# {ro}, existential import and De Morgan

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### Riley Martinez-Lynch

Oct 17, 2014, 5:55:58 AM10/17/14

In researching a question on the mailing list, I came across discussions of the question of whether {ro} has "existential import" -- which is to say, does a true proposition {ro broda cu brode} imply that {su'o broda cu brode} is also true? CLL 16.8 says:

"Lojban universal claims always imply the corresponding existential claims as well."

Which is to say, {ro} has existential import. This is the position of classic/Aristotelian logic, but not modern logic.

It was been pointed out that the documentation of negation boundaries is not consistent with this interpretation of ro. Take these examples from CLL 16.11, which are said to be equivalent:

{naku roda poi verba cu klama su'ode poi ckule} (16.11.7)

{su'oda poi verba ku'o naku klama su'ode poi ckule} (16.11.4, {ku'o}-corrected per errata)

Now let's simplify the examples, replacing the students with unicorns -- there's a tradition of talking about unicorns when considering this question:

{naku ro pavyseljirna cu blabi} == {su'o pavyseljirna naku cu blabi}

Given that {ro} has import, and assuming for the sake of argument that the universe has no unicorns to quantify, {ro pavyseljirna cu blabi} is false, and therefore, {naku ro pavyseljirna cu blabi} is true.

However, {su'o pavyseljirna naku cu blabi} is false, since there are no unicorns to predicate with {blabi}, affirmatively or negatively. The truth value of the proposition has changed despite the assurance that moving the negation boundary and "inverting" the quantifiers accordingly is supposed to preserve the meaning. Some have argued that this shows a violation of De Morgan's laws.

The anomaly does not occur if {ro} is not held to import. In that case, {ro pavyseljirna cu blabi} is true, {naku ro pavyseljirna cu blabi} is false, and {su'o pavyseljirna naku cu blabi} is also false.

This question was discussed extensively from 2002-2003, which is to say, during the BPFK's formative period. There seems to have been near-consensus that {ro} should not be held to import, but there were also emphatic dissents from John Cowan and pc.

I saw indications of an expectation that BPFK would ultimately decide the question, but I have been unable to find a record that the question was discussed or that a decision was taken.The BPFK section on "Inexact Numbers" includes a link in the "Issues" section to the 2003 discussion, but otherwise -- as far as I can discern -- takes no clear position.

Can anyone show me where and how this problem was resolved? Failing that, would anyone care to take this up and once and for all settle the matter?

mi'e la mukti mu'o

### Alex Burka

Oct 17, 2014, 5:19:29 PM10/17/14
Technicality: the original question should be whether {ro broda cu brode} implies {su'o da broda}, correct?

mu'o mi'e la durka
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### John Cowan

Oct 17, 2014, 9:14:21 PM10/17/14
Riley Martinez-Lynch scripsit:

> Which is to say, {ro} has existential import. This is the position of
> classic/Aristotelian logic, but not modern logic.

As pc explained it to me, Aristotelian and Fregean (modern) logic don't
actually contradict one another in this area. However, the *translation*
from Aristotelian "All As are Bs" to Fregean "For all x, if A(x) then
B(x)" is not quite truth-preserving. "All A is B" is taken to be false
if there are no As, whereas "For all x, if A(x) then B(x)" is vacuously
true if there does not exist x such that A(x). Lojban expresses each
of these differently: the Aristotelian claim is "ro broda cu brode"
whereas the Fregean claim is "ro da poi broda cu brode".

Now these can be reconciled in their interpretation if we assume that
"ro" has existential import: then "ro broda cu brode" requires that
there are brodas, whereas "ro da poi broda cu brode" requires only that
there are das. The latter is true except in a completely empty universe,
which is not really worth talking about.

> Can anyone show me where and how this problem was resolved? Failing that,
> would anyone care to take this up and once and for all settle the matter?

In answer to both questions: probably not.

--
John Cowan http://www.ccil.org/~cowan co...@ccil.org
What has four pairs of pants, lives in Philadelphia,
and it never rains but it pours?
--Rufus T. Firefly

### Alex Burka

Oct 17, 2014, 11:08:53 PM10/17/14
I understand {ro broda} to be the same as {ro da poi broda}, whereas {ro lo broda} is the one that's different (= {ro da poi me lo broda}). Not to put words in your mouth, but at least once in 2002[1] you agreed.

mu'o mi'e la durka

### mukti

Oct 18, 2014, 11:58:27 AM10/18/14
On Friday, October 17, 2014 10:14:21 PM UTC-3, John Cowan wrote:
Lojban expresses each of these differently: the Aristotelian claim is "ro broda cu brode"
whereas the Fregean claim is "ro da poi broda cu brode".

