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[lojban] Lojban and Truth-Conditional Semantics



coi rodo,

This xorlo/Mr. broda/kinds/intension/etc/(now recently: "levels") thing goes back and forth and never ends and, I fear, never gets anywhere.  As a longtime lurker and sporadic Lojban learner admittedly not necessarily fully up to snuff on these highly technical topics, I'm going to go out on a limb here and take a pop shot in this interminal conversation, which I have long been observing with interest, and sometimes even amusement, for years (I'm guessing that I have read thousands upon thousands of posts on these issues).  The only way, I suspect, that jbo(ske)pre are ever going to sort out some of these sticky issues involving gadri and related stuff is by adopting a much stronger and more rigorous formalism than has been adopted up to now.  Ultimately it would require a very good mathematician/logician to work out the whole system and then break it down for others (in English or Spanish or whatever metalanguage).  There are many ways to go, but I think what might best serve a logical language is a formalism focused on model-theoretical, truth-conditional semantics.  In other words, from any given Lojan sentence S, e.g. "su'o lo ctuca cu tavla ro le tadni", one ought to be able to work out, in a straightforward manner, every truth condition that would make S true with respect to an interpretation of basic terms (e.g. descriptions & predicates) and a given model (universe of discourse).  If the truth conditions hinge on context (and such hinging might be universal in human languages; I just don't know), then the formalism should specify how to interpret S against any context -- you might want to check into discourse representation theory (DRT) for ideas on how to handle this.  But I think the goal should be an algorithm like this: given any Lojban sentence S,  enumerate the conditions that are true exactly if S is true.  (After that, make sure that any of the various propositions that humans want to say are sayable.  And if you really want to get fancy, explain what and how various logical entailments can be inferred from any Lojban sentence S. But for right now, interpreting Lojban as it stands should be the goal.)  To give a trivial example of how truth-conditions might be specified very, very informally using English as the metalanguage:

S = "la meris prami la djan."

The truth conditions of S are (tentatively) as follows:

- There is an individual entity M whom Speaker denotes as "meris"
- There is an individual entity J whom Speaker denotes as "djan"
- There is a predicate relationship (x1, x2) denoted as "prami", interpreted as the set of all ordered pairs of individuals such that x1 loves x2 (full encyclopedia definition of a predicate can be cited as needed).
- prami'(M, J) is true.  In other words, M loves J.

These conditions could and probably should be given more formally than this, but as given, they at least suggest the idea.  Deriving these conditions can be tedious, and if the system is mathematically/logically formalized, it will get even more tedious -- much more so.  It will be immensely more complicated by adding kinds, quantification, masses, plurals, tenses, modalities, worlds, intensional constructs, and so on.  But quite a bit of research along these lines have been done in natlangs, and ultimately I think this is the approach that is needed for Lojban.  By some method, every S has to be broken down into a finite set of basic truth conditions, and those truth conditions should be expressible both formally in a mathematical metalanguage, and informally in plain English or other natlang.  Along these lines, eventually I think someone has to go to the trouble of working out a complete, systematic formalization of Lojban semantics. Perhaps one could start with simple things and add one language feature at a time, and then periodically go back and organize and straighten everything out, until everything works together.  For example, one could:

1. Give the truth conditions for "lo broda cu brode" (possibly under DRT context)
2. Give the truth conditions for "su'o broda cu brode" (possibly under DRT context)
3. Give the truth conditions for "ro broda cu brode" (possibly under DRT context)
...
101. Give the truth conditions for "lo broda cu brode lo brodi" (possibly under DRT context)
102. Give the truth conditions for "su'o broda cu brode lo brodi" (possibly under DRT context)
...
1001
etc.

The idea here is to describe the semantics of the most primitive formulas, and then systematically build up the framework to describe ever more complex formulas.  Taking into account recursion, scope, interactions, etc. eventually every sentence in the whole language should be reducible to enumerable truth conditions.  Also, and this would follow from the principle of compositionality and and from Lojban's already existing syntactic non-ambiguity, semantics would parallel syntax and every constituent of Lojban would have one meaning -- and ideally transparently so. 

There are other formalisms out there (which I am less familiar with), besides the truth-conditional and model-theoretic thing I've very, very crudely outlined, but I suspect that something like what I am trying to describe would be advantageous.  Montague had a very similar approach to English, and his program is generally acknowledged to be a promising system.  At the very least, it seems to me the best hope to underpin any "logical language".

With all due respect to interlocutors, and despite all the best intentions, there seems to have been a good deal of handwaving and wheel-spinning in these years-long, possibly decades-long conversations.  Can we yet describe what every Lojban sentence means?  It seems not.  And the discussions go on and on.  And on.  And on and on and on.  (And frankly I still don't know what "Mr. Broda" means.)  I suggest that mapping words to meanings expressible both formally and informally in metalanguage might be a fresh approach.  I suspect that even an informally specified program intent on producing truth conditions from ordinary Lojban sentences might be a constructive approach towards grappling with these thorny issues.  I mean this all quite respectfully, words to the wise.  It's just my 2c on a late Saturday night. 

Best
mu'o mi'e .maik.



