RE: [lojban] On functions to various types of things.

["And Rosta" <a.rosta@dtn.ntl.com>]

pc:
> The discussion of {le mamta be ce'u} has gone on rather too long, so 
> a modest proposal (that just messes up a few years of text) seems in 
> order. Since no one seems to mind {ce'u} in the bridi following an 
> abstractor, when the whole stands for a function whose values are 
> abstractions of the kind indicated, {du'u, ni, nu} so far for sure, 
> and since those who have opinions other than mine do object the same 
> structure without any abstractor present, I suggest that we use the 
> now redundant {ka} (just {du'u} with {ce'u} in it and with the 
> disadavantage that it doesn't say what it leads to) to warn of 
> impending {ce'u} in all cases: {le ka du'u ce'u broda}, {le ka ni 
> ce'u broda}, {le ka nu ce'u broda} and (taDA) {le ka broda be ce'u} . 
> The last might takes some fiddling, since it is not always a 
> function to individuals. On the other hand, we could presumably 
> simplify the form down to {le ka broda ce'u}. 

If I understand correctly, you're proposing a fairly radical grammar 
change. It should be Lojbab who replies to your proposal, since he
both respects your sagacity and, on behalf of others, is implacably
opposed to grammar change.

I don't think we've adequately explored alternatives, because
the rest of us are only just getting to grips with what you're
looking for ways to express. So I'm not persuaded that a grammar
change is called for. For instance, Lojbab's suggestion is worth
exploring:

> Not that I've come close to following this discussion, but would it be 
> easier to talk about mamta as a function if, like sumji -> su'i, you were 
> to convert mamta to an operator and use Mex
>
> na'u mamta ["be ce'u" or "be fa ce'u", whichever is appropriate to mark the 
> value apart from the arguments]

You replied to that:

> I'm not sure. It would (I suppose -- though I can imagine all kinds 
> of weaseling going on on even this) make it clear that there is a function 
> being talked about. The problem ten is the temptation to see it as a 
> mathematical function, giving rise to mathemtatical entities as values. 

It would be a good outcome if we overcame the temptation, because it would
show that mex expressions might have some utility for everyday discourse.

> One of the virtues elsewhere has been that the form marked the sort of 
> thing that came out as values {du'u} and propositions, {ni} and qunatities, 
> and so on. 

I can see the force of this argument and the virtue of keeping it in mind
when seeking ways to refer to functions that, when applied, yield sumti.

So, if you can look charitably on my ignorance of mekso, let me sketch out
some thoughts.

1. Lojban has no way to express the mother-of function applied to an argument.

When I said this before, you replied:
> <I would not be saying this, if Lojban had a way to use {mamta} as an 
> applied function rather than only as a predicate. E.g. if *{mamta la 
> djan} functioned as a sumti that referred to the mother of John. That 
> seems to be how you conceive of {le mamta be la djan}, but really that 
> means "x is such that it is nonveridically said to be the case that x 
> mamta la djan", where x is not bound by a quantifier.> 
>
> Well, as you are wont to say, that *is* how Lojban uses {mamta} as an 
> applied function. That role may not follow strictly from the literal 
> meaning of the terms but it is a role that the expression plays -- look 
> at a clear case like {le sumji be le re li mu}. (I would argue that "is 
> non-veridically said to be" is suspect loading, "that the speaker is using" 
> is safer, for the speaker may use it just because it is the veridical thing 
> to say -- and usually does, byt the way). 

"le sumji" is a poor choice of gadri, though I concede that it is hallowed
by usage. At any rate, we seem to agree that Lojban has no way to express 
the mother-of function applied to an argument, and that in those circumstances
where we would use a way to express the mother-of function applied to an 
argument, if we had such a way, we instead use "le mamta be" (or similar
with some other gadri).

2. Lojban's prime exemplars of functions are its mex operators, and Lojban
provides a way to convert a selbri to operator: {na'u mamta}. (I don't see
that we need {na'u mamta (be?) ce'u}.)

3. There seems to be no easy way to convert an operator to a sumti. Does 
{li} tolerate an operandless operator as complement -- {li na'u mamta}?
Otherwise, {li ni'e nu'a na'u mamta} converts from operator to sumti.

4. The applied function could be expressed as {li na'u mamta mo'e la djan}.

--And.