Re: [lojban] non-ka properties

[Jorge Llambías <jjllambias@gmail.com>]

2011/6/23 Felipe Gonçalves Assis <felipeg.assis@gmail.com>:
>
> Could you point me where this general meaning of {kau} is explained?

I don't think there is any detailed explanation of "kau" anywhere,
largely because we haven't agreed on one. There has been a lot of
discussion about it on this list, if you have the patience to search
the archives.

> Anyway, I guess {kau} is just not what we were looking for. You understand
> what things I am trying to express, right? They are just functions, so that
> I can use {zmadu} to say "f(x) > f(y)", {jibni} to say "f(x) is close to f(y)"
> and {traji} to say "f, restricted to X, has maximal/minimal value at x". I am
> just asking how to express f in lojban.

Your first two examples, the way you wrote them, make no reference to
functions, they just make use of one. They would be expressed simply
as, for example: "lo se mitre be ko'a cu zmadu lo se mitre be ko'e" or
"lo se nanca be ko'a cu jibni lo se nanca be ko'e".

But I do understand what you are trying to express, you want a way to
refer to a function, and you are saying that "zmadu" or "jibni" should
take functions as their x3 argument. Those are two separate issues:
(1) how do we refer to a function in Lojban and (2) do "zmadu" and
"jibni" require functions as their third argument.

As for (1), I don't think Lojban provides a grammatical construct to
refer to the functions that can be generated from a predicate, for
example to refer to the function that maps people to their names. You
can of course use "lo cmene be ..." and fill the blank with a
reference to a person, and the resulting expression is a reference to
the name of that person, i.e. the value of the function in question
for that value in the domain, but that's not a reference to the
function.

You could refer to the function in the longwinded fashion: "lo fancu
be lo prenu bei lo valsi bei lo ka makau cmene ce'u", "the function
from people to words by the rule of what their name is", but there is
no cmavo (say "lo'au") that condenses that into something like "lo'au
cmene be ce'u".

As for (2), while it would have been possible to define "zmadu" and
"jibni" that way, they just weren't defined that way as far as I
understand them.

> I really feel that this was the spirit in which these gismu were defined.
> You talk about complex objects, and compare them with functions with
> simpler, structured codomains.

If that was the spirit, they forgot to include the grammatical
machinery to refer to functions, unless they intended to have long
expressions like "lo fancu be ..." in all such places. But to my
knowledge nobody has ever used those places that way.

Your idea of using "lo cmene be ce'u" to refer not to names but to the
function that maps people (or things) to names has been proposed
before, and maybe someone has used "ce'u" like that. Personally I
don't like it, because I think something that starts with "lo cmene"
should refer to names, and the function that maps people to names is
not itself a name. I would suggest using a function cmavo, like
"lo'au", for that. But my feeling is that just as we don't need to
refer to sets because we can say all we want to say about the members
of a set by referring directly to the members, then we probably don't
need a short way to refer to functions because we usually want to say
things about the values of the functions, and not about the functions
themselves.

mu'o mi'e xorxes

-- 
You received this message because you are subscribed to the Google Groups "lojban" group.
To post to this group, send email to lojban@googlegroups.com.
To unsubscribe from this group, send email to lojban+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/lojban?hl=en.