segment)", "among" ('me'), "plural".  Further, at least three languages are involved: ordinary English, mathematics and plural logic/mereology.  I'm not sure that sorting all these out will help (there are deeply paradoxical notions here), but it might help get down to the real problems and away from the superficial confusions.

---

From: guskant <gusni...@gmail.com>
To: loj...@googlegroups.com

Sent: Monday, February 10, 2014 8:19 AM

Subject: Re: [lojban] Individuals and xorlo

Le lundi 10 février 2014 21:38:06 UTC+9, selpa'i a écrit :

la .guskant. cu cusku di'e
> Le lundi 10 février 2014 00:55:01 UTC+9, selpa'i a écrit :
>     Let's say the original single line segment L looks like this:
>

>     |----------------------------- ------------------|   <- {lo linji}

[selpa'i]

la .guskant. cu cusku di'e

> Le lundi 10 février 2014 00:55:01 UTC+9, selpa'i a écrit : Would you

> say that {lo sakta cu me lo najnimryjisra}? For me it would be a very
> definite No.
>
> No, but the current topic is not similar to that but to {lo re prenu
> cu me lo mu prenu}.

Okay, then we still don't understand each other. I (mis-)understood your
{linji} example in a way that is very much like {lo sakta cu me lo
najnimryjisra} and you said my graphical representation described your
views correctly. But judging by your further claims, I now think that
that cannot be the case. So you must have meant something else.

> {lo linji} in that universe of discourse are not individuals but an
> infinite number of non-individuals, because every {lo linji xi my}

> has always another {lo linji xi ny} such that {lo linji xi ny cu me

> lo linji xi my i ku'i naku lo linji xi my cu me lo linji xi ny}, and
> this proposition contradicts the condition for individual {RO DA poi
> ke'a me lo linji xi my zo'u lo linji xi my cu me DA}. Therefore,
> every {lo linji} is neither an individual nor individuals.

Let's try again. Let's use something that can just as easily be imagined
to be infinite: {lo sidbo}. There are infinitely many possible ideas and
thoughts. Let's say that {lo sidbo} contains *all* of them and therefore
has infinitely many referents.

I will enumerate all the referents of {lo sidbo} as s1, s2, s3...

1) [ s1 , s2 , s3, s4 , ... ]

continuing indefinitely.

This first infinitely huge {lo sidbo} can be (randomly) split apart like
this:

2) [ [ s1 , s312 , s15 , ... ] , [ s3 , s9232 , ... ] , [ ... ] ]

Where each sub-bracket again contains infinitely many things that
{sidbo} and each sub-bracket is among {lo sidbo} from step 1.

We can repeat this process infinitely often for each new sub-grouping,
making more and more sub-groupings which will get smaller and smaller
with each step, but will always remain infinite. (Each grouping will
also represent a possible value for a plural variable)

Do you agree up to this point?

If so, why do you think that this entails that {lo sidbo} does not refer
to one or more individuals?

In reality, the []-brackets don't actually do anything other than select
multiple values at once. They don't create new individuals, which would
happen with sets or "masses".

This is as far as I can get trying to understand your argument. Why any
of this should indicate that we can sometimes deal with things other
than individuals is still completely unclear to me.

For me the situation is very simple: Each of the s_x above is an
individual and {lo sidbo} refers to all of them.

Individuals are not a special case to me, they are the only case.

And maybe this helps: Do you see a difference between "referent" and
"individual"? What do you consider the difference to be?

[Jorge Llambías]

On Mon, Feb 10, 2014 at 12:45 AM, guskant <gusni...@gmail.com> wrote:

 However, under the conditions that:

- {lo broda} is defined as a plural constant, and 

- a logical axiom for a plural constant C is given as

F(C) {inaja} there is X such that F(X),

{lo no broda} is now excluded from the language.

Yes, in the same sense that "lo ni'u pa broda" is exluded. They are grammatical expressions but not with any standard meaning.

 

In order to take it back and to give a reasonable meaning for it, we need an additional definition applied only to {lo no broda}.

How do you think the following suggestion?

{lo no broda} =ca'e {naku lo broda} 

only for the case that PA=no.

I think that's how it will be usually understood, yes. I wouldn't make it an official definition though, just because it's unnecessary and breaks the simplicity of other rules (such as "lo PA broda" being a referring expression).

 

{naku lo broda} should be actually {naku lo su'oi broda} with a plural quantifier {su'oi} that you once proposed, but it is not necessary to mention it in the definition if the innner quantifiers are in general an implicit expression of plural quantifiers.

Actually, it should be just "naku lo [su'o] broda", with a generic "lo [su'o] broda", or "naku su'oi lo broda". The so called "inner quantifiers" are not actually true quantifiers but just cardinalities, and only natural numbers or things like "su'o", "za'u", "so'i" etc that can stand for natural numbers really make sense there. I wouldn't know what to make of "lo su'oi broda". 

 

Those problems are caused by the English language, and then I would better abandon using "something".

I would suggest instead:

{lo broda} =ca'e "what is/are broda" 

With this definition, it seems that the problems you remarked on will be avoided.

OK. I don't vouch for the idiomaticity of the results if you use that for direct translations though.

[Jorge Llambías]

On Mon, Feb 10, 2014 at 11:19 AM, guskant <gusni...@gmail.com> wrote:

{lo linji} in that universe of discourse are not individuals but an infinite number of non-individuals, 

I think you want "sirji" (segments), not "linji (lines). In the universe of discourse under consideration there are no segments or lines, there are only points. In that universe, we can use the predicate "linji" but with a slightly different definition than the standard: "x1 are all the points aligned with points x2". And "sirji" can be redefined for the points only universe as "x1 are all the points aligned between point x2 and (different) point x3".

Now "lo sirji be abu bei by cu me lo sirji be abu bei cy" is fine, "the points aligned between point a and point b are among the points aligned between point a and point c". As you say, there is no individual "lo sirji" in this universe. "lo sirji" always refers to an infinite number of points.

The problem arises when you say that "lo sirji is a non-individual". It is not. lo sirji are just points, not "an" anything. You may call it a non-individual in some metalanguage, but in the language you can't, because there are nothing but points in the universe, nothing else. "lo pa sirji", in this universe of discourse, is nonsense, because the only things that can sirji cannot do it alone, they must always do it collectively in infinite numbers. There's only "lo ci'i sirji", "the infinite number of points aligned between two points". If you want to quantify over segments, for example if you want to say something about two segments, you are forced to move to a universe of discourse that has segments in it.

[guskant]

Yes.

 

If so, why do you think that this entails that {lo sidbo} does not refer
to one or more individuals?

{lo sidbo} does not refer to one or more individuals, because, for every {lo sidbo xi my}, there is another {lo sidbo xi ny} such that {lo sidbo xi ny cu me lo sidbo xi my i naku lo sidbo xi my cu me lo sidbo xi ny},  therefore {lo sidbo xi my} does not satisfy the condition for being an individual {RO DA poi ke'a me lo sidbo xi my zo'u lo sidbo xi my cu me DA}. It means that there is no individual {lo sidbo} in this universe of discourse. Therefore {lo sidbo} is neither an individual nor individuals.

 

In reality, the []-brackets don't actually do anything other than select
multiple values at once. They don't create new individuals, which would
happen with sets or "masses".

This is as far as I can get trying to understand your argument. Why any
of this should indicate that we can sometimes deal with things other
than individuals is still completely unclear to me.

For me the situation is very simple: Each of the s_x above is an
individual and {lo sidbo} refers to all of them.

Each of the s_x above is non-individual because of the proof mentioned above.

 

Individuals are not a special case to me, they are the only case.

And maybe this helps: Do you see a difference between "referent" and
"individual"? What do you consider the difference to be?

Yes. The identity of referent is defined as follows:

"X are the same thing as Y" =ca'e {X me Y ije Y me X}

On the other hand, "an individual" is defined as follows:

"X is an individual" =ca'e {RO DA poi ke'a me X zo'u X me DA}

Examples:

- {by jo'u cy} and {cy jo'u dy} are not the same referent because {naku zo'u by jo'u cy me cy jo'u dy ije cy jo'u dy me by jo'u cy};

- {by jo'u cy} and {cy jo'u by} are the same referent because {by jo'u cy me cy jo'u by ije cy jo'u by me by jo'u cy};

- {by jo'u cy} is not an individual, because {by me by jo'u cy i naku by jo'u cy me by}, therefore {by jo'u cy} does not satisfy the condition for an individual {RO DA poi ke'a me by jo'u cy zo'u by jo'u cy me DA}.

- if no other referent besides {by} is x1 of {me by}, then {by} is an individual because {RO DA poi ke'a me by zo'u by me DA} is true in this universe of discourse.

 

[guskant]

Le mardi 11 février 2014 05:42:45 UTC+9, xorxes a écrit :

On Mon, Feb 10, 2014 at 12:45 AM, guskant <gusni...@gmail.com> wrote:

 However, under the conditions that:

- {lo broda} is defined as a plural constant, and 

- a logical axiom for a plural constant C is given as

F(C) {inaja} there is X such that F(X),

{lo no broda} is now excluded from the language.

Yes, in the same sense that "lo ni'u pa broda" is exluded. They are grammatical expressions but not with any standard meaning.

 

In order to take it back and to give a reasonable meaning for it, we need an additional definition applied only to {lo no broda}.

How do you think the following suggestion?

{lo no broda} =ca'e {naku lo broda} 

only for the case that PA=no.

I think that's how it will be usually understood, yes. I wouldn't make it an official definition though, just because it's unnecessary and breaks the simplicity of other rules (such as "lo PA broda" being a referring expression).

 

OK, then I will give it as an unofficial interpretation on my future personal gadri page, because it is necessary for me to include a conversation like

- lo xo prenu cu jmaji gi'e jukpa gi'e citka

 - no

in the language.

 

{naku lo broda} should be actually {naku lo su'oi broda} with a plural quantifier {su'oi} that you once proposed, but it is not necessary to mention it in the definition if the innner quantifiers are in general an implicit expression of plural quantifiers.

Actually, it should be just "naku lo [su'o] broda", with a generic "lo [su'o] broda", or "naku su'oi lo broda". The so called "inner quantifiers" are not actually true quantifiers but just cardinalities, and only natural numbers or things like "su'o", "za'u", "so'i" etc that can stand for natural numbers really make sense there. I wouldn't know what to make of "lo su'oi broda". 

 

Those problems are caused by the English language, and then I would better abandon using "something".

I would suggest instead:

{lo broda} =ca'e "what is/are broda" 

With this definition, it seems that the problems you remarked on will be avoided.

OK. I don't vouch for the idiomaticity of the results if you use that for direct translations though.

Thank you for your opinion. I will include this interpretation on my future personal gadri page.

 

[guskant]

Le mardi 11 février 2014 06:15:45 UTC+9, xorxes a écrit :

On Mon, Feb 10, 2014 at 11:19 AM, guskant <gusni...@gmail.com> wrote:

{lo linji} in that universe of discourse are not individuals but an infinite number of non-individuals, 

I think you want "sirji" (segments), not "linji (lines). In the universe of discourse under consideration there are no segments or lines, there are only points. In that universe, we can use the predicate "linji" but with a slightly different definition than the standard: "x1 are all the points aligned with points x2". And "sirji" can be redefined for the points only universe as "x1 are all the points aligned between point x2 and (different) point x3".

I don't think the definition of {x1 linji x2} =ca'e {x1 se cimde pa da gi'e se cmima x2 noi mokca} excludes line segments, because cimde_2 may have a finite interval. We may call it {sirji} if you prefer, but actually the straightness is unnecessary for the current topic.

 

Now "lo sirji be abu bei by cu me lo sirji be abu bei cy" is fine, "the points aligned between point a and point b are among the points aligned between point a and point c". As you say, there is no individual "lo sirji" in this universe. "lo sirji" always refers to an infinite number of points.

The problem arises when you say that "lo sirji is a non-individual". It is not. lo sirji are just points, not "an" anything. You may call it a non-individual in some metalanguage, but in the language you can't, because there are nothing but points in the universe, nothing else. "lo pa sirji", in this universe of discourse, is nonsense, because the only things that can sirji cannot do it alone, they must always do it collectively in infinite numbers. There's only "lo ci'i sirji", "the infinite number of points aligned between two points". If you want to quantify over segments, for example if you want to say something about two segments, you are forced to move to a universe of discourse that has segments in it.

As you remarked on, our mathematical knowledge of lines prevented us from understanding, and la selpa'i has kindly changed our topic to {lo sidbo}.

 

[selpa'i]

la .guskant. cu cusku di'e

> {lo sidbo} does not refer to one or more individuals, because, for every
> {lo sidbo xi my}, there is another {lo sidbo xi ny} such that {lo sidbo
> xi ny cu me lo sidbo xi my i naku lo sidbo xi my cu me lo sidbo xi ny},
> therefore {lo sidbo xi my} does not satisfy the condition for being an
> individual {RO DA poi ke'a me lo sidbo xi my zo'u lo sidbo xi my cu me
> DA}. It means that there is no individual {lo sidbo} in this universe of
> discourse. Therefore {lo sidbo} is neither an individual nor individuals.

To me it looks more like this entire process of sub-grouping is a
strawman. I don't see why I should be forced to sub-divide {lo sidbo}
into infinitely large {lo sidbo be ny} when I could just as well just
look at each individual {sidbo} in isolation.

[ s1 , s2 , s3 , ... ]

Why can't I just look at s1 by itself, and s2 by itself and so on? For
each s_x, it holds that:

ro'oi da poi ke'a me s_x zo'u: s_x me da

So each s_x is an individual.

> And maybe this helps: Do you see a difference between "referent" and
> "individual"? What do you consider the difference to be?
>
>
>
> Yes. The identity of referent is defined as follows:
> "X are the same thing as Y" =ca'e {X me Y ije Y me X}
>
> On the other hand, "an individual" is defined as follows:
> "X is an individual" =ca'e {RO DA poi ke'a me X zo'u X me DA}

Each s_x satisfies the definition of "individual". Any pair of {s_x,
s_y} fails the "sameness" condition. The two definitions don't exclude
each other.

Every sumti has certain referents, and it might have the same referents
as another sumti, in which case the two sumti are "the same", or they
might have different referents, in which case the two sumti are not the
same. In either case, the referents themselves are individuals.

[guskant]

Le vendredi 14 février 2014 20:59:56 UTC+9, selpa'i a écrit :

la .guskant. cu cusku di'e
> {lo sidbo} does not refer to one or more individuals, because, for every
> {lo sidbo xi my}, there is another {lo sidbo xi ny} such that {lo sidbo
> xi ny cu me lo sidbo xi my i naku lo sidbo xi my cu me lo sidbo xi ny},
>   therefore {lo sidbo xi my} does not satisfy the condition for being an
> individual {RO DA poi ke'a me lo sidbo xi my zo'u lo sidbo xi my cu me
> DA}. It means that there is no individual {lo sidbo} in this universe of
> discourse. Therefore {lo sidbo} is neither an individual nor individuals.

To me it looks more like this entire process of sub-grouping is a
strawman. I don't see why I should be forced to sub-divide {lo sidbo}
into infinitely large {lo sidbo be ny} when I could just as well just
look at each individual {sidbo} in isolation.

It is because the following proposition is given as an axiom in the universe of discourse (UD1) on the current topic.