BPFK gadri formally defines "PA broda" as "PA da poi broda". Does the distinction you are making survive this definition, or are you describing the status quo ante BPFK?

if we assume that "ro" has existential import: then "ro broda cu brode" requires that
there are brodas, whereas "ro da poi broda cu brode" requires only that
there are das.  The latter is true except in a completely empty universe,

If I understand, you describe an interpretation of {ro da poi broda cu brode} such that the "existential import" of {ro} applies only to {da} rather than to {da poi broda} -- i.e. it "requires only that there are das".

Presumably, even if the "importingness" of {ro} is limited to {da}, {ro} can still be said to quantify {da poi broda}: Otherwise, assuming that other PA work similiarly, {ci da poi gerku} would claim precisely three "das" in the universe, indicating among them an unspecified number of those which {gerku}.

Is the idea that, in limiting the importingness of {ro} to {da} while quantifying the entire term, that if in fact there are no "das" which {broda}, the statement may be vacuously true? And although you ruled out this scenario {ro broda}, for example, what about {ro lo broda}?

Suppose {lo broda} describes an irreducible plural. In that case, is {ro lo broda cu brode} false per classical logical logic or true per modern logic? Would the answer be different for {ro lo no broda}, or for {ro lo broda} in a universe without brodas, providing that either of these are possible?

Finally, if {ro broda} and {ro da poi broda} toggles between aristotelian universal affirmatives and modern ones, isn't {ro broda} (as well as any other construction that preserves import) still inconsistent in regard to negation boundaries?

> Can anyone show me where and how this problem was resolved? Failing that,
> would anyone care to take this up and once and for all settle the matter?
In answer to both questions:  probably not.

I hope that doesn't prove true. As pc said in an old jboske thread"the question of existential import seems [too] central to go unsolved." Thank you for weighing in.

### John Cowan

Oct 18, 2014, 9:29:32 PM10/18/14
Alex Burka scripsit:

> I understand {ro broda} to be the same as {ro da poi broda}, whereas {ro
> lo broda} is the one that's different (= {ro da poi me lo broda}). Not
> to put words in your mouth, but at least once in 2002[1] you agreed.

Yes, correct: for "ro da poi broda cu brode" read "ro da zo'u da broda
.inaja da brode"
Sound change operates regularly to produce irregularities;
analogy operates irregularly to produce regularities.
--E.H. Sturtevant, ca. 1945, probably at Yale

### Alex Burka

Oct 19, 2014, 1:55:11 AM10/19/14
Ok, so just to clarify what you were correcting, with importing {ro} you would say {ro broda cu brode} and {ro da poi broda cu brode} are the same thing and require {su'o da broda}, while {ro da ganai broda gi brode} is different and just requires a non-empty universe?

mu'o mi'e la durka

### Alex Burka

Oct 19, 2014, 1:59:20 AM10/19/14

On Saturday, October 18, 2014 at 11:58 AM, mukti wrote:

On Friday, October 17, 2014 10:14:21 PM UTC-3, John Cowan wrote:
Lojban expresses each of these differently: the Aristotelian claim is "ro broda cu brode"
whereas the Fregean claim is "ro da poi broda cu brode".

BPFK gadri formally defines "PA broda" as "PA da poi broda". Does the distinction you are making survive this definition, or are you describing the status quo ante BPFK?

if we assume that "ro" has existential import: then "ro broda cu brode" requires that
there are brodas, whereas "ro da poi broda cu brode" requires only that
there are das.  The latter is true except in a completely empty universe,

If I understand, you describe an interpretation of {ro da poi broda cu brode} such that the "existential import" of {ro} applies only to {da} rather than to {da poi broda} -- i.e. it "requires only that there are das".

Presumably, even if the "importingness" of {ro} is limited to {da}, {ro} can still be said to quantify {da poi broda}: Otherwise, assuming that other PA work similiarly, {ci da poi gerku} would claim precisely three "das" in the universe, indicating among them an unspecified number of those which {gerku}.
Yeah, I agree with you here.

Is the idea that, in limiting the importingness of {ro} to {da} while quantifying the entire term, that if in fact there are no "das" which {broda}, the statement may be vacuously true? And although you ruled out this scenario {ro broda}, for example, what about {ro lo broda}?

Suppose {lo broda} describes an irreducible plural. In that case, is {ro lo broda cu brode} false per classical logical logic or true per modern logic? Would the answer be different for {ro lo no broda}, or for {ro lo broda} in a universe without brodas, providing that either of these are possible?
Can you explain this question further (if it would derail the thread, don't do it)?

