Subject: Toward a {ce'u} record

From: [email-masked]
Date: Sun, 19 Aug 2001 11:25:39 EDT

"A propositional function [roughly, property or relation] is an incomplete 
object whose completion is a proposition" (Frege, loose trat). So, every 
{ka} insofar as it creates a propositional function, property or relation, 
contains at least one hole and that is marked by {ce'u}. Did it contain no 
holes, it would be a complete object and, asuming the original type was 
right, a proposition. 
I*think* everyone agrees thus far.
So, the disagreement is about whether the {ce'u} must always be written in 
and, if not, where the implicit one is.
1) Every {ce'u} must be explicit. . Any slot not filled by an overt marker 
is filled by {zo'e} or some such thing. At least one slot must be filled by 
{ce'u} (unless we collapse the distinction between {ka} and {du'u}, in which 
case, {du'u} are the {ce'u}-less {ka} -- or conversely). An easy rule and 
ambiguity-proof, but possibly verbose.
2) Not so -- some {ce'u} may be implicit, so long as there is a rule for 
identifying the place(s). The rule may now be somewhat more complex, but the 
results will be less verbose (generally).
A) The implicit {ce'u} is always the first (x1) place. This runs into 
immediate conflict with the possibility (indeed, reality) of {ka} phrases in 
which the first place is filled with a content sumti. This is not 
ungrammatical, so it needs an interpretation.
i) Assuming there are no explicit {ce'u} in the phrase, this is treated like 
other {ce'u}-less {ka} -- reduced to {du'u}. With an explicit {ce'u} 
elsewhere, it is taken as the propositional function defined by the explicit 
places, with no implicit ones (it was on a permission, after all).
ii) The {ce'u} is always in the first place, even if something else is also 
there. The something else is
a) an exemplary argument to which the function applies to produce a true 
proposition or a new propositional function (depending on whether there are 
explicit {ce'u}), but the {ka} phrase refers to this an all other such 
functions. This does not seem to really give the first-place phrase any role 
that would justify it being there, unless it is to suggest a range of values 
for {ce'u}, and that would better be done using explicit predicates.
b) as in a), but now the {ka} phrase indicates just the function with the 
sumti in first place. This reduces to i).
c) like a) in all respects except that the sumti in first place markes a 
special relationship between its referent and the function, which is 
different from (but may include) the application relationship a) assumes. 
{leka do xunre} may or may not mean that {do xunre} is true, but it indicates 
a special relationship between you and leka ce'u xunre. The nature of this 
relationship is not specified anywhere that I can find, and so the whole does 
not seem different from {ledo ka ce'u xunre} (to be on the safe side), which 
is also unexplained, but in the same way.
B) The implicit {ce'u} is the first unfilled place in the bridi as written 
(if none then {du'u}). This comes, in a way that A) does not, into conflict 
with other Lojbanic habits, in particular, not filling uninteresting places, 
dropping {zo'e}. Using it correctly requires noticing that the place 
(assuming it is not the first, as it most often will be) is important, since 
it gets a {ce'u} and then dropping that {ce'u}. It thus is harder to use 
than A when it does not have the same effect as A and so harder than A 
altogether, and more likely to errors in what is said.
C) A) and B) save at most a couple of syllables, so could B be generalized 
to, say, all the unfilled spaces up to the first explicit {zo'e}. This is 
actually simpler than B) since we only have to decide that something is 
unimportant and put in a {zo'e}, not decide it is important and then leave 
out a {ce'u} we were going to put in. It also gives rather natural results, 
e.g. {le ka prami} is the love relationship, not either the property of being 
loved or of being a lover. It could be extended (but I doubt it is worth it) 
by returning to {ce'u} after an explicit one after a {zo'e}.

The last example raises a general issue: each occurrence of {ce'u} is new, 
independent of others in the context (like {ma} and unlike {ke'a}). How, 
then, do we force two occurrences to be the same, as we can do with the 
lambda operator from which {ce'u} derives. How, for example, do we talk 
about self-love, leka prami with the two implicit {ce'u} identified. Notice, 
we can't do this with any identity predicate, since that just introduces two 
more {ce'u}, unconnected with the earlier ones. For this and general 
reasons, I suggest that {ce'u}, like KOhA generally, be taken as having 
implicit subscripts (starting with 0) assigned in left to right order. So, 
self -love is le ka ce'uxino prami ce'uxino, which might be shortened somehow 
(to, for example, {le ka prami ce'uxino}) but probably shouldn't be.