P1: 

ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de

In this universe of discourse, the following proposition is a theorem.

P2:

naku ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da

As long as talking about UD1, we are forced to think that P2, that is, there is no individual {lo sidbo}, because it is a proved theorem.

On the other hand, it is also possible that we talk about such a universe of discourse (UD2) that the following proposition is an axiom or a theorem.

P3:

ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da

In UD2, {lo sidbo} is an individual, and a negation of P1 is proved.

Because neither P1 nor P3 is tautology, we are not forced to think that one of them is always true for all the universes of discourse. We have freedom to choose non-logical axioms and a universe of discourse according to context.

 

[ s1 , s2 , s3 , ... ]

Why can't I just look at s1 by itself, and s2 by itself and so on? For
each s_x, it holds that:

   ro'oi da poi ke'a me s_x zo'u: s_x me da

So each s_x is an individual.

That is UD2, not UD1.

 

>     And maybe this helps: Do you see a difference between "referent" and
>     "individual"? What do you consider the difference to be?
>
>
>
> Yes. The identity of referent is defined as follows:
> "X are the same thing as Y" =ca'e {X me Y ije Y me X}
>
> On the other hand, "an individual" is defined as follows:
> "X is an individual" =ca'e {RO DA poi ke'a me X zo'u X me DA}

Each s_x satisfies the definition of "individual". Any pair of {s_x,
s_y} fails the "sameness" condition. The two definitions don't exclude
each other.

The universe of discourse in which each s_x satisfies the definition of "individual" is UD2, not UD1.

 

Every sumti has certain referents, and it might have the same referents
as another sumti, in which case the two sumti are "the same", or they
might have different referents, in which case the two sumti are not the
same. In either case, the referents themselves are individuals.

In UD2, yes. In UD1, no. It depends on our choice of universe of discourse, on the context, not on the language.

[Jorge Llambías]

On Fri, Feb 14, 2014 at 8:36 PM, guskant <gusni...@gmail.com> wrote:

It is because the following proposition is given as an axiom in the universe of discourse (UD1) on the current topic.

P1: 

ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de

 From P1 I get "no da me lo sidbo".

 

In this universe of discourse, the following proposition is a theorem.

P2:

naku ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da

As long as talking about UD1, we are forced to think that P2, that is, there is no individual {lo sidbo}, because it is a proved theorem.

I don't see how P2 follows from P1.

Also, in P2, "lo sidbo" could not refer to a single individual, but it could refer to two individuals. Suppose it refers to two individual ideas I had this morning. Then P2 is true: It is not the case that for every X among those two ideas, those two ideas are among X" (in particular for each one of the ideas, the two ideas are not among it. You must have meant something else.

Because neither P1 nor P3 is tautology, we are not forced to think that one of them is always true for all the universes of discourse. We have freedom to choose non-logical axioms and a universe of discourse according to context.

Even granting that, I think that what we're missing is some motivation for such a seemingly strange universe of discourse. Are there any predicates in natlangs that tend to behave that way? My prediction is that if there was some predicate broda that tended to satisfy P1, it would quickly tend to be replaced by another brode such that ro'oi da poi proda ku'o su'o de poi brode zo'u de gunma da, and then "lo brode", which would have individual referents, would be used instead of "lo broda".

[guskant]

Le samedi 15 février 2014 10:55:19 UTC+9, xorxes a écrit :

On Fri, Feb 14, 2014 at 8:36 PM, guskant <gusni...@gmail.com> wrote:

It is because the following proposition is given as an axiom in the universe of discourse (UD1) on the current topic.

P1: 

ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de

 From P1 I get "no da me lo sidbo".

 

If another axiom that is equivalent to P3 were given on UD1, yes, we would get "no da me lo sidbo". However, we did not give P3 or the equivalent as an axiom on UD1.

 

In this universe of discourse, the following proposition is a theorem.

P2:

naku ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da

As long as talking about UD1, we are forced to think that P2, that is, there is no individual {lo sidbo}, because it is a proved theorem.

I don't see how P2 follows from P1.

Also, in P2, "lo sidbo" could not refer to a single individual, but it could refer to two individuals. Suppose it refers to two individual ideas I had this morning. Then P2 is true: It is not the case that for every X among those two ideas, those two ideas are among X" (in particular for each one of the ideas, the two ideas are not among it. You must have meant something else.

Here is the proof of P2.

da'i 

ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da (to lo se sruma toi)

iseni'ibo

naku su'oi da poi ke'a me lo sidbo ku'o naku zo'u lo sidbo cu me da

iseni'ibo

naku su'oi da poi ke'a me lo sidbo zo'u naku lo sidbo cu me da

iseni'ibo

naku su'oi da zo'u da me lo sidbo ije naku lo sidbo cu me da

iseni'ibo

naku su'oi da zo'u da me lo sidbo ijenai lo sidbo cu me da (to lo bridi xi pa toi)

ita'o

ge

lo sidbo cu me lo sidbo (to lo se ckaji be zo me toi)

gi

ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de (to P1 toi)

iseni'ibo

su'oi de zo'u de me lo sidbo ijenai lo sidbo cu me de (to lo bridi xi re toi)

iku'i 

lo bridi xi re cu natfe lo bridi xi pa

iseni'ibo

naku ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da

uo

It is thus proved that {lo sidbo} is not an individual.

Moreover, it is also proved that {lo sidbo} is not individuals using a property of jo'u:

da'i 

lo sidbo cu me A jo'u B ije A jo'u B cu me lo sidbo ({lo sidbo} is identical to A jo'u B)

ige

A me A jo'u B 

gi

B me A jo'u B

iseni'ibo

ge

A me lo sidbo

gi

B me lo sidbo

i la'e di'u lu'u joi P1 cu nibli lo simsa be lo bridi xi re

iseni'ibo 

ge

naku ro'oi da poi ke'a me A zo'u A cu me da

gi

naku ro'oi da poi ke'a me B zo'u B cu me da

uo

It is thus proved that {lo sidbo} is not individuals.

 

Because neither P1 nor P3 is tautology, we are not forced to think that one of them is always true for all the universes of discourse. We have freedom to choose non-logical axioms and a universe of discourse according to context.

Even granting that, I think that what we're missing is some motivation for such a seemingly strange universe of discourse. Are there any predicates in natlangs that tend to behave that way? My prediction is that if there was some predicate broda that tended to satisfy P1, it would quickly tend to be replaced by another brode such that ro'oi da poi proda ku'o su'o de poi brode zo'u de gunma da, and then "lo brode", which would have individual referents, would be used instead of "lo broda".

I understand that giving an axiom

{ro'oi da su'oi de ro'oi di poi ke'a me de zo'u de me di ije de me da}

(for all X there is Y such that Y is individual and Y {me} X)

is very useful, and also necessary for conforming to mereology with atoms. 

Still, we cannot assert this proposition to be a common axiom to all the universes of discourse, because 

"Something that needs to be noted in general: we, the BPFK, made a consensus decision that we do not make rulings on ontological or metaphysical issues." 

http://www.lojban.org/tiki/How+to+use+xorlo

Asserting "ro'oi da su'oi de" as a common axiom is indeed an ontological commitment, and violates the principle of xorlo.

 

[Jorge Llambías]

On Sat, Feb 15, 2014 at 10:45 AM, guskant <gusni...@gmail.com> wrote:

Le samedi 15 février 2014 10:55:19 UTC+9, xorxes a écrit :

On Fri, Feb 14, 2014 at 8:36 PM, guskant <gusni...@gmail.com> wrote:

It is because the following proposition is given as an axiom in the universe of discourse (UD1) on the current topic.

P1: 

ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de

 From P1 I get "no da me lo sidbo".

 

If another axiom that is equivalent to P3 were given on UD1, yes, we would get "no da me lo sidbo". However, we did not give P3 or the equivalent as an axiom on UD1.

Why doesn't "no da me lo sidbo" follow directly from just P1? 

Suppose "no da me lo sidbo" is false. Then "su'o da me lo sidbo" is true. Then "su'oi da poi ke'a me lo sidbo ku'o no'oi de zo'u de me da ijenai da me de", which contradicts P1. So under P1, "no da me lo sidbo" must be true.

 

 

Here is the proof of P2.

Yes, sorry, P2 does follow from P1. I was confused about something else. P2 says that lo sidbo is not a single individual. But from P1 you can derive a stronger theorem, not just that lo sidbo is not one individual, but also that there are no individuals at all among lo sidbo.

 

Moreover, it is also proved that {lo sidbo} is not individuals using a property of jo'u:

Indeed, that follows from P1, but not just from P2. I was slightly confused because P2 is too weak for what I thought you were saying, which is that lo sidbo is not one or more individuals. 

I understand that giving an axiom

{ro'oi da su'oi de ro'oi di poi ke'a me de zo'u de me di ije de me da}

(for all X there is Y such that Y is individual and Y {me} X)

is very useful, and also necessary for conforming to mereology with atoms. 

Still, we cannot assert this proposition to be a common axiom to all the universes of discourse, because 

"Something that needs to be noted in general: we, the BPFK, made a consensus decision that we do not make rulings on ontological or metaphysical issues." 

http://www.lojban.org/tiki/How+to+use+xorlo

(That page has a few of strange assertions, so I would take it with a grain of salt, but I agree about not making rulings on ontological or metaphysical issues.) 

 

Asserting "ro'oi da su'oi de" as a common axiom is indeed an ontological commitment, and violates the principle of xorlo.

I'm not necessarily disagreeing with you. I'm just curious about what are the things you could say that don't involve individuals. What type of discourse would you analyse as taking place in a universe without individuals? 

[guskant]

Le dimanche 16 février 2014 01:31:01 UTC+9, xorxes a écrit :

On Sat, Feb 15, 2014 at 10:45 AM, guskant <gusni...@gmail.com> wrote:

Le samedi 15 février 2014 10:55:19 UTC+9, xorxes a écrit :

On Fri, Feb 14, 2014 at 8:36 PM, guskant <gusni...@gmail.com> wrote:

It is because the following proposition is given as an axiom in the universe of discourse (UD1) on the current topic.

P1: 

ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de

 From P1 I get "no da me lo sidbo".

 

If another axiom that is equivalent to P3 were given on UD1, yes, we would get "no da me lo sidbo". However, we did not give P3 or the equivalent as an axiom on UD1.

Why doesn't "no da me lo sidbo" follow directly from just P1? 

Suppose "no da me lo sidbo" is false. Then "su'o da me lo sidbo" is true. Then "su'oi da poi ke'a me lo sidbo ku'o no'oi de zo'u de me da ijenai da me de", which contradicts P1. So under P1, "no da me lo sidbo" must be true.

 

Sorry, I was confused it with {no'oi da me lo sidbo}. 

{no da me lo sidbo} is true under only P1. For {no'oi da me lo sidbo}, both P1 and P3 are required, though.

 

 

Here is the proof of P2.

Yes, sorry, P2 does follow from P1. I was confused about something else. P2 says that lo sidbo is not a single individual. But from P1 you can derive a stronger theorem, not just that lo sidbo is not one individual, but also that there are no individuals at all among lo sidbo.

 

Moreover, it is also proved that {lo sidbo} is not individuals using a property of jo'u:

Indeed, that follows from P1, but not just from P2. I was slightly confused because P2 is too weak for what I thought you were saying, which is that lo sidbo is not one or more individuals. 

I understand that giving an axiom

{ro'oi da su'oi de ro'oi di poi ke'a me de zo'u de me di ije de me da}

(for all X there is Y such that Y is individual and Y {me} X)

is very useful, and also necessary for conforming to mereology with atoms. 

Still, we cannot assert this proposition to be a common axiom to all the universes of discourse, because 

"Something that needs to be noted in general: we, the BPFK, made a consensus decision that we do not make rulings on ontological or metaphysical issues." 

http://www.lojban.org/tiki/How+to+use+xorlo

(That page has a few of strange assertions, so I would take it with a grain of salt, but I agree about not making rulings on ontological or metaphysical issues.) 

 

Asserting "ro'oi da su'oi de" as a common axiom is indeed an ontological commitment, and violates the principle of xorlo.

I'm not necessarily disagreeing with you. I'm just curious about what are the things you could say that don't involve individuals. What type of discourse would you analyse as taking place in a universe without individuals? 

I meant I was deceived by the description on the gadri page that {lo broda} "refers generically to any or some individual or individuals". Because I knew what is among and what is individual, I believed that "individual" on the page is something different from what is defined in the theory of among. Actually, the word "individual" is not necessary for definition of {lo}. If {lo} were first defined, and after that "individual" were defined, then I would not have been deceived.

Whether {ro'oi da su'oi de ro'oi di poi ke'a me de zo'u de me di ije de me da} is applied or not to a universe of discourse is not always important in usual conversation. We can talk with each other without mentioning individuals:

- xu do djica tu'a lo ckafi 

 - go'i iji'a tu'a lo sakta

It is not necessary to mention that {lo ckafi} and {lo sakta} are individuals. They can exist as non-individual, as long as we don't apply an outer quantifier to them.

 

[Jorge Llambías]

On Sun, Feb 16, 2014 at 4:40 AM, guskant <gusni...@gmail.com> wrote:

I meant I was deceived by the description on the gadri page that {lo broda} "refers generically to any or some individual or individuals". Because I knew what is among and what is individual, I believed that "individual" on the page is something different from what is defined in the theory of among. Actually, the word "individual" is not necessary for definition of {lo}. If {lo} were first defined, and after that "individual" were defined, then I would not have been deceived.

I agree that the definition is not ideal. It's just the least bad we could come up with at the time. I prefer the one in Lojban.  

Whether {ro'oi da su'oi de ro'oi di poi ke'a me de zo'u de me di ije de me da} is applied or not to a universe of discourse is not always important in usual conversation. We can talk with each other without mentioning individuals:

- xu do djica tu'a lo ckafi 

 - go'i iji'a tu'a lo sakta

It is not necessary to mention that {lo ckafi} and {lo sakta} are individuals. They can exist as non-individual, as long as we don't apply an outer quantifier to them.

I agree, but it doesn't seem harmful to take them as individuals either. If it's followed by "mi ba zi dunda lo re da do", atomicity has been invoked and now they are individuals (each of them one). 

The thing is that the language has from its design a strong bias towards atomicity. Numbers don't make much sense without any atoms to count, and numbers are a very basic feature, not just of Lojban but of most natlangs (maybe all of them except allegedly Piraha). So even if we don't take atomicity as a common ground axiom, in practice it seems that it can always be invoked without any special effort. 

In any case, if you are still thinking of putting in writing a detailed alternative presentation of "lo" I will be interested to read it.

[guskant]

Le dimanche 16 février 2014 23:26:04 UTC+9, xorxes a écrit :

On Sun, Feb 16, 2014 at 4:40 AM, guskant <gusni...@gmail.com> wrote:

I meant I was deceived by the description on the gadri page that {lo broda} "refers generically to any or some individual or individuals". Because I knew what is among and what is individual, I believed that "individual" on the page is something different from what is defined in the theory of among. Actually, the word "individual" is not necessary for definition of {lo}. If {lo} were first defined, and after that "individual" were defined, then I would not have been deceived.

I agree that the definition is not ideal. It's just the least bad we could come up with at the time. I prefer the one in Lojban.  