Finally, if {ro broda} and {ro da poi broda} toggles between aristotelian universal affirmatives and modern ones, isn't {ro broda} (as well as any other construction that preserves import) still inconsistent in regard to negation boundaries?
This is the \$64K question, pe'i...

> Can anyone show me where and how this problem was resolved? Failing that,
> would anyone care to take this up and once and for all settle the matter?
In answer to both questions:  probably not.

I hope that doesn't prove true. As pc said in an old jboske thread"the question of existential import seems [too] central to go unsolved." Thank you for weighing in.

mi'e la mukti mu'o

--

### John Cowan

Oct 19, 2014, 1:08:14 PM10/19/14
Alex Burka scripsit:

> Ok, so just to clarify what you were correcting, with importing {ro}
> you would say {ro broda cu brode} and {ro da poi broda cu brode} are
> the same thing and require {su'o da broda}, while {ro da ganai broda
> gi brode} is different and just requires a non-empty universe?

Right. The difference is between restricted and unrestricted quantification.
Lope de Vega: "It wonders me I can speak at all. Some caitiff rogue
did rudely yerk me on the knob, wherefrom my wits yet wander."
An Englishman: "Ay, belike a filchman to the nab'll leave you
crank for a spell." --Harry Turtledove, Ruled Britannia

### Ozymandias Haynes

Nov 6, 2014, 2:40:37 AM11/6/14
Hi everyone.  la mukti asked me to weigh in on this.  I’ve given it a good bit of thought, as it’s one of the two most serious problems in Lojban foundations as defined in the CLL.

la mukti's analysis is excellent; his simple unicorn sentences demonstrate the contradiction in action and the connection to Aristotelian logic explains how importation might have crept in.  This association with Aristotle also provides an argument against importation.  Modern logic has simply left Aristotle behind, as should, in my opinion, any conlang built on the developments in logic from the last century.

Furthermore, it's not quite right to say that the CLL simply chooses to use Aristotelian logic in this one case.  This is because in Aristotelian logic there are no quantifiers as they are understood in predicate logic (or in Lojban).  In fact this is one of the limitations of Aristotle's rules for reasoning: it ignored a lot of the inner structure of the statements involved and so could not account for the relationships between the objects involved in the statements.  So importing ro here is not actually historical, but anachronistic.  The CLL definition essentially creates a bizarre hybrid of Aristotelian and predicate logic which no one uses.  Incompatibility with the classical negation theorem is one way this break is showing up.  Aristotle would not have said that when moving the negation sign across bound variables you must flip the quantifier to preserve truth values because those things weren't part of his system at all.

There are only three choices here as I see it.  We can use the standard semantics from predicate logic for the universal quantifier and keep the standard negation theorem; or we can keep importing ro and lose the negation theorem; or we can do nothing and allow an internal contradiction to lie in the foundations of Lojban.  A strong argument in favor of importing ro would include an account of the way negation works in this new system.  Although I am solidly in favor of non-importing ro, I will sketch out how to do that in a moment.  But first I'd like to examine John's point.

The way that "All unicorns are white." is represented in predicate logic is with the formula $$\forall x : [ U(x) \rightarrow W(x) ]$$.  (The stuff between the dollar signs is LaTeX markup; if you can't read it you can plug it into an online renderer. \forall is the universal quantifier, x is the bound variable, \rightarrow is implication, and U and W are functions corresponding to 'x is a unicorn' and 'x is white' resp.).  As John says, one way to translate this into Lojban is "ro da zo'u ganai da pavyseljirna gi da blabi".  This is irrelevant to la mukti's construction, however.  He did not use that Lojban sentence in his example, he used one that's formally equivalent to da with poi.  The negation theorem is stated in its full generality in the CLL and not only on sentences of the form above.  Indeed, using that implication form as a definition of "ro da poi X" is precisely what is needed to fit with the negation theorem and with predicate logic, and those are precisely the semantics that I am advocating.

It’s easy to see that these sentences are consistent with the negation theorem.  Recall that a logical implication is a function of statements; it's truth value depends only on the truth value of the statements it acts on.  An IF (...) THEN (...) statement is defined to be false when the first argument, called the antecedent, is true and the second argument, called the consequent, is false.  All other pairs of arguments result in true.

Under our assumption that nothing satisfies pavyseljirna, "ro da zo'u ganai da pavyseljirna gi da blabi" is true because for every value of da, the antecedent is false.  Therefore "naku ro da zo'u ganai da pavyseljirna gi da blabi" is false.  According to the negation theorem "su'o da naku zo'u ganai da pavyseljirna gi da blabi" must also be false.  This says that there must an object which falsifies the implication, and as I said in the last paragraph this can only happen when the antecedent is true and the consequent false.  The antecedent claims that x is a unicorn, so a true antecedent would contradict our assumption about unicorns.  Of course the particular functions we chose, unicorns and white, are not important; all statements of this form are consistent with the negation theorem.