On Sat, Nov 12, 2011 at 7:50 PM, John E. Clifford <kali9putra@yahoo.com> wrote:
OK.  To start with, I have to rewrite your example so that it makes a potential problem for me (& and x might insist there was the same possibility for {su'o cinfo cu broda} but I do disagree with them there).  So, if someone says {su'o lo ctuca cu tavla ro le tadni}, and they mean a certain kind -- or some certain kinds -- of teachers talk to all the students, what can we infer about individual students and teachers?  Surely that every student has been talked to by at least one teacher {ro le tadni cu se tavla su'o ctuci} and probably that each has been talked to by at least one kind of teacher (which follows from the first, assuming each teacher is of some kind or other).  Actually, that listing is backwards, since the second conclusion follows from the start just by  FLO.  The first conclusion involves some assumption about how a kind of teacher talks to students;presumably collectively but possibly conjunctively Or even distributively.  In the latter two cases, we get at least one teacher who talks to all students and, surely every student is talked to by some teacher.  In the collective case, there may not be one teacher who talks to every student, but they divvy up the task so that every student gets a talking to and the result is still achieved.
Now, I agree that I escape some problems here by taking kinds to be bunches.  On the other hand, if they are not bunches, I have trouble working out what {su'o lo cinfo} means when it refers to a kind (rather than a bunch of kinds, say).  Of course, it is always safer to specify you level and Lojban has at least a few devices for doing that.  But it is also often long-winded to do that when it is "perfectly clear" from context.  Whether either of these will help with whatever xorxes is now about remains to be seen.  Past xorxes segments have been given to finding intensional content or mass content in {lo} _expression_ (for each of which there are, alas, historical precedents).  I also am a little worried about apparently focusing on the most general uses of {lo} exressions and coming up with claims that do not fit the more restricted uses.

Sent from my iPad

On Nov 12, 2011, at 11:39 AM, Martin Bays <mbays@sdf.org> wrote:

> * Wednesday, 2011-11-09 at 10:22 -0600 - John E. Clifford <kali9putra@yahoo.com>:
>
>> [...]
>>
>> The point is that the word "lion" (and "lions") can indicate a number
>> of different ontological levels, from the narrowest to the broadest
>> and most abstract.  There is is, though, a default level that turns up
>> in the absence of contrary contextual clues, even though it may be
>> easily overridden by those clues.  We have words for the various
>> levels, which we can use to explicitly set the level or change in mid
>> discussion ("kind", "segment", "meat", "typically" and "species"
>> roughly for the examples above).  Shifting without making note of the
>> shift or starting off at the non-default level without a flag, is
>> a Gricean misdemeanor.
>>
>> What the default level is for a given word varies from word to word:
>> "lion" takes sort of midlevel gross physical objects, "letter" takes
>> a highly abstracted level (there are twenty-six letters in the English
>> alphabet).  Other words probably take lower levels, Buddhist technical
>> terms for components of a person probably somewhere around the bottom.
>> And, as the last example indicates, each level can be expressed in
>> a number of ways.
>>
>> As far as I can figure out, the recent discussion on the {zo'e} thread
>> (or at least one or two of those discussions) hinges on whether we
>> have the same fluidity of levels in Lojban and whether certain moves
>> constitute misdemeanor violation level shifting.  That is, what
>> brodas?  Or, perhaps more precisely, what brodas in what way?
>> A single thing may broda individually; a bunch may do so collectively,
>> or conjunctively, or disjunctively, or statistically, or in many more
>> complex ways.  Also involved is the nature of some levels: are kinds
>> just bunches of things or are the intensional objects of some sort?
>> Are segments parts of objects or independent things to which objects
>> may be related in a way analogous to the way kinds are related to
>> objects?  In general, no side has been very clear (at least in
>> a single continuous statement) on any of these issues, making the
>> whole rather difficult to follow, let alone to critique.  Hopefully,
>> this will change.
>
> OK then. I'll reiterate, with all the clarity I can muster.
>
> Short version: {su'o cinfo cu broda} has to mean that some actual lion
> brodas. Otherwise we have problems. This is largely independent of the
> meaning of {lo cinfo cu broda}, but not of the explanation of that
> meaning.
>
> Long version:
>
> The basic problem as I'm seeing it: if we don't specify levels, then we
> don't really specify quantifier scope.
>
> What I mean by this (i.e. by "really"): if B hears A say {su'o ctuca cu
> tavla ro le tadni}, and B wants to understand what A means to say about
> actual teachers and actual students, and if {ctuca} and {tadni} do not
> specify levels, then B has to guess which levels A intends them to refer
> to. If, for example, B guesses that A is talking about kinds of teacher
> and about actual students, all B can deduce about actual teachers and
> students is that every student was talked to by some teacher.
>
> (Here I'm using 'actual' in opposition to 'kind' - I wish we had
> a better word for it)
>
> (I should also clarify that when I say "{ctuca} does not specify
> a level", I mean that there are *individuals* which are e.g. kinds of
> teachers and which ctuca; if a kind were implemented as being merely
> a bunch of actual teachers, we wouldn't have the problems I'm talking
> about.)
>
> So I conclude that it is not befitting of a logical language for it to
> have no means to specify level - where 'level' refers to whatever it is
> that crossing causes these quantifier scope shifts.
>
> This does not mean that I think lojban should only be able to discuss
> actual teachers and not kinds of teachers - merely that we need to be
> able to distinguish between the two.
>
> I further note that xorlo - or rather, my understanding of xorxes'
> understanding of xorlo - makes this issue less academic than it might
> otherwise be. That's because it has descriptions, e.g. {lo ctuca},
> habitually (though not always) referring to (bunches of) corresponding
> kinds, e.g. to the kind Teacher.
>
> So under xorxes' xorlo, kinds are not rare things summoned up only when
> we specifically want to talk about them - you have to deal with them if
> you want to understand any sentence using a gadri.
>
> (Here I'm using "the kind Teacher" to refer to the whatever-it-is that
> xorxes habitually refers to with {lo ctuca}; I have so far failed to
> understand what this is, but it seems that whatever it is is a level up
> from actual teachers as regards quantifier scope ambiguities, and that's
> all we need to know about it for the present discussion)
>
>
> This leaves the question of how to deal with this problem; we have
> various partial answers, but perhaps I shouldn't complicate this thread
> by discussing them here.
>
> Martin

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