Whether {ro'oi da su'oi de ro'oi di poi ke'a me de zo'u de me di ije de me da} is applied or not to a universe of discourse is not always important in usual conversation. We can talk with each other without mentioning individuals:

- xu do djica tu'a lo ckafi 

 - go'i iji'a tu'a lo sakta

It is not necessary to mention that {lo ckafi} and {lo sakta} are individuals. They can exist as non-individual, as long as we don't apply an outer quantifier to them.

I agree, but it doesn't seem harmful to take them as individuals either. If it's followed by "mi ba zi dunda lo re da do", atomicity has been invoked and now they are individuals (each of them one). 

Yes, and if it is follwed by "mi ba zi dunda cy jo'u sy do", we can still avoid atomicity. As a more vague expression, {xai} of Pierre Abbat instead of {cy jo'u sy} may be suitable. 

Atomicity depends on speakers' epistemology, and Lojban can serve an enough variety of expressions for both atomist and non-atomist.

 

The thing is that the language has from its design a strong bias towards atomicity. Numbers don't make much sense without any atoms to count, and numbers are a very basic feature, not just of Lojban but of most natlangs (maybe all of them except allegedly Piraha). So even if we don't take atomicity as a common ground axiom, in practice it seems that it can always be invoked without any special effort. 

I should agree to the point that Lojban has a strong bias towards atomicity. 

However, as for the current definition in Lojban of inner quantifiers, we can avoid mentioning "individual".

{lo PA broda} =ca'e {zo'e noi ke'a broda gi'e zilkancu li PA lo broda}

As usual custom, we may regard {lo broda} at the end as an individual, but "being an individual" is too strong condition for zilkancu_3 being a unit. zilkancu_3 must have "one-some" in some sense, but "one-some" has broader meaning than "individual".

For example, we may count {lo rokci} by its spatial detachment from environment, by its weight, by its spatial volume, by its radioactivity etc. Even a non-atomist can count {lo rokci} by one-some in some sense: when {lo rokci} is counted by one becquerel, a non-atomist considers that a half of {lo rokci} is also {me lo rokci}, that {lo rokci} is not an individual, and that {lo panono rokci} is still meaningful.

Even though you did not mean non-individual of zilkancu_3 when it was defined, it can be interpreted as above under the condition that {kancu} is defined enough vaguely. I support the current definition of {lo PA broda} in Lojban including such vagueness of zilkancu_3.

 

In any case, if you are still thinking of putting in writing a detailed alternative presentation of "lo" I will be interested to read it.

I am preparing my personal gadri page, and will definitely need your opinion.

 

[Jorge Llambías]

On Mon, Feb 17, 2014 at 9:24 AM, guskant <gusni...@gmail.com> wrote:

For example, we may count {lo rokci} by its spatial detachment from environment, by its weight, by its spatial volume, by its radioactivity etc.

 

I don't know, that sounds more like "merli" than "kancu". I think "kancu" must always use integers. If "kancu" was so wide open, we could have used "klani" rather than "zilkancu" to define the inner quantifiers.

  

Even a non-atomist can count {lo rokci} by one-some in some sense: when {lo rokci} is counted by one becquerel, a non-atomist considers that a half of {lo rokci} is also {me lo rokci}, that {lo rokci} is not an individual, and that {lo panono rokci} is still meaningful.

It may be difficult to define what a one-some is without individuals. One way of defining the "PA mei" predicates goes something like this:

Start with "ro'oi da su'o [pa] mei". 

Then define "su'o N mei" in terms of "su'o N-1 mei" as

ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u  ge da su'o N-1 mei gi de na me da   

And then define "N mei" as:

ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

I'm not sure if that requires atomicity or not, since all the quantifiers used are plural.

The definition for "lo PA broda" then doesn't require "zilkancu":

lo PA broda := zo'e noi ke'a PA mei gi'e broda

[guskant]

I prefer that definition to the current one because the system of counting is clearer than {zilkancu}, though atomicity is still not required for {PA mei}.

If we really need atomicity for {lo PA broda}, we could add a condition of individual for {lo pa broda}:

{lo pa broda} =ca'e {zo'e noi ro'oi da poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me da gi'e broda}

However, I think atomicity is not necessary for a definition of inner quantifier. 

 

[Jorge Llambías]

On Tue, Feb 18, 2014 at 10:13 AM, guskant <gusni...@gmail.com> wrote:

Le mardi 18 février 2014 07:41:04 UTC+9, xorxes a écrit :

lo PA broda := zo'e noi ke'a PA mei gi'e broda

I prefer that definition to the current one because the system of counting is clearer than {zilkancu}, though atomicity is still not required for {PA mei}.

Atomicity is not strictly required for the definition, but it's kind of implicit. If atomicity is false, then "su'o N mei" is always true. They are just a series of tautological predicates. And "N mei" is always false for any finite N, a series of contradictory predicates. So we _can_ define "PA mei" in the absence of atomicity, but actually using those predicates for anything meaningful requires atomicity. In the absence of atoms, anything at all satisfies su'o N mei and consequently nothing at all satisfies N mei.

If we really need atomicity for {lo PA broda}, we could add a condition of individual for {lo pa broda}:

{lo pa broda} =ca'e {zo'e noi ro'oi da poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me da gi'e broda}

However, I think atomicity is not necessary for a definition of inner quantifier. 

I agree it's not necessary for the definition, but the use of a finite inner quantifier presupposes individuals.

[guskant]

I don't yet understand how the definitions on {PA mei} could suggest implicit atomicity.

The definitions on the topic are:

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(I interpret here {su'oi da su'oi de zo'u de na me da} = {su'oi da su'oi de naku zo'u de me da} in accordance with your suggestion http://www.lojban.org/tiki/scope+of+na , not {naku su'oi da su'oi de zo'u de me da} of CLL.)

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

Actually, (D2) fails on N=1:

ko'a pa mei 

= ko'a su'o pa mei gi'e nai su'o re mei 

= ge 

su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u 

ge da su'o no mei gi de naku me da -----(S1)

gi 

naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u 

ge da su'o pa mei gi de naku me da -----(S2)

Consider (S1): because {su'oi da no mei} is false, (S1) actually says only {su'oi da poi me ko'a zo'u ge da su'o pa mei gi de naku me da}. It contradicts (S2).

For precise definitions on {PA mei}, we need therefore an explicit definition of {ko'a su'o pa mei} besides (D1).

Once {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are valid for an integer N>=1. (D2) is expanded as follows:

(D2) ko'a N mei 

= ko'a su'o N mei gi'e nai su'o N+1 mei 

= ge ko'a su'o N mei -----(S1)

gi naku ko'a su'o N+1 mei -----(S2)

(S2)

= naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u 

ge da su'o N mei 

gi de naku me da

= ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u

naku ge da su'o N mei 

gi de naku me da

= ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u

ganai da su'o N mei 

gi de me da

Therefore,

ko'a N mei 

= ge (S1) gi (S2) 

= ge ko'a su'o N mei

gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u

ganai da su'o N mei 

gi de me da

Then {ko'a N mei} implies also 

ro'oi de poi me ko'a zo'u de me ko'a

When N=1, 

ko'a pa mei 

= ge ko'a su'o pa mei

gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u

ganai da su'o pa mei 

gi de me da 

In every derivation from (D1) and (D2), {ko'a} may have {ko'e} such that {ko'e me ko'a ijenai ko'a me ko'e}. There seems to be no reason for {ko'a} beeing an individual {ro'oi da me ko'a zo'u ko'a me da} or individuals. If atomicity is implied, that should be caused by the expression {ko'a su'o pa mei}, which is not yet defined.

As a reasonable definition for {ko'a su'o pa mei}, I would suggest as follows:

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

When a condition {ije da me de} is also satisfied with (D1-1), {ko'a} is an individual.

Otherwise, {ko'a} of (D1-1) is individuals or non-individual.

(D1-1) says nothing related the number one, but it reflects a property of one-some of non-individual: any non-individual sumti can be one-some. Once non-individual B such that {B me ko'a} is fixed as one-some {B pa mei}, and if C such that {C me ko'a} satisfies conditions (D1) and (D2), C is counted to be an integer, and it is meaningful: at least, an order of cardinality is given to the pair of B and C.

It may be off topic, but if there were a definition for inner fractional quantifier 

{lo piPA broda} =ca'e {zo'e noi ke'a piPA si'e be lo pa broda}

then the language would be richer; this definition would be avaiable both atomist and non-atomist.

Actually, an outer fractional quantifier {piPA sumti} =ca'e {lo piPA si'e be pa me sumti} is available to atomists only.

[Jorge Llambías]

On Thu, Feb 20, 2014 at 1:50 AM, guskant <gusni...@gmail.com> wrote:

I don't yet understand how the definitions on {PA mei} could suggest implicit atomicity.

The definitions on the topic are:

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

For precise definitions on {PA mei}, we need therefore an explicit definition of {ko'a su'o pa mei} besides (D1).

That's why I started by saying "ro'oi da su'o pa mei", which is to say that "su'o pa mei" is a tautological predicate, always true of anything.

 

Once {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are valid for an integer N>=1. (D2) is expanded as follows:

[...]

Then {ko'a N mei} implies also 

ro'oi de poi me ko'a zo'u de me ko'a

 

"ro'oi de poi me ko'a zo'u de me ko'a" is true independently of whether "ko'a N mei" is true or not. It's just a case of the general "ro'oi de poi broda zo'u de broda". 

 

When N=1, 

ko'a pa mei 

= ge ko'a su'o pa mei

gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u

ganai da su'o pa mei 

gi de me da 

Yes, and since "su'o pa mei" is a tautology, that reduces to:

ko'a pa mei 

= ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

which says that "ko'a" is an individual. (Which is to be expected, what else would a one-some be if not an individual?)

 

In every derivation from (D1) and (D2), {ko'a} may have {ko'e} such that {ko'e me ko'a ijenai ko'a me ko'e}.

I don't think that can happen if "ko'a pa mei" is true.

 

As a reasonable definition for {ko'a su'o pa mei}, I would suggest as follows:

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

Since that is also a tautology ("ko'a" itself will instantiate "su'oi da poi me ko'a"), it works, but it's more complicated that it needs to be. We can just as well define it as:

ko'a su'o pa mei := ko'a me ko'a

or:

ko'a su'o pa mei := ko'a du ko'a

or any other tautology. Or just state that "su'o pa mei" is the tautological predicate.  

 

(D1-1) says nothing related the number one, but it reflects a property of one-some of non-individual: any non-individual sumti can be one-some. Once non-individual B such that {B me ko'a} is fixed as one-some {B pa mei}, and if C such that {C me ko'a} satisfies conditions (D1) and (D2), C is counted to be an integer, and it is meaningful: at least, an order of cardinality is given to the pair of B and C.

If by "one-some" you mean "pa mei", then only indiciduals can satisfy it. If you mean "su'o pa mei", then yes, anything satisfies it, it's a tautology. Or am I missing something?

 

It may be off topic, but if there were a definition for inner fractional quantifier 

{lo piPA broda} =ca'e {zo'e noi ke'a piPA si'e be lo pa broda}

then the language would be richer; this definition would be avaiable both atomist and non-atomist.

Actually, an outer fractional quantifier {piPA sumti} =ca'e {lo piPA si'e be pa me sumti} is available to atomists only.

I assume "lo piPA broda" will have some such meaning , but it's a different system. And it relies on a previous definition of "si'e", which we don't have from basics like the ones we're discussing here for "mei".

[guskant]

Le vendredi 21 février 2014 06:43:48 UTC+9, xorxes a écrit :

On Thu, Feb 20, 2014 at 1:50 AM, guskant <gusni...@gmail.com> wrote:

I don't yet understand how the definitions on {PA mei} could suggest implicit atomicity.

The definitions on the topic are:

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

For precise definitions on {PA mei}, we need therefore an explicit definition of {ko'a su'o pa mei} besides (D1).

That's why I started by saying "ro'oi da su'o pa mei", which is to say that "su'o pa mei" is a tautological predicate, always true of anything.

 

Yes, and in order to say "ro'oi da su'o pa mei", an axiom that is not an logical axiom should be given. That's why an explicit definition for {ko'a su'o pa mei} is necessary especially for the case that ko'a is an individual.

 

Once {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are valid for an integer N>=1. (D2) is expanded as follows:

[...]

Then {ko'a N mei} implies also 

ro'oi de poi me ko'a zo'u de me ko'a

 

"ro'oi de poi me ko'a zo'u de me ko'a" is true independently of whether "ko'a N mei" is true or not. It's just a case of the general "ro'oi de poi broda zo'u de broda". 

 

When N=1, 

ko'a pa mei 

= ge ko'a su'o pa mei

gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u

ganai da su'o pa mei 

gi de me da 

Yes, and since "su'o pa mei" is a tautology, that reduces to:

ko'a pa mei 

= ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

which says that "ko'a" is an individual. (Which is to be expected, what else would a one-some be if not an individual?)

 

Because "ro'oi da su'o pa mei" is based on a non-logical axiom, it cannot be called "tautology" in normal meaning. With this axiom, {ko'a pa mei} says that "ko'a" is an individual, of course.

 

In every derivation from (D1) and (D2), {ko'a} may have {ko'e} such that {ko'e me ko'a ijenai ko'a me ko'e}.

I don't think that can happen if "ko'a pa mei" is true.

 

You are right under the condition that "ro'oi da su'o pa mei" is true. However, it is a non-logical axiom or the equivalent. I discussed that (D1) (D2) (D3) without any non-logical axioms are meaningful even in the case that ko'a is non-individual in the point that they give an order of cardinality.

 

As a reasonable definition for {ko'a su'o pa mei}, I would suggest as follows:

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

Since that is also a tautology ("ko'a" itself will instantiate "su'oi da poi me ko'a"), it works, but it's more complicated that it needs to be. We can just as well define it as:

ko'a su'o pa mei := ko'a me ko'a

or:

ko'a su'o pa mei := ko'a du ko'a

or any other tautology. Or just state that "su'o pa mei" is the tautological predicate.  

The complicated form of (D1-1) is intended to add a non-logical part {ije da me de} in order to say explicitly the case that ko'a is an individual.

 

 

(D1-1) says nothing related the number one, but it reflects a property of one-some of non-individual: any non-individual sumti can be one-some. Once non-individual B such that {B me ko'a} is fixed as one-some {B pa mei}, and if C such that {C me ko'a} satisfies conditions (D1) and (D2), C is counted to be an integer, and it is meaningful: at least, an order of cardinality is given to the pair of B and C.

If by "one-some" you mean "pa mei", then only indiciduals can satisfy it. If you mean "su'o pa mei", then yes, anything satisfies it, it's a tautology. Or am I missing something?

 

I mean "pa mei" by "one-some". As I mentioned above, In order to say {pa mei} is an individual, a non-logical part {ije da me de} is necessary to be added to (D1-1). This addition is equivalent to a non-logical axiom "ro'oi da su'o pa mei", but explicitly mentions the condition for ko'a being an individual. Because (D1) (D2) (D3) give only an order of cardinality, they alone can be used both cases of individuals and non-individual. Starting with a non-logical axiom "ro'oi da su'o pa mei" is available only to the case that ko'a is an individual or individuals, but (D1) (D2) (D3) themselves are more generally available without non-logical axioms.