So if we wanted to keep the importing semantics, how would negation have to work?  We first rewrite "ro da poi P" in the importing sense as a formula in predicate logic to manipulate it symbolically, then translate it back into Lojban.  This still uses the implication, but includes the additional restriction that something must satisfy P.  We therefore represent "naku ro da poi P zo’u Q" as $$\neg \forall x \exists y : P(y) \land [P(x) \rightarrow Q(x)])$$.  Applying the theorem to the formula, we get $$\exists x \forall y : \neg (P(y) \land [P(x) \rightarrow Q(x)])$$ which is equivalent by another elementary theorem to $$\exists x \forall y : \neg P(y) \lor \neg (P(x) \rightarrow Q(x))$$ which can be translated back into Lojban as “ro da su’o de zo’u de P inajanai ganai da P gi da Q”.  Notice in particular that there are now two sumti involved.  This is because in the importing sense there are really two different claims being made and each use their own variable.  I played with this for about half an hour tonight and couldn’t find an equivalent form that resulted in more elegant Lojban; perhaps an importing advocate can do better.

That’s one of four cases; three others are treated similarly, and then negation dragging across unrestricted da operates according to the normal rules.  Imagine trying to move naku around in an ordinary sentence under these rules!

I don’t know what pc said to John but it is simply not true that the Aristotelian sense of “All P are Q” is compatible with predicate logic.  On page 54 of Hilbert and Ackermann’s classic _Principles of Mathematical Logic_ appears the following:

“According to Aristotle the sentence ‘All A is B’ is valid only when there are objects which are A.  Our deviation from Aristotle in this respect is justified by the mathematical applications of logic, in which the Aristotelian interpretation would not be useful.”

Its possible that there is some confusion over an elementary theorem which states $$\forall x : P(x)$$ implies $$\exists x : P(x)$$.  If we look closely at that we see that, in John’s words, the quantification there corresponds to Lojban’s unrestricted logical variables; restricted logical variables must first be rewritten as pure formulae, as I did above, before applying the theorem.

mi’e az

### John Cowan

Nov 8, 2014, 7:46:33 PM11/8/14
Ozymandias Haynes scripsit:

> The way that "All unicorns are white." is represented in predicate logic is
> with the formula $$\forall x : [ U(x) \rightarrow W(x) ]$$.

This is precisely the point that pc (and following him, I) disputed.
This first-order predicate logic (FOPL) translation is *not* semantically
identical to the natural-language (NL) claim (which the Aristotelian
formulation follows), precisely because the FOPL version does not have
existential import (EI), whereas the NL version does. If you ask someone
"Do all unicorns fly?" they do not normally reply "Yes"; they either say
"No" or reject the question metalinguistically.

Pc and I hold that there is good reason to provide Lojban expressions
of both the FOPL and the NL versions of the claim, since they are
semantically distinct. This can be easily done by saying that "ro da"
without a following "poi" (unrestricted quantification) takes the FOPL
interpretation, whereas "ro da poi broda" (restricted quantification)
takes the NL interpretation. This does not in any way restrict FOPL,
since FOPL has *only* unrestricted variables, not restricted ones. So it
would be easy to say that "ro" has EI in restricted quantifications,
and lacks EI in unrestricted ones.

Pc's further insight, however, is that it is essentially harmless to
extend "ro" to have EI in all cases. Given the sentence, "ro da zo'u
ganai da broda gi da brode", it is obvious that this does not entail
"da broda", since it is under negation, and negated claims can never
have EI. However, it is safe to replace "ro da" with "so'u da", *except*
in the case of an entirely empty universe. If we are willing to give
up the desire to make vacuous universal claims about empty universes,
we have no trouble taking "ro" to always have EI.

