From LOJBAN@CUVMB.BITNET Sat Mar 6 22:45:26 2010 Reply-To: Jorge Llambias Sender: Lojban list Date: Fri Dec 1 15:22:36 1995 From: Jorge Llambias Subject: Re: lambdas to the slaughter X-To: lojban@cuvmb.cc.columbia.edu, jorge@minerva.phyast.pitt.edu To: John Cowan Status: OR X-From-Space-Date: Fri Dec 1 15:22:36 1995 X-From-Space-Address: LOJBAN%CUVMB.BITNET@UBVM.CC.BUFFALO.EDU Message-ID: pc: > First, lambdacation is totally general in logic: given any kind of > variable,x, and any kind of expression, P, you can make an expression > \x(P) (imagine the other leg of the lambda) which names a function > from things of the type of P. In Lojban usage, we seem only to be using > the notion for functions where the variables are of type individual and > the expressions are of type sentence, giving lambda expressions of the > type predicate. Well, yes in a sense, but not in the interesting sense. Yes in the sense that everything in Lojban is of type individual, i.e. a proposition is an individual, as is a function \x(P). But if you were to assume that there were different types of objects in Lojban (e.g. propositions vs. individuals) then the notion of function would apply as well to those. To take one of McCawley's weird examples: le ka ke'a na'arme'a le ke'a speni cu ckaji le ka ke'a se ckaji ro tolcitskecre The property of being younger than one's spouse has the property of being a property of every archeologist. In this case, the lambda variable in the first case is for individuals, but the one in the second case is of type "property", or "function from individual to proposition". So if we classify Lojban sumti into types, the lambda variable ke'a can indeed be of any type, as can the bound variables da, de, di. > _lo ka_ (note, despite our habit, > not _le ka_, veridicality is essential and selection is never an issue -- You take the main difference between {lo} and {le} to be veridicality, so I understand your note. I don't take that view. I take the view that {le} corresponds to cases where selection has been resolved for the audience, and {lo} to cases where it has not. Therefore {le} is the better choice for singular referents, as in this case. {lo} works too, because an unresolved selection from one is not in essence unresolved. (Probably I'm using all the wrong technical words for what I'm trying to say, please try to interpret from the home meanings of the words.) I understand {lo ka} to mean "at least one of the properties given by ". There is only one such property, so I must be talking about it. On the other hand, I undersand {le ka} to say "the property that to my mind is given by ". That property will usually be the veridical one. The fact that {le} allows you in some cases to mean another property is not very important. For successful communication you must mean the one that your audience will understand. Jorge