 

It may be off topic, but if there were a definition for inner fractional quantifier 

{lo piPA broda} =ca'e {zo'e noi ke'a piPA si'e be lo pa broda}

then the language would be richer; this definition would be avaiable both atomist and non-atomist.

Actually, an outer fractional quantifier {piPA sumti} =ca'e {lo piPA si'e be pa me sumti} is available to atomists only.

I assume "lo piPA broda" will have some such meaning , but it's a different system. And it relies on a previous definition of "si'e", which we don't have from basics like the ones we're discussing here for "mei".

I agree. I just want to suggest it on my personal gadri page for symmetry of definitions of quantifiers.

 

[Jorge Llambías]

On Thu, Feb 20, 2014 at 10:01 PM, guskant <gusni...@gmail.com> wrote:

Le vendredi 21 février 2014 06:43:48 UTC+9, xorxes a écrit :

On Thu, Feb 20, 2014 at 1:50 AM, guskant <gusni...@gmail.com> wrote:

For precise definitions on {PA mei}, we need therefore an explicit definition of {ko'a su'o pa mei} besides (D1).

That's why I started by saying "ro'oi da su'o pa mei", which is to say that "su'o pa mei" is a tautological predicate, always true of anything

Yes, and in order to say "ro'oi da su'o pa mei", an axiom that is not an logical axiom should be given. That's why an explicit definition for {ko'a su'o pa mei} is necessary especially for the case that ko'a is an individual.

No, I'm defining "su'o pa mei" as the tautological predicate, a predicate true of anything. I'm doing exactly the same thing you do with D1-1

 

You are right under the condition that "ro'oi da su'o pa mei" is true. However, it is a non-logical axiom or the equivalent. I discussed that (D1) (D2) (D3) without any non-logical axioms are meaningful even in the case that ko'a is non-individual in the point that they give an order of cardinality.

Definitions D1 are not a valid set of definitions without a starting point. "su'o re mei" is undefined if "su'o pa mei" is not defined first, and then "su'o ci mei" is also undefined, and so on.

 

I mean "pa mei" by "one-some". As I mentioned above, In order to say {pa mei} is an individual, a non-logical part {ije da me de} is necessary to be added to (D1-1). This addition is equivalent to a non-logical axiom "ro'oi da su'o pa mei", but explicitly mentions the condition for ko'a being an individual. Because (D1) (D2) (D3) give only an order of cardinality, they alone can be used both cases of individuals and non-individual. Starting with a non-logical axiom "ro'oi da su'o pa mei" is available only to the case that ko'a is an individual or individuals, but (D1) (D2) (D3) themselves are more generally available without non-logical axioms.

I'm sorry, I don't follow you now. Are these the definitions we are discussing:

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

?

Do you agree that with just those definitions:

ko'a pa mei

= ko'a su'o pa mei gi'e nai su'o re mei

= na ku ko'a su'o re mei

= na ku su'oi da poi me ko'a su'oi de poi me ko'a zo'u ge da su'o pa mei gi de na me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku  de me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da

which is pretty much what an individual is. If there are no individuals in the world, "ko'a pa mei" is false, because whatever ko'a refers to, it won't satisfy that anything Y among it will be among anything X among it. Only individuals satisfy that. I'm not sure what you say has to be added. In a world without individuals, "pa mei" is false of everything (and so are all of the "N mei" with finite N) , and in such a world not just "su'o pa mei", but every "su'o N mei" are tautologies. In such a world all these numeric predicates are pretty useless. That's why by using any of these predicates we invoke a world with individuals. That doesn't mean we can't have a universe of discourse without individuals, it just means that in such a universe of discourse we won't be using the numeric predicates, because they all reduce to tautologies and contradictions.

[guskant]

Le vendredi 21 février 2014 10:51:11 UTC+9, xorxes a écrit :

On Thu, Feb 20, 2014 at 10:01 PM, guskant <gusni...@gmail.com> wrote:

Le vendredi 21 février 2014 06:43:48 UTC+9, xorxes a écrit :

On Thu, Feb 20, 2014 at 1:50 AM, guskant <gusni...@gmail.com> wrote:

For precise definitions on {PA mei}, we need therefore an explicit definition of {ko'a su'o pa mei} besides (D1).

That's why I started by saying "ro'oi da su'o pa mei", which is to say that "su'o pa mei" is a tautological predicate, always true of anything

Yes, and in order to say "ro'oi da su'o pa mei", an axiom that is not an logical axiom should be given. That's why an explicit definition for {ko'a su'o pa mei} is necessary especially for the case that ko'a is an individual.

No, I'm defining "su'o pa mei" as the tautological predicate, a predicate true of anything. I'm doing exactly the same thing you do with D1-1

(D1-1) is not the same. (D1-1) says only that there is a largest referent of what is {me ko'a}. It is a tautology, and says nothing particular. The difference from {ro'oi da su'o pa mei} is that the speaker fixes {ko'a} to be {su'o pa mei}: once {ko'a} is fixed, the other thing that is {me ko'a} is not called {su'o pa mei}. (D1-1) says nothing, but a kind of dummy to make (D1) (D2) (D3) be meaningful also to non-individual.

When another condition {ije da me de} is added to (D1-1), (D1-1) is not a tautology, and {ko'a} is an individual (not only {ko'a su'o pa mei} but also {ko'a pa mei}, though): then the conditions are equivalent to {ro'oi da su'o pa mei}, which makes {ko'a su'o pa mei} always true.

As long as talking about among theory, (D1-1)+{ije da me de} is not a logical axiom or equivalent, though it is necessary for comforming to mereology with atoms.

 

 

You are right under the condition that "ro'oi da su'o pa mei" is true. However, it is a non-logical axiom or the equivalent. I discussed that (D1) (D2) (D3) without any non-logical axioms are meaningful even in the case that ko'a is non-individual in the point that they give an order of cardinality.

Definitions D1 are not a valid set of definitions without a starting point. "su'o re mei" is undefined if "su'o pa mei" is not defined first, and then "su'o ci mei" is also undefined, and so on.

That is the reason why I added (D1-1), a dummy definition for {ko'a su'o pa mei}, so that (D1) is meaningful without {ro'oi da su'o pa mei}.

 

 

I mean "pa mei" by "one-some". As I mentioned above, In order to say {pa mei} is an individual, a non-logical part {ije da me de} is necessary to be added to (D1-1). This addition is equivalent to a non-logical axiom "ro'oi da su'o pa mei", but explicitly mentions the condition for ko'a being an individual. Because (D1) (D2) (D3) give only an order of cardinality, they alone can be used both cases of individuals and non-individual. Starting with a non-logical axiom "ro'oi da su'o pa mei" is available only to the case that ko'a is an individual or individuals, but (D1) (D2) (D3) themselves are more generally available without non-logical axioms.

I'm sorry, I don't follow you now. Are these the definitions we are discussing:

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

?

Yes, and please note that (D1-1) is not equivatent to {ro'oi da su'o pa mei}. 

 

Do you agree that with just those definitions:

ko'a pa mei

= ko'a su'o pa mei gi'e nai su'o re mei

= na ku ko'a su'o re mei

= na ku su'oi da poi me ko'a su'oi de poi me ko'a zo'u ge da su'o pa mei gi de na me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku  de me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da

The result requires {ro'oi da su'o pa mei}. As I discussed above, (D1-1) is a kind of dummy to say {ko'a su'o pa mei} for a particular ko'a. With (D1-1), once ko'a is said to be {su'o pa mei}, {ro'oi da su'o pa mei} is not true, and we don't get the same result.

 

which is pretty much what an individual is. If there are no individuals in the world, "ko'a pa mei" is false, because whatever ko'a refers to, it won't satisfy that anything Y among it will be among anything X among it. Only individuals satisfy that. I'm not sure what you say has to be added. In a world without individuals, "pa mei" is false of everything (and so are all of the "N mei" with finite N) , and in such a world not just "su'o pa mei", but every "su'o N mei" are tautologies. In such a world all these numeric predicates are pretty useless. That's why by using any of these predicates we invoke a world with individuals. That doesn't mean we can't have a universe of discourse without individuals, it just means that in such a universe of discourse we won't be using the numeric predicates, because they all reduce to tautologies and contradictions.

With a dummy defintion (D1-1), "PA mei" is not meaningless even for non-individual.

Set {B su'o pa mei} according to (D1-1). Suppose {C na me B}. From a property of {jo'u}, {B me B jo'u C} and {C me B jo'u C}. Then {B jo'u C su'o re mei} according to (D1).

A non-atomist speaker must fix a referent of sumti to be {su'o pa mei}. For enjoying atomicity, just add a condition {ije da me de} to (D1-1), then it becomes clear that {ko'a} is an individual.

Starting with {ro'oi da su'o pa mei} is useful, but excludes non-individual from expressions {lo PA broda}. (D1-1) makes (D1) (D2) (D3) available also to non-individual.

 

[Jorge Llambías]

On Fri, Feb 21, 2014 at 3:46 AM, guskant <gusni...@gmail.com> wrote:

(D1-1) is not the same. (D1-1) says only that there is a largest referent of what is {me ko'a}.

Namely, ko'a themselves, right?

 

It is a tautology, and says nothing particular. The difference from {ro'oi da su'o pa mei} is that the speaker fixes {ko'a} to be {su'o pa mei}: once {ko'a} is fixed, the other thing that is {me ko'a} is not called {su'o pa mei}. (D1-1) says nothing, but a kind of dummy to make (D1) (D2) (D3) be meaningful also to non-individual.

Exactly. And "ro'oi da su'o mei" is also a statement that says nothing, it can never be false. If "ro'oi da broda" is true, then the one-place predicate "broda" is tautological, and conversely, if the one-place predicate broda is tautological then "ro'oi da broda" is true. Your choice D1-1 to define the tautological one-place predicate "su'o pa mei" is fine. Any other equivalent definition would have the same effect, for example:

(D1-2) ko'a su'o pa mei := ko'a me ko'a

or my current favourite:

(D1-3) Ko'a su'o pa mei := su'oi da me ko'a

I like it because it can be easily generalized to "no mei", "ro mei" and "me'i mei":

(D4) ko'a no mei := no'oi da me ko'a

(D5) ko'a ro mei := ro'oi da me ko'a

(D6) ko'a me'i mei := me'oi da me ko'a

"no mei" is the contradictory predicate, nothing can satisfy it, but there may or may not be something that satisfies "ro mei".

 

When another condition {ije da me de} is added to (D1-1), (D1-1) is not a tautology, and {ko'a} is an individual (not only {ko'a su'o pa mei} but also {ko'a pa mei}, though): then the conditions are equivalent to {ro'oi da su'o pa mei}, which makes {ko'a su'o pa mei} always true.

I don't follow that. What do you mean by adding a condition to D1-1? 

If you change D1-1 to

(D1-1b) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da ije da me de

then you no longer have a useful definition. Now "su'o pa mei" is no longer true of "mi jo'u do", for example, Why would you want to define "su'o pa mei" in a way that "mi jo'u do su'o pa mei" is false? I think your new definition (D1-1b) is equivalent to my definition of "pa mei".  

 

And I don't see how that is equivalent to "ro'oi da su'o pa mei". "ro'oi da su'o pa mei" entails "mi jo'u do su'o pa mei", for example.

 

As long as talking about among theory, (D1-1)+{ije da me de} is not a logical axiom or equivalent, though it is necessary for comforming to mereology with atoms.

I have to disagree with that.  (D1-1)+{ije da me de} just doesn't work as a useful definition of "su'o pa mei".

 

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

Yes, and please note that (D1-1) is not equivatent to {ro'oi da su'o pa mei}. 

(D1-1) entails "ro'oi da su'o pa mei", and conversely "ro'oi da su'o pa mei" requires "su'o pa mei" to be a tautological predicate. It doesn't require that the specific tautological form D1-1 be chosen to define it, of course, any other tautological one-place predicate will do just as well.

 

Do you agree that with just those definitions:

ko'a pa mei

= ko'a su'o pa mei gi'e nai su'o re mei

= na ku ko'a su'o re mei

= na ku su'oi da poi me ko'a su'oi de poi me ko'a zo'u ge da su'o pa mei gi de na me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku  de me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da

The result requires {ro'oi da su'o pa mei}.

If by that you mean that it requires D1-1, i.e. it requires that "su'o pa mei" is tautological, yes. Otherwise, I don't understand what you mean. 

 

As I discussed above, (D1-1) is a kind of dummy to say {ko'a su'o pa mei} for a particular ko'a. With (D1-1), once ko'a is said to be {su'o pa mei}, {ro'oi da su'o pa mei} is not true, and we don't get the same result.

How does giving a value to "ko'a" make "ro'oi da su'o pa mei" not true?  "ro'oi da su'o pa mei" is independent of what values are assigned to "ko'a". It doesn't even mention ko'a.

 

With a dummy defintion (D1-1), "PA mei" is not meaningless even for non-individual.

Set {B su'o pa mei} according to (D1-1). Suppose {C na me B}. From a property of {jo'u}, {B me B jo'u C} and {C me B jo'u C}. Then {B jo'u C su'o re mei} according to (D1).

For someone who holds the following as an axiom (the anti-atomist):

(AA) no'oi da ro'oi de poi me da zo'u da me de 

it can be shown that, for every natural N, "ro'oi da su'o N mei" and "no'oi da N mei", which is to say that for the anti-atomist all the numeric predicates are trivial (either tautologies or contradictions).

For someone who holds the opposite position (the atomist):

(A) su'oi da ro'oi de poi me da zo'u da me de 

then the numeric predicates are non-trivial: they are true of some things and false of other things (except for "su'o pa mei" which is still a tautology, and its negation "no mei" which is of course a contradiction).

Perhaps by "non-individual" you mean someone who holds neither (A) nor (AA) as axioms, someone who doesn't know or doesn't care which one of (A) or (AA) is true. The that person (the atom-agnostic), the numeric predicates are also non-trivial, but if they ever assert that something satisfies "pa mei", or "re mei", or "ci mei", etc, then they are thereby commited to (A). They can still say things like "B jo'u C su'o re mei" without commiting to either (A) or (AA). Is that what you mean?

A non-atomist speaker must fix a referent of sumti to be {su'o pa mei}. For enjoying atomicity, just add a condition {ije da me de} to (D1-1), then it becomes clear that {ko'a} is an individual. 

I think you are mistaken that you can add "ije da me de" to D1-1 in order to satisfy the atomist, Adding that breaks the definition of "su'o pa mei" for everyone.

"ko'a su'o mei" is always true for all three, for the atomist, the anti-atomist, and the atom-agnostic.

"ko'a pa mei" can be true or false for the atomist, depending on what "ko'a" refers to, it must be false for the anti-atomist, no matter what "ko'a"refers to, and can be false, but not true, for the atom-agnostic (If it's true for them, then they've become atomists, if it's false, they can remain as atom-agnostics.) 

Starting with {ro'oi da su'o pa mei} is useful, but excludes non-individual from expressions {lo PA broda}. (D1-1) makes (D1) (D2) (D3) available also to non-individual.

If by PA you mean a natural number (it's better to use N in that case, for PA could stand for "su'o" for example), then "lo N broda" is useless for the anti-atomist. It cannot refer to anything for them, because starting from (AA) it can be shown that "... noi ke'a broda gi'e N mei" will be always false.

