From: John E Clifford <kali9putra@yahoo.com>
To: "lojban@googlegroups.com" &l= t;lojban@googlegroups.com>
Se= nt: Wednesday, December 26, 2012 5:26 PM
Subject: [lojban] The gap between log and lan= g

A couple of recent threads have gone back and forth on the issue th= at there was no logical way to do something in Lojban or that the way to do= it in Lojban wasn't very logical. Given relevant readings of "logica= l", these claims are true. But uninteresting. Lojban is n= ot merely logical (in the relevant restricted senses), it is also a languag= e and the things that are illogical to say in Lojban are things peculiar to= language, without any logical significance (or significance that can be in= troduced into logic only with difficulty).

The matter of t= he comments inserted into quotations is purely a language matter, style, in fact (logic notoriously does not have style in the short run). Repeating = "Alice said" or "said Alice" at the beginning or ending of every paragraph = is monotonous. So you find other ways to do it without interfering wi= th the structure and metastructural inserts do the job quite nicely. = The quote is not "really" split, of course, because the {sei ...se'u} phras= e is not really there (i.e. in the place it appears to be). Illogical= because deceptive in appearance and unnecessary in the structure -- except= for speaking and reading humans.

The "any" case is slight= ly more complex, because one can force some logical distinction into it som= etimes. "Any" is broad scope universal quantifier which (quite logica= lly) sometimes serves as a narrow scope particular in negative contexts (and, perhaps, some other odd contexts as well -- dialects vary a= nd donkey sentences make their own muck). That is the language situat= ion. And the logic situation is not much different, but the use of an= imperative form creates a problem, since it is not clear about the relativ= e scopes of the quantifier and the speech-act indicator. Usually, the= speech-act indicator has to come first, because, otherwise, we would have = a sentence without performance instructions, but in complex situations this= need not be a problem. But here we have a simple case: Give me an ap= ple. That is, logicially, Imp(( Sx: apple x) you give x to me) (roughly spe= aking). A sentence which is "true" (fulfilled) if you give me somethi= ng, anything, that is an apple. But, you say, suppose I want a partic= ular apple -- or want to explicitly exclude that possibility. The exc= lusion is easy -- the given English (or {ko dando da poi plise/ su'o plise}in Lojban) does the trick. I have explicitly NOT restricted th= e choice of apples. If I do want to restrict that choice, I have to t= ake another step, either moving the quantifier (or marking it as move= d), explicitly specifying some further restriction on the apple, or appeali= ng implicitly to some aspect of the situation not in the present sentence: = "There is an apple I want, give it to me", "Give me a certain apple", "Give= me the golden apple", "Give me the apple". The first of these is, as= noted, tricky to transcribe in strict logical form (though the dialogical = form is probably straightforward). The second is equally difficult, s= ince logic does not generally have expressions like "a certain" that have b= road scope even in restricted contexts (that is language again, not logic).= The third is obvious. The fourth uses some sort of descriptor,= {le} or {lo} depending (more or less) on whether the implicit context is internal or external. A case can be made that {lo} also f= unctions as a long scope particular quantifier, running back at least to th= e introduction of its bound predicate, and so might also be used for the se= cond case (again, this passes beyond logic somewhat to dialogical analysis,= but that seems to be the wave of the future anyhow).

Oh yeah= , the stuff about proofs goes into the one place where Logic does have styl= e. We can, with a suitable proof system, either extend this complicat= ion or contract it. Generally, in logic, it is bad form to use the sa= me notation for bound and free terms (and, indeed, the free terms are stric= tly only dummies, not really in the language at all). The descent to = Bob and the like, rather than x4, say, is misleading in its specificity, as= it were. The best solution (theoretically -- practically it is a nig= htmare) is to use the most likely F and the least likely F, which is a modified version of Skolem's system: to prove {AxFx}, prove {F the least= like x to be F}, to instantiate {Sx Fx} use {F the most likely x to be F}.= For the rest, spelling out the steps carefully usually makes it clea= r -- eventually (or course, what constitutes a step is an extralogical issu= e: if you know how it goes, then you can skip it; if you don't, you have to= have it in).

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