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| Llamban is not my favorite language. It is so close to Lojban that, like old Loglan, it interferes with my learning Lojban. It has, after all, virtually the same morphemes as Lojban and, for the most past, the same meanings -- or (and this is the problem) meanings just a half-a-bubble off. One feature of Llamban newly discovered is that, for every Lojban brivla, {broda}, it has another predicate, usually {kairbroda}. From the Lojban point of view, this looks like a lujvo, two predicates ({ckaji} and {broda}) put together, each component contributing something to the meaning of the whole. However, in Llamban these predicates are primitive and the whole contributes some information about the meaning of the latter part. That these predicates are primitive might be disputed, since there is an explanation of sorts for what they mean, working with one of the anomolous Lojban/Llamban predicates, {sisku}, whose corresponding predicate of this sort is {busku} not {kairsku}. Actually, the analogy -- perhaps the axiom for {kair} predicates, though it is called a definition -- is between {busku} and ordinary predicates and {sisku} and {kair} predicates. The definition or axiom for {busku} runs as follows: << tu'o ka ce'u goi ko'a ce'u goi ko'e ce'u goi ko'i zo'u ko'a buska ko'e ko'i cu du tu'o ka ce'u goi ko'a ce'u goi ko'e ce'u goi ko'i zo'u ko'a sisku tu'o ka ce'u du ko'e kei ko'i >> i.e. The ({tu'o} is AFAM hieroglyphics or standard Lllamban for {le pa}) relation represented by {busku} is identical to the the relation represented by {sisku} with the second place, x, replaced by the property of being identical with x (haeceity or seity of x, not the propositional function that returns True only when x is the argument). Then we have a second axiom (or contextual definition) for {lo'e} -- which apparently has a special role in Llamban which this axiom is to explain: << buska lo'e broda = sisku tu'o ka ce'u broda >> From these it follows that << Notice that from DEF1 we know that: buska lo'e broda = sisku tu'o ka ce'u du lo'e broda and from DEF2 we know that: buska lo'e broda = sisku tu'o ka ce'u du lo broda So we have that: tu'o ka ce'u du lo'e broda = tu'o ka ce'u du lo broda >> and then the further claim that << [this]does not in any way entail that {lo'e broda} can be replaced by {lo broda} in other contexts. >> Because (working through the expressions in standard ways) << buska lo'e broda = sisku tu'o ka da poi broda zo'u ce'u du da buska lo broda = da poi broda zo'u sisku tu'o ka ce'u du da which are clearly different. >> From this, we generalize to the {kair} predicates: Axiom Schema 3: tu'o ka ce'u goi ko'a zo'u [ko'a broda] cu du tu'o ka ce'u goi ko'a zo'u [kairbroda tu'o ka ce'u du ko'a kei] (where [ko'a broda] and [kairbroda ...] put ko'a in any place in broda and the property of being ko'a in the same place, all otehr places being the same) and Axiom Schema 4: [broda lo'e brode] = [kairbroda tu'o ka ce'u broda] I assume that this exposition of Llamban was meant to explain something in Lojban, else why put it on Lojban list. Whatever it is it is to explain, it pretty clearly fails to explain the use of {lo'e}, since AS4 is generally false in Lojban, where the complexities seem to reduce {lo'e} to {lo} everywhere and {lo'e} is both different from {lo} virtually everywhere (maybe it collapses for a predicate that necessarily has only one member) and also different from some simple direct involvement of various properties and members of sets (which may be empty, after all). Well, is it then at least coherent in Llamban. Not obviously. We are told that {lo'e broda} = {lo broda} in some context. Presumably, the context involved is {tu'u ka ce'u du...}, that is, the property of being identical with lo'e broda is the same as the property of being identical with lo broda (some broda, that is). But, if the proeprties are the same, then what has those properties must be the same (whether we take properties in intension or extension) and, since each of these critters obviously has the property of being identical with what it is, they are identical with one another, though a single thing being identical with a range of things is a bit problematic). So, we must assume that the context is {sisku tu'o ka ce'u du...} or, maybe generalized to {[kairbroda t'uo ka ce'u du ...]}. But that means, by 1 and 2, the two mean the same in [... broda] ( in particular , {busku ...}), as a sumti in any place of any predicate. Now, is there any other place that {lo broda} and {lo'e broda} can occur? In Lojban, all sumtitcita are just predicate places which happen not to be mentioned in the definition of the predicate, so -- in Lojban, at least -- they are covered by the above equation. I suppose vocatives are separate, but calling on either of these creatures seems odd (or, rather calling this creature by either name). I am not sure about the status of sumti tcita in Llamban, but I have never before seen any evidence that it was different from Lojban in this respect, nor given a clue about how it would be different. That is, taking "=" as used in xorxes' exposition in even its weakest sense, material equivalence, we have that, in Lojban -- the langauge without {kairbroda} -- that something is true of lo'e brode just in case it is true of lo brode. So, while the concepts involved may be different, the effect of that difference is nullified at the truth level -- their extensions are the same. ({sisku2} may be an exception to this, but then, neither {lo'e} nor {lo} would nortmally appear in that place.) But worse, applying axiom 1 to << buska lo'e broda = sisku tu'o ka ce'u du lo broda >> gives, as already noted, busku lo'e broda = busku lo broda. Combining that with the claimed differences between {lo'e} and {lo} gives sisku tu'o ka da poi broda zo'u ce'u du da = da poi broda zo'u sisku tu'o ka ce'u du da. Taking this again in the weakest sense, material equivalence, the claim is false. If there are no broda, then RHS is false, since it makes an existential claim about brodas, but LHS may be true, since someone might well be looking for an instance of a property wwhich, in fact, had no instances. Presumably, all these results could also be expanded to cover {kairbrode} for every {brode}. Since the whole scheme, as applied to, Lojban gives results that are pretty clearly wrong viewed one way and redundant viewed another, the {lo'e} question in Lojban is not solved by all this. But, since the system, even within Llamban, leads inevitably to a false result, it is not even coherent in that langauge. |