[guskant]

Le samedi 22 février 2014 07:16:34 UTC+9, xorxes a écrit :

On Fri, Feb 21, 2014 at 3:46 AM, guskant <gusni...@gmail.com> wrote:

(D1-1) is not the same. (D1-1) says only that there is a largest referent of what is {me ko'a}.

Namely, ko'a themselves, right?

Yes. 

 

It is a tautology, and says nothing particular. The difference from {ro'oi da su'o pa mei} is that the speaker fixes {ko'a} to be {su'o pa mei}: once {ko'a} is fixed, the other thing that is {me ko'a} is not called {su'o pa mei}. (D1-1) says nothing, but a kind of dummy to make (D1) (D2) (D3) be meaningful also to non-individual.

Exactly. And "ro'oi da su'o mei" is also a statement that says nothing, it can never be false. If "ro'oi da broda" is true, then the one-place predicate "broda" is tautological, and conversely, if the one-place predicate broda is tautological then "ro'oi da broda" is true. Your choice D1-1 to define the tautological one-place predicate "su'o pa mei" is fine. Any other equivalent definition would

Because {su'o mei} is neither a sequence of logical elements, nor expanded to a sequence of logical elements, a sentence including {su'o mei} itself cannot be a logical axiom or the equivalent. I call a sentence "tautology" only when it is expressed with a sequence of logical elements that is a logical axiom or the equivalent. 

When {ro'oi da su'o mei} is applied to (D1) (D2) for N=1, we obtain {ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da}, which is a sequence of logical elements, which is equivalent to the condition for ko'a being an individual, and which is not a logical axiom or the equivalent.

It means that when we started with "ro'oi da su'o mei", it restricts the usage of {su'o mei} to an individual or individuals. It defines the meaning of {su'o mei}, and (D1) (D2) (D3) are therefore valid.

What I tried to do is to make (D1) (D2) (D3) valid with another meaning on {su'o mei}, without using {ro'oi da su'o mei}, so that an expression with {N mei} is available to non-individual referent.

 

have the same effect, for example:

(D1-2) ko'a su'o pa mei := ko'a me ko'a

or my current favourite:

(D1-3) Ko'a su'o pa mei := su'oi da me ko'a

I like it because it can be easily generalized to "no mei", "ro mei" and "me'i mei":

(D4) ko'a no mei := no'oi da me ko'a

(D5) ko'a ro mei := ro'oi da me ko'a

(D6) ko'a me'i mei := me'oi da me ko'a

"no mei" is the contradictory predicate, nothing can satisfy it, but there may or may not be something that satisfies "ro mei".

Any of them are fine. (D1-1) is only a "one-shot" definition of a particular ko'a in a particular universe of discourse defined by a speaker. It is not for general use. Actually we don't need the part {su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da}. It says only that {ko'a} is a plural constant. I am happy with only

(D1-7) ko'a su'o pa mei

as a "one-shot" definition instead of (D1-1). It defines a meaning of {su'o pa mei} with a particular ko'a, and {su'o pa mei} is not necessarily applied to other referents in the universe of discourse.

The form (D1-1) was given because I intended to use 

(D1-1b) ko'e su'o pa mei := {su'oi da poi me ko'e ku'o ro'oi de poi me ko'e zo'u de me da ije da me de}

with minimal modification to (D1-1). It is a very trivial reason, and we may discuss with (D1-7) instead of (D1-1).

(D1-1b) is also a "one-shot" definition by a speaker to be used on a particular ko'a that is an individual. It is not for general use.

 

 

When another condition {ije da me de} is added to (D1-1), (D1-1) is not a tautology, and {ko'a} is an individual (not only {ko'a su'o pa mei} but also {ko'a pa mei}, though): then the conditions are equivalent to {ro'oi da su'o pa mei}, which makes {ko'a su'o pa mei} always true.

I don't follow that. What do you mean by adding a condition to D1-1? 

If you change D1-1 to

(D1-1b) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da ije da me de

then you no longer have a useful definition. Now "su'o pa mei" is no longer true of "mi jo'u do", for example, Why would you want to define "su'o pa mei" in a way that "mi jo'u do su'o pa mei" is false? I think your new definition (D1-1b) is equivalent to my definition of "pa mei".  

 

And I don't see how that is equivalent to "ro'oi da su'o pa mei". "ro'oi da su'o pa mei" entails "mi jo'u do su'o pa mei", for example.

 

As long as talking about among theory, (D1-1)+{ije da me de} is not a logical axiom or equivalent, though it is necessary for comforming to mereology with atoms.

I have to disagree with that.  (D1-1)+{ije da me de} just doesn't work as a useful definition of "su'o pa mei".

Even with (D1-1b), "mi jo'u do su'o pa mei" is true.

(D1-1b) is also a "one-shot" definition defined by a speaker on a particular ko'a that is an individual, and is not applied generally. 

It gives a meaning to {su'o pa mei} with a particular ko'a.

For example, suppose a speaker applies (D1-1b) to {mi}:

(D1-1b) mi su'o pa mei := su'oi da poi me mi ku'o ro'oi de poi me mi zo'u de me da ije da me de

Then {mi jo'u do} satisfies (D1) of N=2:

mi jo'u do su'o re mei

From (D1), 

ganai ko'a su'o N mei gi ko'a su'o N-1 mei

is always true.

(proof:

da'i

ge ko'a su'o N mei gi naku ko'a su'o N-1 mei

iseni'ibo

ge su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

gi naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-2 mei gi de na me da

iseni'ibo

ge su'oi da poi me ko'a ku'o su'oi de poi me ko'a ku'o su'oi di_1 poi me da ku'o su'oi di_2 poi me da zo'u 

ge ge di_1 su'o N-2 mei gi di_2 na me di_1 gi de na me da

gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u naku ge da su'o N-2 mei gi de na me da

ita'o 

di_1 me da ijebo da me ko'a inaja di_1 me ko'a (A property of {me})

iseni'ibo

lo du'u 

su'oi da poi me ko'a ku'o su'oi de poi me ko'a ku'o su'oi di_1 poi me da zo'u ge di_1 su'o N-2 mei gi de na me da

cu natfe

lo du'u 

ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u naku ge da su'o N-2 mei gi de na me da

iseni'ibo 

naku ge ko'a su'o N mei gi naku ko'a su'o N-1 mei

iseni'ibo

ganai ko'a su'o N mei gi ko'a su'o N-1 mei

uo

)

Therefore 

mi jo'u do su'o pa mei

is also true.

 

 

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

Yes, and please note that (D1-1) is not equivatent to {ro'oi da su'o pa mei}. 

(D1-1) entails "ro'oi da su'o pa mei", and conversely "ro'oi da su'o pa mei" requires "su'o pa mei" to be a tautological predicate. It doesn't require that the specific tautological form D1-1 be chosen to define it, of course, any other tautological one-place predicate will do just as well.

(D1-1) or (D1-7) requires that any referent _can be_ {su'o pa mei}, but a speaker does not necessarily select all the referents to be {su'o pa mei}. The speaker gives meaning to {su'o pa mei}. If the speaker finally does not select all the referents to be {su'o pa mei}, the given meaning is different from what is given by {ro'oi da su'o pa mei}.

 

 

Do you agree that with just those definitions:

ko'a pa mei

= ko'a su'o pa mei gi'e nai su'o re mei

= na ku ko'a su'o re mei

= na ku su'oi da poi me ko'a su'oi de poi me ko'a zo'u ge da su'o pa mei gi de na me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku  de me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da

The result requires {ro'oi da su'o pa mei}.

If by that you mean that it requires D1-1, i.e. it requires that "su'o pa mei" is tautological, yes. Otherwise, I don't understand what you mean. 

I meant the following part:

= na ku su'oi da poi me ko'a su'oi de poi me ko'a zo'u ge da su'o pa mei gi de na me da

= ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku  de me da

This derivation requires {ro'oi da su'o pa mei}. 

When the meaning of {su'o pa mei} is given by (D1-1) or (D1-7),

ko'a su'o pa mei

is true because it is defined, but {su'o pa mei} is not defined to other referents.

If ko'a is non-individual, that is to say, if a speaker regards {ro'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u de me da ijenai da me de} is true, {ro'oi da su'o pa mei} is false.

 

 

As I discussed above, (D1-1) is a kind of dummy to say {ko'a su'o pa mei} for a particular ko'a. With (D1-1), once ko'a is said to be {su'o pa mei}, {ro'oi da su'o pa mei} is not true, and we don't get the same result.

How does giving a value to "ko'a" make "ro'oi da su'o pa mei" not true?  "ro'oi da su'o pa mei" is independent of what values are assigned to "ko'a". It doesn't even mention ko'a.

 

When (D1-1) or (D1-7) is used, the speaker arbitrarily defines "ko'a su'o pa mei" to a particular ko'a. 

When (D1-1b) is used, the selection of ko'a is restricted to an individual.

For example, suppose that a speaker regards {lo nanba} is non-individual:

ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da ijenai da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}. 

Even though there is no individual {lo nanba}, an expression {N mei} is available with (D1-7) (D1) (D2) (D3).

The speaker arbitrarily fix a referent to be {lo pa nanba}. If another {lo nanba xi re} is given, {lo pa nanba jo'u lo nanba xi re} is {lo re nanba}.

 

With a dummy defintion (D1-1), "PA mei" is not meaningless even for non-individual.

Set {B su'o pa mei} according to (D1-1). Suppose {C na me B}. From a property of {jo'u}, {B me B jo'u C} and {C me B jo'u C}. Then {B jo'u C su'o re mei} according to (D1).

For someone who holds the following as an axiom (the anti-atomist):

(AA) no'oi da ro'oi de poi me da zo'u da me de 

it can be shown that, for every natural N, "ro'oi da su'o N mei" and "no'oi da N mei", which is to say that for the anti-atomist all the numeric predicates are trivial (either tautologies or contradictions).

When (AA) is true, "ro'oi da su'o N mei" is false, because it with (D1) (D2) on N=1 results in "ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da", and contradicts (AA).

As for "no'oi da N mei", (AA) says nothing. If the speaker select a particular ko'a as {ko'a su'o pa mei}, "no'oi da N mei" is false; otherwise no meaning is given to {N mei}.

 

For someone who holds the opposite position (the atomist):

(A) su'oi da ro'oi de poi me da zo'u da me de 

then the numeric predicates are non-trivial: they are true of some things and false of other things (except for "su'o pa mei" which is still a tautology, and its negation "no mei" which is of course a contradiction).

Perhaps by "non-individual" you mean someone who holds neither (A) nor (AA) as axioms, someone who doesn't know or doesn't care which one of (A) or (AA) is true. The that person (the atom-agnostic), the numeric predicates are also non-trivial, but if they ever assert that something satisfies "pa mei", or "re mei", or "ci mei", etc, then they are thereby commited to (A). They can still say things like "B jo'u C su'o re mei" without commiting to either (A) or (AA). Is that what you mean?

That is not what I meant. 

I discussed only a particular ko'a, not all the referents in a universe of discourse.

However, even (AA) holds with (D1-1) or (D1-7) (D1) (D2) (D3).

 

A non-atomist speaker must fix a referent of sumti to be {su'o pa mei}. For enjoying atomicity, just add a condition {ije da me de} to (D1-1), then it becomes clear that {ko'a} is an individual. 

I think you are mistaken that you can add "ije da me de" to D1-1 in order to satisfy the atomist, Adding that breaks the definition of "su'o pa mei" for everyone.

It does not break (D1) (D2) (D2) because (D1-1b) is only a "one-shot" definition for a particular ko'a that is an individual. {su'o pa mei} is not defined to other sumti.

 

"ko'a su'o mei" is always true for all three, for the atomist, the anti-atomist, and the atom-agnostic.

"ko'a pa mei" can be true or false for the atomist, depending on what "ko'a" refers to, it must be false for the anti-atomist, no matter what "ko'a"refers to, and can be false, but not true, for the atom-agnostic (If it's true for them, then they've become atomists, if it's false, they can remain as atom-agnostics.) 

It is meaningless to compare "ko'a su'o mei" for all three, because the meaning of {su'o mei} is different between them. Atomist gives meaning to {su'o pa mei} with your starting point {ro'oi da su'o pa mei}, or with (D1-1b). Anti-atomist does with (D1-1) or (D1-7).

 

Starting with {ro'oi da su'o pa mei} is useful, but excludes non-individual from expressions {lo PA broda}. (D1-1) makes (D1) (D2) (D3) available also to non-individual.

If by PA you mean a natural number (it's better to use N in that case, for PA could stand for "su'o" for example), then "lo N broda" is useless for the anti-atomist. It cannot refer to anything for them, because starting from (AA) it can be shown that "... noi ke'a broda gi'e N mei" will be always false.

 

As I discussed above, When (AA) holds, "ro'oi da su'o N mei" is false, and an expression {N mei} is still available with (D1-1) or (D1-7) (D1) (D2) (D3).

[Jorge Llambías]

On Sat, Feb 22, 2014 at 5:02 AM, guskant <gusni...@gmail.com> wrote:

Because {su'o mei} is neither a sequence of logical elements, nor expanded to a sequence of logical elements, a sentence including {su'o mei} itself cannot be a logical axiom or the equivalent. I call a sentence "tautology" only when it is expressed with a sequence of logical elements that is a logical axiom or the equivalent. 

But we _are_ defining "su'o mei" (as well as all the other "su'o N mei" and "N mei") as logical elements! That's the whole point of what we're doing, isn't it? Why would you want to give "su'o mei" different meanings in differnet contexts?

 

"su'o mei" is just the tautological predicate. It has nothing to do with whether or not there are individuals. It is true of anything at all.

Any of them are fine. (D1-1) is only a "one-shot" definition of a particular ko'a in a particular universe of discourse defined by a speaker. It is not for general use.

But what does D1 even mean if you only know what "su'o mei" means when applied to a particular ko'a? According to D1

ko'a su'o re mei := su'o da poi me ko'a su'o de poi me ko'a zo'u ge da su'o mei gi nai de me da

How is that a complete definition of "ko'a su'o re mei", when there is an undefined term on the right hand side? 

In all my definitions "ko'a" was intended as a place holder. They otherwise don't make sense as definitions of the predicates.

 

Even with (D1-1b), "mi jo'u do su'o pa mei" is true.

(D1-1b) is also a "one-shot" definition defined by a speaker on a particular ko'a that is an individual, and is not applied generally. 

It gives a meaning to {su'o pa mei} with a particular ko'a.

For example, suppose a speaker applies (D1-1b) to {mi}:

(D1-1b) mi su'o pa mei := su'oi da poi me mi ku'o ro'oi de poi me mi zo'u de me da ije da me de

Then {mi jo'u do} satisfies (D1) of N=2:

mi jo'u do su'o re mei

From (D1), 

ganai ko'a su'o N mei gi ko'a su'o N-1 mei

is always true. 

(proof:

I didn't check your proof in detail, but it seems to me you must be be relying on D1-1, not just on D1. Otherwise both "su'o N mei" and "su'o N-1 mei" are undefined. With D1-1b in effect, the statement is false. From "mi jo'u do su'o re mei" we cannot conclude "mi jo'u do su'o pa mei" if "D1-1b" applies to "mi jo'u do".

 

Therefore 

mi jo'u do su'o pa mei

is also true.

As long as D1-1b applies only to "mi", and D1-1 applies to "mi jo'u do", yes. But why would you use different definitions of "su'o mei" in the same context?

