From pycyn@aol.com Sun Aug 19 08:25:43 2001 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_3_1); 19 Aug 2001 15:25:43 -0000 Received: (qmail 71304 invoked from network); 19 Aug 2001 15:25:43 -0000 Received: from unknown (10.1.10.142) by l9.egroups.com with QMQP; 19 Aug 2001 15:25:43 -0000 Received: from unknown (HELO imo-m09.mx.aol.com) (64.12.136.164) by mta3 with SMTP; 19 Aug 2001 15:25:42 -0000 Received: from Pycyn@aol.com by imo-m09.mx.aol.com (mail_out_v31_r1.4.) id r.133.42fe10 (4533) for ; Sun, 19 Aug 2001 11:25:39 -0400 (EDT) Message-ID: <133.42fe10.28b13473@aol.com> Date: Sun, 19 Aug 2001 11:25:39 EDT Subject: Toward a {ce'u} record To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_133.42fe10.28b13473_boundary" X-Mailer: AOL 6.0 for Windows US sub 10531 From: pycyn@aol.com X-Yahoo-Message-Num: 9787 --part1_133.42fe10.28b13473_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit "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. --part1_133.42fe10.28b13473_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit "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. --part1_133.42fe10.28b13473_boundary--