When I first heard this argument, I didn't accept it either. It took pc
about an hour of intensive two-way conversation to convince me that this
view is both self-consistent and consistent with FOPL-as-we-know-it (apart
from empty universes), so I don't expect you to swallow it as a result of
a brief email. Nevertheless, however counterintuitive to people who know
FOPL, it is I believe sound, and has desirable properties for ordinary
NL statements, while in no way inhibiting properly formulated FOPL Lojban.
My confusion is rapidly waxing
> > <javascript:>
> > Lope de Vega: "It wonders me I can speak at all. Some caitiff rogue
> > did rudely yerk me on the knob, wherefrom my wits yet wander."
> > An Englishman: "Ay, belike a filchman to the nab'll leave you
> > crank for a spell." --Harry Turtledove, Ruled Britannia
> >

--
John Cowan http://www.ccil.org/~cowan co...@ccil.org
If you have ever wondered if you are in hell, it has been said, then
you are on a well-traveled road of spiritual inquiry. If you are
absolutely sure you are in hell, however, then you must be on the Cross
Bronx Expressway. --Alan Feuer, New York Times, 2002-09-20

### John Cowan

Nov 8, 2014, 7:48:16 PM11/8/14
Scripsi:

> This does not in any way restrict FOPL,

I meant to write "This does not in any way contradict FOPL".
He played King Lear as though someone had played the ace.
--Eugene Field

### Ozymandias Haynes

Nov 9, 2014, 4:19:51 AM11/9/14
je'e la djan io

> from empty universes), so I don't expect you to swallow it as a result of
> a brief email. Nevertheless, however counterintuitive to people who know

Oh, there's no danger of that. I'm not the swallowing type.

What I am here to do is engage in a substantive discussion about a
fine point of Lojban semantics. I'm sure you're busy, and I imagine
you are very tired indeed of having conversations about something you
wrote seventeen years ago. Particularly, as la mukti notes, on a
topic that's been discussed before.

I suspect that the point you're making with your dual translations fit
better in one of those previous conversations.

As I said in my first message, your dual translation of "All A is B"
is irrelevant to the point that la mukti carefully articulated in his
original post. He was not translating any English sentences; he was
quoting directly from the CLL. In examples 11.5 through 11.7, the
predicate logic negation theorem is applied to "ro da poi" statements.
The section is online here: http://lojban.github.io/cll/16/11/ or at
the bottom of page 405 in the physical book.

This is the text of the relevant passage:

"As explained in Section 9, when a prenex negation boundary expressed
by "naku" moves past a quantifier, the quantifier has to be inverted.
The same is true for "naku" in the bridi proper. ... Thus, the
following are equivalent to Example 11.4:

11.5) su'oda poi verba cu klama rode poi ckule naku
...
11.6) su'oda poi verba cu klama naku su'ode poi ckule
...
11.7) naku roda poi verba cu klama su'ode poi ckule"

la mukti and I are not arguing that the CLL does not assign
Aristotelian semantics to "ro da poi" statements and reserve the
predicate logic semantics solely for "ro da zo'u ganai" statements.
We are arguing that when you do that, the predicate logic negation
theorem does not hold for "ro da poi" statements. The CLL says that
it does.

la mukti carefully walks through the reasoning in his post by
constructing a simpler sentence (but one still structurally similar)
and then evaluating its truth using the Aristotelian semantics given
in the CLL for "ro da poi" statements and which you are advocating in
this thread. Then he evaluates its truth using the negation theorem.

If the predicate logic negation theorem had simply been stated to
apply only to unrestricted universal quantification rather than "ro da
poi" clauses then there would be no contradiction.

construction, if you find the time. Do you think the construction is
valid, and that a contradiction obtains? If not, at what specific
point in his argument does the construction fail?

-Oz

### And Rosta

Nov 9, 2014, 7:42:50 AM11/9/14

When we discussed this at great length a dozen years ago, the arguments mustered -- which I can't reconstruct from memory -- led to the clear conclusion that {ro} (given its undisputed properties) means "however many there are", i.e. a cardinal number whose value can be zero, but this did not mean that there should not be another word meaning an existential import universal quantifier.

So there are two or three different and separate arguments here, all confounding each other:
1. What does ro mean, and does it have EI? (A question settled a dozen years ago.)
2. Should there be a non-EI universal quantifier?
3. Should there be an EI universal quantifier? This is the question John seems to be addressing.

Furthermore, an additional separate question would be

4. In any bpfk revision of the CLL specification, which meaning should be paired with the phonological form /ro/?

--And.

### John Cowan

Nov 9, 2014, 10:21:03 AM11/9/14
Ozymandias Haynes scripsit:

> In examples 11.5 through 11.7, the
> predicate logic negation theorem is applied to "ro da poi" statements.

Ah. In that case, those examples are wrong and should be fixed (someone
should mark the wiki, or wherever the errata go nowadays). As I'm sure
you can imagine, it's damned hard to keep a consistent point of view
throughout such a book, especially when the semantic interpretations
changed during the period of writing it.