    For example, suppose that a speaker regards {lo nanba} is non-individual:

ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da ijenai da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}. 

Yes.

 

Even though there is no individual {lo nanba}, an expression {N mei} is available with (D1-7) (D1) (D2) (D3).

No:

"lo nanba cu su'o pa mei" is true

"lo nanba cu su'o re mei" is true

"lo nanba cu su'o ci mei" is true

and so on, but:

"lo nanba cu pa mei" 

= "lo nanba cu su'o pa mei gi'e nai su'o re mei" is false

"lo nanba cu re mei"

= "lo nanba cu su'o re mei gi'e nai su'o ci mei" is false

and so on. "lo nanba cu su'o N mei" is true for all N, while "lo nanba cu N mei" is false for all (finite) N.

 

The speaker arbitrarily fix a referent to be {lo pa nanba}. If another {lo nanba xi re} is given, {lo pa nanba jo'u lo nanba xi re} is {lo re nanba}.

If "lo pa nanba" satisfies D1-1 and D1 and it also satisfies "ro'oi da poi me lo pa nanba ku'o su'oi de poi me lo pa nanba zo'u de me da ijenai da me de", then it cannot satisfy D2. 

[guskant]

Le samedi 22 février 2014 22:40:42 UTC+9, xorxes a écrit :

On Sat, Feb 22, 2014 at 5:02 AM, guskant <gusni...@gmail.com> wrote:

Because {su'o mei} is neither a sequence of logical elements, nor expanded to a sequence of logical elements, a sentence including {su'o mei} itself cannot be a logical axiom or the equivalent. I call a sentence "tautology" only when it is expressed with a sequence of logical elements that is a logical axiom or the equivalent. 

But we _are_ defining "su'o mei" (as well as all the other "su'o N mei" and "N mei") as logical elements! That's the whole point of what we're doing, isn't it? Why would you want to give "su'o mei" different meanings in differnet contexts?

 

"su'o mei" is just the tautological predicate. It has nothing to do with whether or not there are individuals. It is true of anything at all.

{ro'oi da su'o pa mei} alone cannot be expanded to logical elements only, (D1) (D2) neither, because a predicate {N mei} is not a logical element: {N mei} is a predicate that reflects natural number theory, not only predicate logic. They are _distributively_ not tautology.

{ro'oi da su'o pa mei}, (D1) and (D2) give _collectively_ a sequence of logical elements:

ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da

and it is not a logical axiom or the equivalent. {ro'oi da su'o pa mei}, (D1) and (D2) are _collectively_ not tautology.

(D1) and (D2) gives only an order to {su'o N mei} and {N mei}, and they don't give a meaning to the predicate {su'o pa mei}.

The starting point {ro'oi da su'o pa mei} gives indeed a meaning to {su'o pa mei}.

 

Any of them are fine. (D1-1) is only a "one-shot" definition of a particular ko'a in a particular universe of discourse defined by a speaker. It is not for general use.

But what does D1 even mean if you only know what "su'o mei" means when applied to a particular ko'a? According to D1

ko'a su'o re mei := su'o da poi me ko'a su'o de poi me ko'a zo'u ge da su'o mei gi nai de me da

How is that a complete definition of "ko'a su'o re mei", when there is an undefined term on the right hand side? 

In all my definitions "ko'a" was intended as a place holder. They otherwise don't make sense as definitions of the predicates.

It seems that using "ko'a" as a place holder causes a problem.

I use {ko'a} as a plural constant, not as a place holder. 

For a place holder, {ke'a} and {ce'u} are suitable, because they are free variables: such usage is not described in CLL, but it is useful at least in the current discussion.

When {ce'u} appears more than two times in a sequence of words, different sumti can be substituted for them, while only a common sumti can be substituted for {ke'a}s. For the current purpose, using {ke'a} is better.

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1) and (D2) are applied to a particular sumti, ke'a are replaced with it. As for (D3), ke'a is in noi-clause, and it is already fixed to zo'e, and is not replaced with another sumti, of course. 

Because (D1-7) defines only for {ko'a}, (D1) (D2) (D3) are valid only for sumti that involves a referent of {ko'a} such as {ko'e noi ko'a me ke'a}, {ko'i no'u ko'a jo'u ko'o} etc. (D1) (D2) (D3) are not used for other sumti unless (D1-7) is applied to one of the referents that is involved by the sumti.

 

 

Even with (D1-1b), "mi jo'u do su'o pa mei" is true.

(D1-1b) is also a "one-shot" definition defined by a speaker on a particular ko'a that is an individual, and is not applied generally. 

It gives a meaning to {su'o pa mei} with a particular ko'a.

For example, suppose a speaker applies (D1-1b) to {mi}:

(D1-1b) mi su'o pa mei := su'oi da poi me mi ku'o ro'oi de poi me mi zo'u de me da ije da me de

Then {mi jo'u do} satisfies (D1) of N=2:

mi jo'u do su'o re mei

From (D1), 

ganai ko'a su'o N mei gi ko'a su'o N-1 mei

is always true. 

(proof:

I didn't check your proof in detail, but it seems to me you must be be relying on D1-1, not just on D1. Otherwise both "su'o N mei" and "su'o N-1 mei" are undefined. With D1-1b in effect, the statement is false. From "mi jo'u do su'o re mei" we cannot conclude "mi jo'u do su'o pa mei" if "D1-1b" applies to "mi jo'u do".

I used only (D1) and logical axioms including transitivity of {me}. Any mention of {su'o pa mei} is not necessary for the proof.

 

 

Therefore 

mi jo'u do su'o pa mei

is also true.

As long as D1-1b applies only to "mi", and D1-1 applies to "mi jo'u do", yes. But why would you use different definitions of "su'o mei" in the same context?

If you need {su'o mei} for other sumti that does not involve {mi} in the same context, you must use (D1-7) or (D1-1b) to that sumti. For {ko'a noi naku mi me ke'a}, {ko'a su'o mei} is not defined otherwise.

 

    For example, suppose that a speaker regards {lo nanba} is non-individual:

ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da ijenai da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}. 

Yes.

 

Even though there is no individual {lo nanba}, an expression {N mei} is available with (D1-7) (D1) (D2) (D3).

No:

"lo nanba cu su'o pa mei" is true

"lo nanba cu su'o re mei" is true

"lo nanba cu su'o ci mei" is true

I call them {lo nanba xi re} and {lo nanba xi ci} respectively for convenience.

If

(D1-7) lo nanba xi pa cu su'o pa mei

is defined, and if {naku ge lo nanba xi pa cu me lo nanba xi re/ci gi naku lo nanba xi re/ci cu me lo nanba xi pa}, the first sentence is true, and the second and the third are false.

That is to say, if {(D1-7) lo nanba cu su'o pa mei} is defined, and if all the appearances of {lo nanba} have a common referent, the first sentence is true, and the second and the third are false.

 

 

 

The speaker arbitrarily fix a referent to be {lo pa nanba}. If another {lo nanba xi re} is given, {lo pa nanba jo'u lo nanba xi re} is {lo re nanba}.

If "lo pa nanba" satisfies D1-1 and D1 and it also satisfies "ro'oi da poi me lo pa nanba ku'o su'oi de poi me lo pa nanba zo'u de me da ijenai da me de", then it cannot satisfy D2. 

(D1) is meaningless for N=1, because (D1)+(D2) for N=1 produces contradiction.

The meaning of {su'o pa mei} is defined by the starting point {ro'oi da su'o pa mei} XOR (D1-7), not by (D1).

(D1) is meaningful only for N>=2, in both procedures of starting with {ro'oi da su'o pa mei} and of using (D1-7).

When 

(D1-7) lo nanba cu su'o pa mei

is defined, (D1-7), (D1) for N=2, (D2) and (D3) produce a meaningful {lo pa nanba}. (D1) for N=1 is not used here.

When another {ko'e noi nanba} is given, (D1) can be used for saying {lo nanba (ku) jo'u ko'e noi nanba cu su'o re mei}. Please note that the referent of the first {lo nanba} is different from ko'e.

 

[Jorge Llambías]

On Sat, Feb 22, 2014 at 11:45 PM, guskant <gusni...@gmail.com> wrote:

{ro'oi da su'o pa mei} alone cannot be expanded to logical elements only, (D1) (D2) neither, because a predicate {N mei} is not a logical element: {N mei} is a predicate that reflects natural number theory, not only predicate logic. They are _distributively_ not tautology.

I agree that before "su'o pa mei" is defined, "ro'oi da su'o pa mei" is not a tautology. It is only a tautology once "su'o pa mei" has been introduced as a tautological predicate. In the context I brought it up, I was in the process of defining the "PA mei" series of predicates, and I started by defining "su'o pa mei" such that "ro'oi da su'o pa mei". I did not explicitly write down any definition for "su'o pa mei", but the only definition of "su'o pa mei" that makes "ro'oi da su'o pa mei" true is one that defines it as a tautological predicate. 

One thing I should have said, and which I took for granted, but I see you didn't from something you say below, is that all the "PA mei" predicates must be non-distributive. We don't want to infer from "ko'a jo'u ko'e re mei" that "ko'a re mei" or "ko'e re mei". That would kill the very meaning of these predicates.

 

It seems that using "ko'a" as a place holder causes a problem.

I use {ko'a} as a plural constant, not as a place holder. 

For a place holder, {ke'a} and {ce'u} are suitable, because they are free variables: such usage is not described in CLL, but it is useful at least in the current discussion.

When {ce'u} appears more than two times in a sequence of words, different sumti can be substituted for them, while only a common sumti can be substituted for {ke'a}s. For the current purpose, using {ke'a} is better.

When using the language, yes. We don't need free variables for ordinary use of the language. But when talking about the language, as we are doing here, using ko'a, ko'e, ko'i, ... is more convenient. We may need to use more than one free variable. (The next step is defining the restricted series of numerical predicates, with two places,  "ko'a PA mei ko'e", and using subscripts for the different places in addition to the numbers in the predicate just adds a lot of confusion.)  Also, sometimes we need the free variable to appear within a relative clause. I have always used ko'a, ko'e, ... as the place holders when writing definitions for brivla. I haven't found anything else more convenient. Some people prefer to write their definitions with "ka", "ce'u" and subscripts, but I find them unnecessarily cumbersome.

 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1) and (D2) are applied to a particular sumti, ke'a are replaced with it. As for (D3), ke'a is in noi-clause, and it is already fixed to zo'e, and is not replaced with another sumti, of course. 

Because (D1-7) defines only for {ko'a}, (D1) (D2) (D3) are valid only for sumti that involves a referent of {ko'a} such as {ko'e noi ko'a me ke'a}, {ko'i no'u ko'a jo'u ko'o} etc. (D1) (D2) (D3) are not used for other sumti unless (D1-7) is applied to one of the referents that is involved by the sumti.

If D1-7 defines only for ko'a, then it is not necessarily valid for ro'oi da poi me ko'a. You need "ro'oi da poi me ko'a cu su'o mei" if you want it to be valid for anything among ko'a. But that won't make it valid for ko'a jo'u ko'o if something in ko'o is not in ko'a. 

I used only (D1) and logical axioms including transitivity of {me}. Any mention of {su'o pa mei} is not necessary for the proof. 

Then there must be something wrong in the proof.  You just cannot prove "ganai ko'a su'o N mei gi ko'a su'o N-1 mei" for N=2 from just D1, because D1 does not define "su'o pa mei". You may have forgotten the restriction on N somewhere in the proof.

 

    For example, suppose that a speaker regards {lo nanba} is non-individual:

ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da ijenai da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}. 

Yes.

 

Even though there is no individual {lo nanba}, an expression {N mei} is available with (D1-7) (D1) (D2) (D3).

No:

"lo nanba cu su'o pa mei" is true

"lo nanba cu su'o re mei" is true

"lo nanba cu su'o ci mei" is true

I call them {lo nanba xi re} and {lo nanba xi ci} respectively for convenience.

But it's the same "lo nanba"! 

lo nanba cu su'o pa mei gi'e su'o re mei gi'e su'o ci mei gi'e ..." is true.

 

If

(D1-7) lo nanba xi pa cu su'o pa mei

is defined, and if {naku ge lo nanba xi pa cu me lo nanba xi re/ci gi naku lo nanba xi re/ci cu me lo nanba xi pa}, the first sentence is true, and the second and the third are false.

I don't see how that makes the second and third false.

 

That is to say, if {(D1-7) lo nanba cu su'o pa mei} is defined, and if all the appearances of {lo nanba} have a common referent, the first sentence is true, and the second and the third are false.

No. Your starting point was that every part of lo nanba has a proper part, so for lo nanba, and for every one of its parts, "su'o N mei" is true for every natural N, and for "lo nanba", and for every one of its parts, "N mei" is false for every natural N.

.

[guskant]

Le dimanche 23 février 2014 22:55:14 UTC+9, xorxes a écrit :

On Sat, Feb 22, 2014 at 11:45 PM, guskant <gusni...@gmail.com> wrote:

{ro'oi da su'o pa mei} alone cannot be expanded to logical elements only, (D1) (D2) neither, because a predicate {N mei} is not a logical element: {N mei} is a predicate that reflects natural number theory, not only predicate logic. They are _distributively_ not tautology.

I agree that before "su'o pa mei" is defined, "ro'oi da su'o pa mei" is not a tautology. It is only a tautology once "su'o pa mei" has been introduced as a tautological predicate. In the context I brought it up, I was in the process of defining the "PA mei" series of predicates, and I started by defining "su'o pa mei" such that "ro'oi da su'o pa mei". I did not explicitly write down any definition for "su'o pa mei", but the only definition of "su'o pa mei" that makes "ro'oi da su'o pa mei" true is one that defines it as a tautological predicate. 

One thing I should have said, and which I took for granted, but I see you didn't from something you say below, is that all the "PA mei" predicates must be non-distributive. We don't want to infer from "ko'a jo'u ko'e re mei" that "ko'a re mei" or "ko'e re mei". That would kill the very meaning of these predicates.

You give {su'o pa mei} to all the referent that are individual(s) of a universe of discourse, while I give {su'o pa mei} to certain members of it, including non-indiviidual members, not to all. Once {su'o pa mei} is given to a referent, it satisfies the predicate _non-distributively_. When "ko'a jo'u ko'e re mei" is true, "ko'a re mei" and "ko'e re mei" are false according to (D1) and (D2). To smaller part of {ko'a} or {ko'e}, {su'o N mei} is not applied.

 

 

It seems that using "ko'a" as a place holder causes a problem.

I use {ko'a} as a plural constant, not as a place holder. 

For a place holder, {ke'a} and {ce'u} are suitable, because they are free variables: such usage is not described in CLL, but it is useful at least in the current discussion.

When {ce'u} appears more than two times in a sequence of words, different sumti can be substituted for them, while only a common sumti can be substituted for {ke'a}s. For the current purpose, using {ke'a} is better.

When using the language, yes. We don't need free variables for ordinary use of the language. But when talking about the language, as we are doing here, using ko'a, ko'e, ko'i, ... is more convenient. We may need to use more than one free variable. (The next step is defining the restricted series of numerical predicates, with two places,  "ko'a PA mei ko'e", and using subscripts for the different places in addition to the numbers in the predicate just adds a lot of confusion.)  Also, sometimes we need the free variable to appear within a relative clause. I have always used ko'a, ko'e, ... as the place holders when writing definitions for brivla. I haven't found anything else more convenient. Some people prefer to write their definitions with "ka", "ce'u" and subscripts, but I find them unnecessarily cumbersome.

