Subject: Re: [lojban] Re: noxemol ce'u

From: [email-masked]
Date: Tue, 25 Sep 2001 17:27:58 EDT

In a message dated 9/25/2001 11:37:53 AM Central Daylight Time, 
[email-masked] writes:

> The property of loving the property of having a
> #> mother? I'd do that as 
> #> 
> #> ka/du'u ce'u prami lo/tu'o ka/du'u da mamta ce'u
> #
> #NO, it means the preoperty of loving the mother-of function.  
> 
> I don't perceive a difference between "the property of loving the
> property of having a mother" and "the property of loving the mother-of
> function", unless it is somehow essential to your point that 'mother-of'
> be a function -- i.e. that if x has a mother then x has exactly one mother.
> Can we change the example to "pendo be ce'u" without destroying
> your point? We can make that change without affecting my point.
> AFAICS, Lojban grants no special status to functions -- they are
> treated as ordinary binary predicates.
> 

Both the mother-of function and the property of having a mother are 
functions, one to mothers and one to propositions. This seems to me a 
crucial difference, since I don't send propositions mother's day card, for 
example, even the proposition that I have a mother. Lojban does, of course, 
grant a special status to item valued functions: they are sumti (just as in 
formal logic), though the connection is not as tidy as might be liked, as 
witnes the question of {pendo be c'eu} -- a puzzling expression, ill-formed 
as it stands. so, presumably what is wanted is this expression with some 
gadri in front. But what gadri? If {le} we used in this case, the result 
would not be unique, unless there some use of the "the ONE I mean" ploy of 
{le}; {lo} would be worse; {loi} introduces the dubious "thing" the mass, but 
otherwise works ok; {lo'i} is safe in some contexts (the ever popular {dunli} 
and {frica} for example) but a total miss in others. And the same applies 
for most cases where more than one thing satisfies the first gap for each 
second filler in {ce'u broda ce'u}. I am not sure what happens in these 
cases, when the wrong gadri is picked. With the right one, however, you get 
a nice function that explains a situation succinctly. I am not too sure 
what happens when you pick the wrong gadri with {ka} or {ni} or ... either, 
though there it generally seems to be that there is only one natural and that 
covers all contexts (but I haven't really looks that closely yet). 

<Oh hang on, I think you mean {tu'odu'u/ka ce'u mamta ce'u} --
*that's* the mother-of relation>

That is indeed the mother-of relation, but not the mother-of function, even 
though, in one sense of "extension," they ahve the same extension. The 
perform different roles and behave distinctly syntactically even in set 
theory.

<#<#Clearly, we need a way of saying ^xf<x> in Lojban 
#
#which we uncontroversially have, right?>
#
#Well, you seem to be amking it controversial, unless you have something else 
#in mind that I have forgotten about or don't know of.

bigness = tu'odu'u ce'u barda

is that not an example of ^xFx?>

It is indeed. And the point is? The request was for an example of ^xf<x> (I 
am writing a paper for my website on the language of Logic and how it relates 
to the logical language to remind or inform people who get into these 
discussions just what it is we are talking about.)

<However, normally a bridi preserves its meaning when subordinated (e.g.
placed within an abstraction), so if {la djoun mamta ke'a} and {la djoun
mamta ce'u} have a certain meaning as main clauses then that meaning
ought to preserved when the bridi is subordinate. And that would then
seem to stymie the meaning that ce'u and ke'a already have when
within ka/du'u and noi bridi.>

I don't find this particularly persuasive, since it is inside out. We have 
these critters well-defined in subordinate positions and not as main clauses, 
so we can't say that the main clause meaning stymies the subordinate meaning. 
We might say that it is hard to imagine a main clause meaning that would not 
stymie the subordinate clause meaning, and that may be true of {kea}. I am 
less sure about {ce'u}. And, of course, we know exactly how it works for 
interrogatives, which are more or less related to {ce'u} (scope aside). But 
arguing from what we hard a hard time imagining to "it ain't so" is generally 
an awfully weak argument, since it collapses so easily to someone with a bit 
more imagination.

<We also need to remember that ke'a and ce'u were chosen from among
competing implementations of semantically equivalent devices, and not
all devices would have raised the questions you're raising. For example,
if we had an explicit way of binding variables to NOI and to ka/du'u
-- call it "goi'i" then we could replace ke'a and ce'u by da variables:

   NOI  .... ke'a = NOI goi'i da ... da
  ka/du'u ... ce'u = ka/du'u goi'i da .... da

That would have been longerwinded than the current system, but would
have overtly and explicitly expressed the way I understand ke'a and
ce'u to work.>

Well, I don't think that is historically accurate about how {ke'a} and {ce'u} 
were selected nor do I know of any devices of the sort you mention (other 
than {zo'u} constructions like the ones I used -- but those give the wrong 
sorts of things, as ordinary bound variables seem likely to do), still there 
could be such a system, and, indeed, the Lojban system may be one such. But 
that is not specified anywhere that I can find and the use of "lambda 
variable" cuts against it in the case of {ce'u} (less so for {kea} where the 
binding is by the gadri -- though this is never said outright).  

<#I don't understand what it would mean for ce'u to be transitive or 
#intransitive.>
#
#If it is in a construction within a construction then it is in the outer 
#construction, rather than being confined to the inner.  

Okay. Well then, yes, in a sense I want ke'a and ce'u to be sometimes
transitive and sometime intransitive. But I think it is fairer to say that
I want them to always be intransitive relative to the 'operator' that
binds them, and transitive relative to everything else. da-series
variables work exactly the same way.>

This presupposes that {ka} et a few cetera bind {ce'u}, but, aside from the 
fact that {ka} requires {ce'u} and some others permit it (maybe even require 
it, but I don't think so -- {ka} really is, as I have said all along, 
peculiar here), I don't see that it binds {ce'u} in the way that LE binds 
{ke'a}. On the contrary, {ce'u} seems to contain its own binding operator 
(the lambda), as witness the fact that it is different each time it occurs 
(cf. {ma}, which is bound by nothing but itself -- and similarly all the 
interrogatives).  

<Okay. Well at least I see your position now. In a sense, on your position ka
seems redundant: if {ka ce'u goi cy zo'u da prami le mamta be cy} is
the property of having a beloved mother, then would not {da poi ke'a se prami 
be de gi'e mamta be ce'u} do equally well?>

Well, no, since they are different syntactic categories in Lojban (and do the 
sumti really have to have {be} in poi clauses -- and if so, why doesn't 
{ke'a}? -- or is this one of the messes with {gi'e}?): one a predicate, the 
other a sumti (or, I would say, sumti function). However, I see that the 
same situation underlies the two. I don't think they are intertranslatable, 
however.   

<And your position opens many cans of worms. For example, does a
"le mamta be ce'u be'o poi xendo" mean "the property of having a kind mother"
or "the kind property of having a mother"? Do we really want to have to
grapple with all these problems that simply don't exist on the standard story
about ce'u?>

Neither, of course -- no properties here. What is the rule in general? I 
recall that it is that {poi} clauses modify the whole sumti, so it would be 
"the mother-of function that is kind" not "the kind-mother-of function." To 
be sure, I suppose that the distinction is hard to make in ordinary cases : 
the friends of Jerry who are kind are probably Jery's kind friends, and so 
on.  

<It must be me that is missing something, since, as I say above, I think the
way is {tu'odu'u/ka ce'u mamta ce'u}. This is standard uncontroversial
Lojban.>

And again, what you are missing is that that is a function which gives 
propositions (as the {du'u} versions says) while we are talking (well, I am; 
you are confused) about a function that gives individuals.