Sorry for the noise.
You tollerday donsk? N. You tolkatiff scowegian? Nn.
You spigotty anglease? Nnn. You phonio saxo? Nnnn.
Clear all so! Tis a Jute.... (Finnegans Wake 16.5)

### Gleki Arxokuna

Nov 9, 2014, 11:19:15 AM11/9/14
2014-11-09 18:20 GMT+03:00 John Cowan :
Ozymandias Haynes scripsit:

> In examples 11.5 through 11.7, the
> predicate logic negation theorem is applied to "ro da poi" statements.

Ah.  In that case, those examples are wrong and should be fixed (someone
should mark the wiki

Could you please provide the correct text of those examples?
The current CLL text is in
https://lojban.github.io/cll/

If you provide the corrected text i will put it tothe Errata page which is
http://www.lojban.org/tiki/CLL,+aka+Reference+Grammar,+Errata

, or wherever the errata go nowadays).  As I'm sure
you can imagine, it's damned hard to keep a consistent point of view
throughout such a book, especially when the semantic interpretations
changed during the period of writing it.

Sorry for the noise.

--
John Cowan          http://www.ccil.org/~cowan        co...@ccil.org
You tollerday donsk?  N.  You tolkatiff scowegian?  Nn.
You spigotty anglease?  Nnn.  You phonio saxo?  Nnnn.
Clear all so!  Tis a Jute.... (Finnegans Wake 16.5)

### Alex Burka

Nov 9, 2014, 1:24:00 PM11/9/14
I really appreciate your explanation of the historical discussion here, but it seems to me if it were "essentially harmless" to make {ro} importing all the time, it wouldn't break De Morgan's law or invalidate simple examples. So I'm still confused.

### mukti

Nov 9, 2014, 1:34:23 PM11/9/14
On Sunday, November 9, 2014 9:42:50 AM UTC-3, And Rosta wrote:

1. What does ro mean, and does it have EI? (A question settled a dozen years ago.)
2. Should there be a non-EI universal quantifier?
3. Should there be an EI universal quantifier? This is the question John seems to be addressing.

4. In any bpfk revision of the CLL specification, which meaning should be paired with the phonological form /ro/?

I believe that #1 and #4 are the question I'm trying to ask -- which hopefully have the same answer -- and I'm sorry if I invited the detour into other questions.

CLL 16.8 says:

sumti of the type “ro da poi klama” requires that there are things which “klama”

It's not entirely explicit in the section what the consequences when the requirements of the sumti are not met. I have assumed that according to this requirement, {ro da poi klama cu pavyseljirna} is then considered to be false in the case of {no da klama}. (If it has another truth value which is neither true nor false, then I'm barking up the wrong tree!)

However, if such sentences are considered to be false, then the definition of {ro} is incompatible with the description of how negation boundaries work. Supposing, for old time's sake, a universe without unicorns:

{su'o pavyseljirna na ku cu blabi} => There is at least one unicorn, such that it is not white. => FALSE.

Now we move the boundary, and "invert" the quantifier, while preserving the truth value of the statement:

{na ku ro pavyseljirna cu blabi} => It is not true that all unicorns are white. => FALSE.

But then we negate that and get:

{ro pavyseljirna cu blabi} => All unicorns are white. => TRUE.

The {ro} derived from these transformation is not one that "impl[ies] the corresponding existential claims". Either that definition of {ro} is invalid, or the derivation of {ro} from {su'o} by moving negation boundaries is. It's not just faulty examples at stake. The rules don't work together.

When I started this thread, I was under the impression that the BPFK section on "Inexact Numbers" took no clear position on this problem. I now see that there is indeed a commitment to preserving the negation boundaries formula, although it is buried in the formal definitions and obscured by bad formatting. The part I'm looking at is this:

ro da = da'ano da = no da naku = naku su'o da naku

If this definition holds, then {ro pavyseljirna cu blabi} has the same truth value as {na ku su'o pavyseljirna na ku cu blabi}. If {ro} were held to import, then both sentences would be false. Wouldn't that commit us to hold the negation of the second sentence to be true?

{su'o pavyseljirna na ku cu blabi} => "There is at least one unicorn, such that it is not white."

If I have made a mistake in my reasoning, please point it out. Otherwise, I will assume that BPFK has settled questions #1 and #4 per the equivalence for {ro da} == {naku su'o da naku} on the "Inexact Numbers" page.

### Ilmen

Nov 9, 2014, 6:02:31 PM11/9/14
As for {ro} and existential import, I would like to highlight that if {ro} never implies existential import by itself, there is still a very simple way to add the existential import nuance: {ro su'o (pa)}.
In CLL Chapter 18 Section 8 Example 18, it is shown how {ro} can be combined with another number, implying that {ro} and this other number have the same value:

8.18)  mi viska le rore gerku
I saw the all-of/two dogs.
I saw both dogs.