 

I agree. However, for the current discussion, distinction between plural constant and free plural variable is necessary. For this purpose, I use {ke'a} as a free plural variable as "zasni" here.

 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1) and (D2) are applied to a particular sumti, ke'a are replaced with it. As for (D3), ke'a is in noi-clause, and it is already fixed to zo'e, and is not replaced with another sumti, of course. 

Because (D1-7) defines only for {ko'a}, (D1) (D2) (D3) are valid only for sumti that involves a referent of {ko'a} such as {ko'e noi ko'a me ke'a}, {ko'i no'u ko'a jo'u ko'o} etc. (D1) (D2) (D3) are not used for other sumti unless (D1-7) is applied to one of the referents that is involved by the sumti.

If D1-7 defines only for ko'a, then it is not necessarily valid for ro'oi da poi me ko'a. You need "ro'oi da poi me ko'a cu su'o mei" if you want it to be valid for anything among ko'a. But that won't make it valid for ko'a jo'u ko'o if something in ko'o is not in ko'a. 

No. When (D1-7) defines for {ko'a}, the referent of {ko'a} satisfies {su'o pa mei} _non-distributively_. 

Any other referents that are {me ko'a} do not satisfy {su'o pa mei}.

 

I used only (D1) and logical axioms including transitivity of {me}. Any mention of {su'o pa mei} is not necessary for the proof. 

Then there must be something wrong in the proof.  You just cannot prove "ganai ko'a su'o N mei gi ko'a su'o N-1 mei" for N=2 from just D1, because D1 does not define "su'o pa mei". You may have forgotten the restriction on N somewhere in the proof.

An order of all integers including zero and negative numbers is used for the proof, not only for N>=3. (D1)+(D2) for N=1 produces contradiction, but (D1) alone does not produce contradiction for every integer, although it is meaningless. I used a larger set of numbers than what is required by the proved proposition. It is just like using a higher dimensional space in a proof on a figure in a lower dimensional space. It is a valid procedure.

 

 

    For example, suppose that a speaker regards {lo nanba} is non-individual:

ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da ijenai da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}. 

Yes.

 

Even though there is no individual {lo nanba}, an expression {N mei} is available with (D1-7) (D1) (D2) (D3).

No:

"lo nanba cu su'o pa mei" is true

"lo nanba cu su'o re mei" is true

"lo nanba cu su'o ci mei" is true

I call them {lo nanba xi re} and {lo nanba xi ci} respectively for convenience.

But it's the same "lo nanba"! 

lo nanba cu su'o pa mei gi'e su'o re mei gi'e su'o ci mei gi'e ..." is true.

 

It cannot be true when 

(D1-7} lo nanba cu su'o pa mei

is defined to {lo nanba}. 

In the definition 

(D1) lo nanba cu su'o re mei := su'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u ge da su'o pa mei gi de na me da

{da su'o pa mei} is true only for the referent of {lo nanba} used in (D1-7), that is, {lo nanba} itself, and it satisfies {su'o pa mei} _non-distributively_. The other referents in the domain of {da poi me lo nanba} do not satisfy {da su'o pa mei}. Therefore, there is no referent that satisfies {ge da su'o pa mei gi de na me da}.

 

If

(D1-7) lo nanba xi pa cu su'o pa mei

is defined, and if {naku ge lo nanba xi pa cu me lo nanba xi re/ci gi naku lo nanba xi re/ci cu me lo nanba xi pa}, the first sentence is true, and the second and the third are false.

I don't see how that makes the second and third false.

 

As I discussed above, (D1-7) is defined only on a referent selected by a speaker, and the referent satisfies {su'o pa mei} _non-distributively_. When 

(D1-7) lo nanba cu su'o pa mei

is defined, any smaller part of {lo nanba} is not {su'o pa mei}. Therefore, the second and the third sentences cannot be produced for the same referent.

 

That is to say, if {(D1-7) lo nanba cu su'o pa mei} is defined, and if all the appearances of {lo nanba} have a common referent, the first sentence is true, and the second and the third are false.

No. Your starting point was that every part of lo nanba has a proper part, so for lo nanba, and for every one of its parts, "su'o N mei" is true for every natural N, and for "lo nanba", and for every one of its parts, "N mei" is false for every natural N.

.

There are infinite referents that are {me lo nanba}, but {su'o pa mei} was defined only on the referent of {lo nanba} itself _non-distributively_. Any other referents that are {me lo nanba} do not satisfy {su'o pa mei}, therefore {su'o N mei} neither.

 

[Jorge Llambías]

On Sun, Feb 23, 2014 at 2:07 PM, guskant <gusni...@gmail.com> wrote:

You give {su'o pa mei} to all the referent that are individual(s) of a universe of discourse,

No, not just individuals. Everything and anything satisfies "su'o pa mei", including any non-individuals that there may be in the universe of discourse..

 

while I give {su'o pa mei} to certain members of it, including non-indiviidual members, not to all.

But why? Why do you want some things not to satisfy "su'o pa mei" which basically should mean "x1 is/are something(s)"? You still haven't explained why you want to define "su'o pa mei" in such a particular way.  

 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1) and (D2) are applied to a particular sumti, ke'a are replaced with it. As for (D3), ke'a is in noi-clause, and it is already fixed to zo'e, and is not replaced with another sumti, of course. 

Because (D1-7) defines only for {ko'a}, (D1) (D2) (D3) are valid only for sumti that involves a referent of {ko'a} such as {ko'e noi ko'a me ke'a}, {ko'i no'u ko'a jo'u ko'o} etc. (D1) (D2) (D3) are not used for other sumti unless (D1-7) is applied to one of the referents that is involved by the sumti.

If D1-7 defines only for ko'a, then it is not necessarily valid for ro'oi da poi me ko'a. You need "ro'oi da poi me ko'a cu su'o mei" if you want it to be valid for anything among ko'a. But that won't make it valid for ko'a jo'u ko'o if something in ko'o is not in ko'a. 

No. When (D1-7) defines for {ko'a}, the referent of {ko'a} satisfies {su'o pa mei} _non-distributively_. 

Any other referents that are {me ko'a} do not satisfy {su'o pa mei}.

You don't know, that's not part of D1-7. If that's what you want, then you need something like:

(D1-8) ke'a su'o pa mei := ke'a du ko'a

Now you would have a full definition, and we would know that only ko'a satisfies "su'o pa mei", while everything else doesn't. 

With (D1-7) as is, we know that ko'a satisfies "su'o pa mei" but we have no way of knowing whether anything else does. 

 

    For example, suppose that a speaker regards {lo nanba} is non-individual:

ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da ijenai da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}. 

Yes.

 

Even though there is no individual {lo nanba}, an expression {N mei} is available with (D1-7) (D1) (D2) (D3).

No:

"lo nanba cu su'o pa mei" is true

"lo nanba cu su'o re mei" is true

"lo nanba cu su'o ci mei" is true

I call them {lo nanba xi re} and {lo nanba xi ci} respectively for convenience.

But it's the same "lo nanba"! 

lo nanba cu su'o pa mei gi'e su'o re mei gi'e su'o ci mei gi'e ..." is true. 

It cannot be true when 

(D1-7} lo nanba cu su'o pa mei

is defined to {lo nanba}. 

In the definition 

(D1) lo nanba cu su'o re mei := su'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u ge da su'o pa mei gi de na me da

{da su'o pa mei} is true only for the referent of {lo nanba} used in (D1-7), that is, {lo nanba} itself, and it satisfies {su'o pa mei} _non-distributively_. The other referents in the domain of {da poi me lo nanba} do not satisfy {da su'o pa mei}.

With the definition you gave, there's no way of knowing what else besides "lo nanba" will satisfy "su'o pa mei". If you mean something like (D1-8) instead of (D1-7) then yes, "lo nanba cu su'o re mei" will be false, and "lo nanba cu pa mei" will be true. "mi pa mei" will also be false, "mi jo'u do re mei" will be false, and so on. How can you possibly justify a definition like that for these predicates? They end up meaning nothing like "is one", "are two", "are three", and so on. 

Those definitions, with either (D1-7) or (D1-8), just don't make any sense to me. With (D1-7) it's not even a complete definition.

I will stick with these (using "ko'a" as a place-holder):

(D0) ko'a su'o pa mei := su'oi da me ko'a

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da  [N>=2]

(D2) ko'a N mei  := ko'a su'o N mei gi'e nai su'o N+1 mei  [N>=1] 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

[guskant]

Le lundi 24 février 2014 10:38:21 UTC+9, xorxes a écrit :

On Sun, Feb 23, 2014 at 2:07 PM, guskant <gusni...@gmail.com> wrote:

You give {su'o pa mei} to all the referent that are individual(s) of a universe of discourse,

No, not just individuals. Everything and anything satisfies "su'o pa mei", including any non-individuals that there may be in the universe of discourse..

Sorry, you are right, though {ro'oi da su'o pa mei} + (D1) (D2) (D3) excludes non-individual referents from expressions with {N mei} and {lo N broda}.

I correct my sentence as follows:

You give {su'o pa mei} to all referents of a universe of discourse,

while I give {su'o pa mei} to certain members of it, not to all. 

 

while I give {su'o pa mei} to certain members of it, including non-indiviidual members, not to all.

But why? Why do you want some things not to satisfy "su'o pa mei" which basically should mean "x1 is/are something(s)"? You still haven't explained why you want to define "su'o pa mei" in such a particular way.  

It is for the purpose of giving expressions with {N mei} and {lo N broda} to non-individual referents. 

Even if speakers regard {lo nanba} as non-individual, they may want to use {N mei} to a particular referent of {lo nanba}, because the expressions of {N mei} and {lo N nanba} are useful for giving a mapping from an order of quantity into transitivity of {me}. These expressions facilitate comparison of quantity between {ko'a me lo nanba} and {ko'e me lo nanba} without using other unit than what is defined by speakers.

 

 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1) and (D2) are applied to a particular sumti, ke'a are replaced with it. As for (D3), ke'a is in noi-clause, and it is already fixed to zo'e, and is not replaced with another sumti, of course. 

Because (D1-7) defines only for {ko'a}, (D1) (D2) (D3) are valid only for sumti that involves a referent of {ko'a} such as {ko'e noi ko'a me ke'a}, {ko'i no'u ko'a jo'u ko'o} etc. (D1) (D2) (D3) are not used for other sumti unless (D1-7) is applied to one of the referents that is involved by the sumti.

If D1-7 defines only for ko'a, then it is not necessarily valid for ro'oi da poi me ko'a. You need "ro'oi da poi me ko'a cu su'o mei" if you want it to be valid for anything among ko'a. But that won't make it valid for ko'a jo'u ko'o if something in ko'o is not in ko'a. 

No. When (D1-7) defines for {ko'a}, the referent of {ko'a} satisfies {su'o pa mei} _non-distributively_. 

Any other referents that are {me ko'a} do not satisfy {su'o pa mei}.

You don't know, that's not part of D1-7. If that's what you want, then you need something like:

(D1-8) ke'a su'o pa mei := ke'a du ko'a

Now you would have a full definition, and we would know that only ko'a satisfies "su'o pa mei", while everything else doesn't. 

With (D1-7) as is, we know that ko'a satisfies "su'o pa mei" but we have no way of knowing whether anything else does. 

(D1-7) ko'a su'o pa mei 

with (D1) (D2) will make {ko'a jo'u ko'e su'o pa mei} true. (D1-8) contradicts it.

As for (D1-7), speakers who talk about non-individual referents may select not only {ko'a} but also any arbitrary {ko'e} {ko'i}... as {su'o pa mei} as long as the selected referents don't conflict each other.

(D1-7) is only a sample for discussion. Speakers arbitrarily select referents to be {su'o pa mei}, not only {ko'a}.

In other words, (D1-7) gives a subjective unit to non-individual referents. If you don't call it definition, you may exclude it from a set of definitions on {N mei}. In any case, the meaning of {su'o pa mei} is entrusted to speakers, and it is not necessarily {ro'oi da su'o pa mei}.

Defining {su'o pa mei} involves giving a unit to a set of referents that are related with transitivity of {me}. I want to let speakers have the right to define a unit.

The meaning of {su'o pa mei} with (D1)(D2)(D3) gives a subjective unit that is not necessarily regarded as an individual. It depends on context, and not defined for common use. I prefer leaving it as an undefined predicate, not restricted with {ro'oi da su'o pa mei}, neither (D0). A unit of counting is to be defined by speakers according to context.

Giving this vagueness to a unit is not strange. Even if a speaker regards {lo nanba} as an individual, selection of referent to be an individual depends on context. On the other hand, if a speaker regards {lo nanba} as non-individual, selection of referent to be a unit depends on context. 

[Jorge Llambías]

On Mon, Feb 24, 2014 at 9:59 AM, guskant <gusni...@gmail.com> wrote:

You give {su'o pa mei} to all referents of a universe of discourse,

while I give {su'o pa mei} to certain members of it, not to all. 

 Right, which to me sounds like you want some things in the universe of discourse that don't count as "somethings". 

 

It is for the purpose of giving expressions with {N mei} and {lo N broda} to non-individual referents. 

Even if speakers regard {lo nanba} as non-individual, they may want to use {N mei} to a particular referent of {lo nanba}, because the expressions of {N mei} and {lo N nanba} are useful for giving a mapping from an order of quantity into transitivity of {me}. These expressions facilitate comparison of quantity between {ko'a me lo nanba} and {ko'e me lo nanba} without using other unit than what is defined by speakers.

It seems to me that it would be better to use "si'e" rather than "mei" for that purpose, and "pagbu" instead of "me". If you allow things like "so'i da poi me lo pa nanba" you pretty much destroy "me" as "among" and you turn it into "pagbu".

 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1-7) defines for {ko'a}, the referent of {ko'a} satisfies {su'o pa mei} _non-distributively_. 

Any other referents that are {me ko'a} do not satisfy {su'o pa mei}.

As for (D1-7), speakers who talk about non-individual referents may select not only {ko'a} but also any arbitrary {ko'e} {ko'i}... as {su'o pa mei} as long as the selected referents don't conflict each other.

What do you mean by "conflict"? Overlap? Or do you mean that some things are selected as pseudo-atoms, so that, for example:

ko'a su'o mei

ko'e su'o mei

ko'i goi ko'a jo'u ko'e su'o mei

So ko'a and ko'e are pseudo-atoms, because nothing among them (besides themselves) satisfies "su'o mei", but "ko'i" is not a pseudo-atom, because there are things among them, different from ko'i itself, that do satisfy "su'o mei". 

Then all and only the pseudo-atoms will satisfy "pa mei", and only things composed of one or more pseudo-atoms will satisfy "su'o mei"..

 

(D1-7) is only a sample for discussion. Speakers arbitrarily select referents to be {su'o pa mei}, not only {ko'a}.

In other words, (D1-7) gives a subjective unit to non-individual referents. If you don't call it definition, you may exclude it from a set of definitions on {N mei}. In any case, the meaning of {su'o pa mei} is entrusted to speakers, and it is not necessarily {ro'oi da su'o pa mei}.

Defining {su'o pa mei} involves giving a unit to a set of referents that are related with transitivity of {me}. I want to let speakers have the right to define a unit.

