Re: lambdas to the slaughter

[Jorge Llambias <jorge@PHYAST.PITT.EDU>]

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 <lambdacated bridi>".
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 <lambdacated bridi>". 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