In a similar way, {ro su'o (pa) da} would mean "everything, which is at least one thing".

Another similar option —although longer— could be {vei ro .e su'o (pa) da}.

mi'e la .ilmen. mu'o

### And Rosta

Nov 11, 2014, 8:09:30 AM11/11/14
mukti, On 09/11/2014 18:34:
> On Sunday, November 9, 2014 9:42:50 AM UTC-3, And Rosta wrote:
>
> 1. What does ro mean, and does it have EI? (A question settled a dozen years ago.)
> 2. Should there be a non-EI universal quantifier?
> 3. Should there be an EI universal quantifier? This is the question John seems to be addressing.
>
> 4. In any bpfk revision of the CLL specification, which meaning should be paired with the phonological form /ro/?
>
> I believe that #1 and #4 are the question I'm trying to ask -- which
> hopefully have the same answer -- and I'm sorry if I invited the
> detour into other questions.

I felt that in response to you asking Question #1, John was answering Question #3. But considering the rivers of sweat that went into answering the question a dozen years ago, I think anyone unwilling to consider it a settled question should reread the old discussion and engage with the reasoning therein. (I can't remember it.)

> CLL 16.8 says:
>
> sumti of the type “ro da poi klama” requires that there are things which “klama”

I would have thought that under that view, "no da poi klama" likewise requires that there are things which "klama". That is, it's the "da poi" rather than the "ro" that has EI. Hence, for instance, {lo'i (ro) broda} doesn't entail {lo'i su'o broda} and doesn't exclude {lo'i no broda}. Whether EI "da poi" is consistent with CLL and logic, I no longer have the powers to opine on. IIRC, xorxes thinks "lo broda" is inconsistent with "lo no broda", so if "ro/no da poi broda" = "ro/no (lo) broda" then xorxes must think "da poi" has EI.

> It's not entirely explicit in the section what the consequences when
> the requirements of the sumti are not met. I have assumed that
> according to this requirement, {ro da poi klama cu pavyseljirna} is
> then considered to be false in the case of {no da klama}. (If it has
> another truth value which is neither true nor false, then I'm barking
> up the wrong tree!)

If I may dare to presume to venture to second-guess xorxes, I think he might view the EI as presupposed, in which case {ro da poi klama cu pavyseljirna} would have a truth value only when {su'o da klama} is true. And in that case -- i.e. in the case of that view being deemed correct -- you would be barking up the wrong tree.

[...]
> If I have made a mistake in my reasoning, please point it out.
> Otherwise, I will assume that BPFK has settled questions #1 and #4
> per the equivalence for {ro da} == {naku su'o da naku} on the
> "Inexact Numbers" page.

I think your assumption/conclusion is correct. But it may additionally be the case that restricted da presupposes EI.

--And.

### Jorge Llambías

Nov 11, 2014, 6:14:42 PM11/11/14
On Tue, Nov 11, 2014 at 10:09 AM, And Rosta wrote:

If I may dare to presume to venture to second-guess xorxes, I think he might view the EI as presupposed, in which case {ro da poi klama cu pavyseljirna} would have a truth value only when {su'o da klama} is true.

Given the four forms:

(1) ro lo broda cu brode
(2) ro broda cu brode
(3) ro da poi broda cu brode
(4) ro da ga nai broda gi brode

I think most people would agree that (1) presupposes that there are brodas and (4) doesn't, and that (2) and (3) are equivalent to each other. In the absence of brodas (4) is true and (1) is meaningless.

I would strongly disagree that any of these sentences is false in the absence of brodas. Whether (2) and (3) are vacuously true or meaningless doesn't seem to matter much, because in practice we don't quantify over empty domains. I'm not sure if this is due to strict presupposition or just Gricean good manners.

mu'o mi'e xorxes

### guskant

Nov 23, 2014, 11:44:22 PM11/23/14
From a theoretical point of view, Chapter 16 of CLL describes something out of a language. As long as it introduces a theory on truth value, it is a kind of model theory. The problems regarding the current text of Chapter 16 are caused by two points:

1-1. It does not make clear the distinction between a language and a model;
1-2. It mixes up several models (of Aristotle and of a classical predicate logic guessing from the previous discussion of the current thread) without making clear which model each statement is based on.