"Defining a unit" sounds a lot to me like defining what counts as one, what the individuals are in our discourse. 

Since what counts as an individual is context-dependent anyway, why add a second layer? Why have first-class things (which count) and second-class things (which don't count)? 

[guskant]

Le mardi 25 février 2014 07:59:04 UTC+9, xorxes a écrit :

On Mon, Feb 24, 2014 at 9:59 AM, guskant <gusni...@gmail.com> wrote:

You give {su'o pa mei} to all referents of a universe of discourse,

while I give {su'o pa mei} to certain members of it, not to all. 

 Right, which to me sounds like you want some things in the universe of discourse that don't count as "somethings". 

 

It is for the purpose of giving expressions with {N mei} and {lo N broda} to non-individual referents. 

Even if speakers regard {lo nanba} as non-individual, they may want to use {N mei} to a particular referent of {lo nanba}, because the expressions of {N mei} and {lo N nanba} are useful for giving a mapping from an order of quantity into transitivity of {me}. These expressions facilitate comparison of quantity between {ko'a me lo nanba} and {ko'e me lo nanba} without using other unit than what is defined by speakers.

It seems to me that it would be better to use "si'e" rather than "mei" for that purpose, and "pagbu" instead of "me". If you allow things like "so'i da poi me lo pa nanba" you pretty much destroy "me" as "among" and you turn it into "pagbu".

 

When {lo nanba} is non-individual, {so'i da poi me lo pa nanba} is not allowed. non-individual referents cannot be in the domain of {so'i da}, because only individuals are allowed in the domain of singular variables. Mapping from {N mei} into {me} of non-individual referents is only non-surjective, and (D1) with (D2) reflects transitivity of {me}. {me}-relation holds even if {N mei}-relation is applied.

If {P si'e} were allowed for P>1, {si'e} would have been better than {me} for non-individual referents. 

(I have once suggested an interpretation of {P si'e} for other than P<=1, though nobody agreed: https://groups.google.com/d/msg/lojban/6LRA8XntyGc/6MFRVIfGDMMJ .)

If it is not allowed, then {si'e} is not convenient for counting up.

According to the current definition:

x1 number si'e x2 x1 pagbu x2 gi'e klani li number lo se gradu be x2

it seems that a number followed by {si'e} cannot be larger than 1 unless {pagbu} is interpreted very broadly so that x1 of {pagbu} can be larger than x2.

Under this condition, if {P si'e} is used for counting up, a number followed by {si'e} should be changed every time another referent becomes to be considered.

ko'a pa si'e

i

ko'a fi'u re si'e ije ko'a jo'u ko'e pa si'e

i

ko'a fi'u ci si'e ije ko'a jo'u ko'e jo'u ko'i pa si'e

...

Speakers may not want change the number applied to {ko'a} in such a way. 

Using {mei}, speakers can fix a number to the same referent even when counting up.

 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1-7) defines for {ko'a}, the referent of {ko'a} satisfies {su'o pa mei} _non-distributively_. 

Any other referents that are {me ko'a} do not satisfy {su'o pa mei}.

As for (D1-7), speakers who talk about non-individual referents may select not only {ko'a} but also any arbitrary {ko'e} {ko'i}... as {su'o pa mei} as long as the selected referents don't conflict each other.

What do you mean by "conflict"? Overlap? Or do you mean that some things are selected as pseudo-atoms, so that, for example:

ko'a su'o mei

ko'e su'o mei

ko'i goi ko'a jo'u ko'e su'o mei

So ko'a and ko'e are pseudo-atoms, because nothing among them (besides themselves) satisfies "su'o mei", but "ko'i" is not a pseudo-atom, because there are things among them, different from ko'i itself, that do satisfy "su'o mei". 

Then all and only the pseudo-atoms will satisfy "pa mei", and only things composed of one or more pseudo-atoms will satisfy "su'o mei"..

 

Yes. 

(D1-7) is only a sample for discussion. Speakers arbitrarily select referents to be {su'o pa mei}, not only {ko'a}.

In other words, (D1-7) gives a subjective unit to non-individual referents. If you don't call it definition, you may exclude it from a set of definitions on {N mei}. In any case, the meaning of {su'o pa mei} is entrusted to speakers, and it is not necessarily {ro'oi da su'o pa mei}.

Defining {su'o pa mei} involves giving a unit to a set of referents that are related with transitivity of {me}. I want to let speakers have the right to define a unit.

"Defining a unit" sounds a lot to me like defining what counts as one, what the individuals are in our discourse. 

Since what counts as an individual is context-dependent anyway, why add a second layer? Why have first-class things (which count) and second-class things (which don't count)? 

Non-individual referents are excluded from outer quantified sumti and singular bound variables of official Lojban. (If su'oi, ro'oi etc become official, it is not the case, though.) Possibility of quantification on non-individual referents are left only in expressions with inner quantifier. If inner quantifiers are allowed to non-individual referents, speakers who regards {lo nanba} as non-individual consider that a half of {lo pa nanba} is also {me lo nanba}. If inner quantifier is given only to individual(s), the language restrict thought of speakers so that they should consider that "a half of {lo pa nanba} is not {me lo nanba}". 

 

[Jorge Llambías]

On Tue, Feb 25, 2014 at 11:04 AM, guskant <gusni...@gmail.com> wrote:

Le mardi 25 février 2014 07:59:04 UTC+9, xorxes a écrit :

It seems to me that it would be better to use "si'e" rather than "mei" for that purpose, and "pagbu" instead of "me". If you allow things like "so'i da poi me lo pa nanba" you pretty much destroy "me" as "among" and you turn it into "pagbu".

When {lo nanba} is non-individual, {so'i da poi me lo pa nanba} is not allowed. non-individual referents cannot be in the domain of {so'i da}, because only individuals are allowed in the domain of singular variables.

Right, but then you need an additional constraint on your pseudo-individuals: they must be either individuals themselves, or they must be atomless, they cannot properly contain any individuals. By "non-individual" I assume you mean atomless, not containing any individuals at all, rather than merely not being an individual.

 

If {P si'e} were allowed for P>1, {si'e} would have been better than {me} for non-individual referents. 

(I have once suggested an interpretation of {P si'e} for other than P<=1, though nobody agreed: https://groups.google.com/d/msg/lojban/6LRA8XntyGc/6MFRVIfGDMMJ .)

It seems that nobody disagreed either. I can't say I understand the negative si'e, but I don't have a problem with the greater than one. 

 

According to the current definition:

x1 number si'e x2 x1 pagbu x2 gi'e klani li number lo se gradu be x2

it seems that a number followed by {si'e} cannot be larger than 1 unless {pagbu} is interpreted very broadly so that x1 of {pagbu} can be larger than x2.

I'd keep "pagbu" as normal, and define si'e more carefully so that it can cover more cases.

  

Under this condition, if {P si'e} is used for counting up, a number followed by {si'e} should be changed every time another referent becomes to be considered.

ko'a pa si'e

i

ko'a fi'u re si'e ije ko'a jo'u ko'e pa si'e

i

ko'a fi'u ci si'e ije ko'a jo'u ko'e jo'u ko'i pa si'e

...

ko'a pa si'e ko'a gi'e fi'u re si'e ko'a jo'u ko'e gi'e fi'u ci si'e ko'a jo'u ko'e jo'u ko'i 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1-7) defines for {ko'a}, the referent of {ko'a} satisfies {su'o pa mei} _non-distributively_. 

Any other referents that are {me ko'a} do not satisfy {su'o pa mei}.

As for (D1-7), speakers who talk about non-individual referents may select not only {ko'a} but also any arbitrary {ko'e} {ko'i}... as {su'o pa mei} as long as the selected referents don't conflict each other.

What do you mean by "conflict"? Overlap? Or do you mean that some things are selected as pseudo-atoms, so that, for example:

ko'a su'o mei

ko'e su'o mei

ko'i goi ko'a jo'u ko'e su'o mei

So ko'a and ko'e are pseudo-atoms, because nothing among them (besides themselves) satisfies "su'o mei", but "ko'i" is not a pseudo-atom, because there are things among them, different from ko'i itself, that do satisfy "su'o mei". 

Then all and only the pseudo-atoms will satisfy "pa mei", and only things composed of one or more pseudo-atoms will satisfy "su'o mei".. 

Yes. 

You will also need to modify your (D1) to:

 (D1') ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a gi'e su'o mei zo'u ge da su'o N-1 mei gi de na me da

Otherwise, if ko'a and ko'e are both atomless "ko'a jo'u ko'e cu re mei" will be false. Without the additional restriction in (D1) "ko'a jo'u ko'e su'o N mei" will be true for any positive N, because you only need ko'a as your starting point and then you can keep adding pieces of ko'e to count up because the original (D1) doesn't require the add ons to be su'o mei. (For my definition, the additional restriction doesn't change anything, because everything satisfies it so it's not really any restriction.)

 

Non-individual referents are excluded from outer quantified sumti and singular bound variables of official Lojban. (If su'oi, ro'oi etc become official, it is not the case, though.) Possibility of quantification on non-individual referents are left only in expressions with inner quantifier. If inner quantifiers are allowed to non-individual referents, speakers who regards {lo nanba} as non-individual consider that a half of {lo pa nanba} is also {me lo nanba}. If inner quantifier is given only to individual(s), the language restrict thought of speakers so that they should consider that "a half of {lo pa nanba} is not {me lo nanba}". 

That's because "me" is supposed to mean "among", not "part of". Your thought is not restricted, you just have to choose the words that better express your thoughts.

[guskant]

Le mercredi 26 février 2014 06:49:07 UTC+9, xorxes a écrit :

On Tue, Feb 25, 2014 at 11:04 AM, guskant <gusni...@gmail.com> wrote:

Le mardi 25 février 2014 07:59:04 UTC+9, xorxes a écrit :

It seems to me that it would be better to use "si'e" rather than "mei" for that purpose, and "pagbu" instead of "me". If you allow things like "so'i da poi me lo pa nanba" you pretty much destroy "me" as "among" and you turn it into "pagbu".

When {lo nanba} is non-individual, {so'i da poi me lo pa nanba} is not allowed. non-individual referents cannot be in the domain of {so'i da}, because only individuals are allowed in the domain of singular variables.

Right, but then you need an additional constraint on your pseudo-individuals: they must be either individuals themselves, or they must be atomless, they cannot properly contain any individuals. By "non-individual" I assume you mean atomless, not containing any individuals at all, rather than merely not being an individual.

Right.

 

 

If {P si'e} were allowed for P>1, {si'e} would have been better than {me} for non-individual referents. 

(I have once suggested an interpretation of {P si'e} for other than P<=1, though nobody agreed: https://groups.google.com/d/msg/lojban/6LRA8XntyGc/6MFRVIfGDMMJ .)

It seems that nobody disagreed either. I can't say I understand the negative si'e, but I don't have a problem with the greater than one. 

 

According to the current definition:

x1 number si'e x2 x1 pagbu x2 gi'e klani li number lo se gradu be x2

it seems that a number followed by {si'e} cannot be larger than 1 unless {pagbu} is interpreted very broadly so that x1 of {pagbu} can be larger than x2.

I'd keep "pagbu" as normal, and define si'e more carefully so that it can cover more cases.

  

That is what I wish.

 

Under this condition, if {P si'e} is used for counting up, a number followed by {si'e} should be changed every time another referent becomes to be considered.

ko'a pa si'e

i

ko'a fi'u re si'e ije ko'a jo'u ko'e pa si'e

i

ko'a fi'u ci si'e ije ko'a jo'u ko'e jo'u ko'i pa si'e

...

ko'a pa si'e ko'a gi'e fi'u re si'e ko'a jo'u ko'e gi'e fi'u ci si'e ko'a jo'u ko'e jo'u ko'i 

Yes, and speakers may not want to change the unit every time counting up.

 

Using {ke'a}, our definitions are described as follows:

(D1-7) ko'a su'o pa mei

(D1) ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ke'a N mei  := ke'a su'o N mei gi'e nai su'o N+1 mei 

(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

When (D1-7) defines for {ko'a}, the referent of {ko'a} satisfies {su'o pa mei} _non-distributively_. 

Any other referents that are {me ko'a} do not satisfy {su'o pa mei}.

As for (D1-7), speakers who talk about non-individual referents may select not only {ko'a} but also any arbitrary {ko'e} {ko'i}... as {su'o pa mei} as long as the selected referents don't conflict each other.

What do you mean by "conflict"? Overlap? Or do you mean that some things are selected as pseudo-atoms, so that, for example:

ko'a su'o mei

ko'e su'o mei

ko'i goi ko'a jo'u ko'e su'o mei

So ko'a and ko'e are pseudo-atoms, because nothing among them (besides themselves) satisfies "su'o mei", but "ko'i" is not a pseudo-atom, because there are things among them, different from ko'i itself, that do satisfy "su'o mei". 

Then all and only the pseudo-atoms will satisfy "pa mei", and only things composed of one or more pseudo-atoms will satisfy "su'o mei".. 

Yes. 

You will also need to modify your (D1) to:

 (D1') ke'a su'o N mei := su'oi da poi me ke'a ku'o su'oi de poi me ke'a gi'e su'o mei zo'u ge da su'o N-1 mei gi de na me da

Otherwise, if ko'a and ko'e are both atomless "ko'a jo'u ko'e cu re mei" will be false. Without the additional restriction in (D1) "ko'a jo'u ko'e su'o N mei" will be true for any positive N, because you only need ko'a as your starting point and then you can keep adding pieces of ko'e to count up because the original (D1) doesn't require the add ons to be su'o mei. (For my definition, the additional restriction doesn't change anything, because everything satisfies it so it's not really any restriction.)

 

Right. I need (D1') for proper definition of {N mei} for non-individuals. I was implicitly requiring it as "non-conflict selection of {su'o pa mei}", but it should have been explicit.

 

Non-individual referents are excluded from outer quantified sumti and singular bound variables of official Lojban. (If su'oi, ro'oi etc become official, it is not the case, though.) Possibility of quantification on non-individual referents are left only in expressions with inner quantifier. If inner quantifiers are allowed to non-individual referents, speakers who regards {lo nanba} as non-individual consider that a half of {lo pa nanba} is also {me lo nanba}. If inner quantifier is given only to individual(s), the language restrict thought of speakers so that they should consider that "a half of {lo pa nanba} is not {me lo nanba}". 

That's because "me" is supposed to mean "among", not "part of". Your thought is not restricted, you just have to choose the words that better express your thoughts.

The thought of "a half of {lo pa nanba} is also {me lo nanba}" is not related to the concept {part of} as long as {lo pa nanba} is a non-individual referent related to other non-individual referents with {me}. Non-individual {lo pa nanba} as well as "a half of" {lo pa nanba} is only an ordinary vertex of an infinite tree constructed with {me}. I said "a half of" because I don't know an appropriate short expression in English. Only when a unit is equalized with an individual, a half of {lo pa nanba} is regarded as {part of}. Actually there is no other method for expressing non-individual quantification; there is no choice of the words that better express the thought of non-individual with quantification. 

If {M si'e} is properly defined so that M>1 is accepted, {lo PA pi broda} and {lo pi PA broda} may represent non-individual quantification, which are expanded to expressions with {M si'e}. If it is realized, the language design will be more universal.