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
--
You received this message because you are subscribed to the Google Groups "BPFK" group.
To unsubscribe from this group and stop receiving emails from it, send an email to bpfk-list+...@googlegroups.com.
To post to this group, send email to bpfk...@googlegroups.com.
Visit this group at http://groups.google.com/group/bpfk-list.
For more options, visit https://groups.google.com/d/optout.
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".
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,
> 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.
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}.
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.mi'e la mukti mu'o
--
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.
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.
--
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)
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/?
sumti of the type “ro da poi klama” requires that there are things which “klama”
{su'o pavyseljirna na ku cu blabi} => There is at least one unicorn, such that it is not white. => FALSE.
{na ku ro pavyseljirna cu blabi} => It is not true that all unicorns are white. => FALSE.
{ro pavyseljirna cu blabi} => All unicorns are white. => TRUE.
ro da = da'ano da = no da naku = naku su'o da naku
{su'o pavyseljirna na ku cu blabi} => "There is at least one unicorn, such that it is not white."
8.18) mi viska le rore gerku I saw the all-of/two dogs. I saw both dogs.
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.
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?
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.
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.
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.