My idea to improve the text of Chapter 16 consists of three points:

2-1. Assert first that Lojban is a language, and that this chapter describes some models that can be expressed by Lojban.
2-2. Explain mainly a model based on the classical first-order predicate logic, because this model is most widely used in modern scientific theories.
2-3. However, emphasize that Lojban can do more, including intuitionistic logic, modal logic, multivalued logic, higher-order logic etc. (Actually I spoke to philisophers on this idea last year in Japanese : http://youtu.be/lzqhNYCWKLo?list=UU0k-Re5fyJXl4bGKSJLpkSA
I am very sorry for not yet translating it into English. You will find some traces of the speech also in la jbovlaste, for example http://jbovlaste.lojban.org/dict/bu'ai .) We _can_ take even a model aristotelian, though the model is too weak to be applied for modern sciences.

If some of you agree to my idea, I will prepare an unofficial version of Chapter 16 of CLL, just like I did for xorlo gadri (http://www.lojban.org/tiki/tiki-index.php?page=gadri:+an+unofficial+commentary+from+a+logical+point+of+view ) but trying to write in easier style to be understood by non-logicians.

pei mu'o

### mukti

Nov 29, 2014, 12:12:20 PM11/29/14
I'm a fan of the "unofficial commentary" on the gadri, and would be interested in reading another such treatment of this distinction -- between the language and the model.

The idea that the language need not be committed to a particular model appeals to me: There seems to have been a lot of argumentation about which model is "better" -- whether "better" is understood as more intuitive, closer to natural language usage, more in tune with modern/traditional logic, etc. Perhaps it's the undecidable nature of such arguments which led John Cowan to predict that there would be no resolution to my original questions.

I'm not inclined to accept that no resolution is possible: It seems to me that there is sufficient general agreement to ensure that subsequent descriptions of the language handle this issue in such a way as to address the concerns that have been raised in the past. I welcome guskant's offer to elaborate such a proposal.

mi'e la mukti mu'o

### selpa'i

Nov 29, 2014, 12:26:00 PM11/29/14
la mukti cu cusku di'e
> I'm not inclined to accept that no resolution is possible: It seems to
> me that there is sufficient general agreement to ensure that subsequent
> descriptions of the language handle this issue in such a way as to
> address the concerns that have been raised in the past.

What I don't understand is why, after achieving such a high consensus,
we still cannot seem to call the question of existential import settled.
I cannot recall many cases where so many Lojbanists all agreed on a
thing, and here I see Lojbanists from completely different communities
(as well as from different times) agreeing that {ro} should not have
existential import. Is this not a democratic institution/committee? Or
is it just that the two (?) nays are louder than the dozens of yays, again?

mi'e la selpa'i mu'o

### mukti

Nov 30, 2014, 9:22:23 AM11/30/14
On Saturday, November 29, 2014 11:26:00 AM UTC-6, la selpa'i ku wrote:
What I don't understand is why, after achieving such a high consensus,
we still cannot seem to call the question of existential import settled.
Is this not a democratic institution/committee?

BPFK is bound by the Baseline Policy of 2002, from which it draws its charter, to pursue near-consensus when considering changes to "baseline documents":

Changes must be approved by consensus, with specific procedures to determine consensus decided by the byfy subject to Board of Directors review. In general, a single objector shall not be presumed to deny consensus.

There's been a tradition of interpreting this as "consensus-minus-one". There is little guidance on the determination of who is counted towards/against consensus. The committee is bound to respect a notion of "open membership", which seems to extend to anyone who participates in committee activity. The Policy explicitly says that the chair of BPFK must seek approval of the Directors if the chair wishes to determine membership in some other fashion.

It's worth noting that the very consideration of such a change, as well as the order in which it is considered relative to other committee business, may be restricted by the Policy. In 2003, when BPFK was chaired by Nick Nicholas, it was so interpreted by lojbab:

the byfy should NOT be considering any proposals for changes to the baseline documents (which fall under the final task) UNTIL it has finished the primary, secondary, and tertiary tasks.

This interpretation does not seem to have been consistently enforced since that time, but the Policy from which the intepretation was derived has not been amended.

To return to the question of how to settle an issue like the one at hand: It appears to me that the only way to record a decision like this is for the chair to declare the matter decided. The declaration would, according to the Policy, be open to recall by the Directors on questions of consensus. The Directors or the President might also challenge a decision on the basis of other restrictions imposed by the Baseline Policy, such as the order of committee business.

Is it any wonder that, given the extent to which the authority of BPFK has been undermined, both pre-emptively and after the fact, the chair might be reluctant to make such declarations?

I submit that the current arrangement has long failed to achieve the objectives it was explicitly intended to forward, that it is no longer consonant with the will of the lojban-using community, and that it is time to consider another way forward. To that end, I hope that when baseline policy is raised at the annual meeting of LLG (currently in session), that members of this committee as well as the general body, will consider a measure to provide BPFK with a new charter.

### Alex Burka

Dec 1, 2014, 9:21:08 AM12/1/14