TECH: Higley on "noi"/relative clauses

["(Logical Language Group)" <lojbab@GREBYN.COM>]

                      Quantification and noi

      A potential problem has come to my attention regarding the
quantification of sumti modified by relative bridi.  Since this
"problem" almost invariably pops up when noi is involved, I will dis-
cuss it as it relates to noi only, and its occurrence with other
relative clause cmavo can be inferred.1
1This problem does not seem to occur with poi.
      All sumti that are not explicitly are implicitly quantified.  In
the following discussion I will deal only with those that are made by
the addition of a gadri (article) to a selbri.  With all such sumti,
whether the quantification is implicit or explicit, there are two
"points" of quantification, one (the selected subset) before the gadri
and one (the "inner" set - so called because of its position) after
it.  (I shall henceforth refer to the "inner" set as I and the
selected subset as S.)
      Put simply, the question/problem is this:  In a non-restrictive
relative clause, does the cmavo "ke'a" refer to I or to S?2  If we
take the analogy of poi, it refers directly to I, and thus to S as a
subset of I.  In the sentence "mi pu viska ci le vo prenu poi ca
vave'a litru", four people were moving around in a medium-sized area a
medium distance away, but I saw only three of them.  Thus ke'a refers
to I.  If we replace poi with noi in this example, we get "mi pu viska
ci le vo prenu noi ca vave'a litru".  For this a colloquial English
translation will be helpful:  "I saw three of the four people, who
were (at the same time) traveling (i.e. moving on/across/via some
unspecified surface) a medium distance away in a medium-sized area."
Based on the English translation, it is quite impossible to tell, in
the absence of context, whether three or four people were "traveling",
although it is certainly clear that only three were visible to me.
Since of course we cannot take the analogy of English -- we would be
rightly guilty of malglico -- we must conclude that noi is analogous
with poi in this respect3, and that ke'a always refers to I in a non-
restrictive relative clause.
2In referring to I, ke'a always refers to S as a subset of I.  But the
question here is whether ke'a might ever refer directly to S, thus
excluding some members of I.
3Since we have no reason to think otherwise.  I have never seen a rule
of the grammar that specifically states whether ke'a refers to I or to
S.
      But here's where we run into a problem.  If noi and poi are
analogous in this respect, many Lojbanists, myself included, are
making the mistake of assuming that ke'a can sometimes refer to S,
particularly if S is quantified explicitly and I is not.  The examples
below will show what I mean:

      1.   mi viska ci le vo ninmu noi melbi  "I see three of the
           four women, who are beautiful."
      2.   mi viska ci le ninmu noi melbi  "I see three of the
           women, who are beautiful."
      3.   mi viska le ninmu noi melbi  "I see the woman, who is
           beautiful."  "I see the women, who are beautiful."
      4.   mi viska ci ninmu noi melbi  "I see three (of the set
           of all?) women, who are beautiful."

      Look carefully at these examples and their colloquial English
translations.  If ke'a always refers to I, then we may run into
occasional problems, particularly if we definitely do not want it to
refer to I.  As for example 4, I would venture to guess that most
Lojbanists would not take ke'a as referring to all women!  But this
is the interpretation we must accept if ke'a always refers to I.  If,
on the other hand, ke'a always refers to S in noi clauses, we run
into the problem from the other end.  For this, look at example 1.
What if we want to show that all of the women are, incidentally,
beautiful, while I only see three of them?
      One solution to this is to divide ke'a into two cmavo.  One
that refers to I, and another that refers to S.  For the following
examples, I have assigned the experimental cmavo "xai" the meaning of
S-referring relative sumti, and ke'a refers to I:


      1a.  mi viska ci le vo ninmu noi xai melbi  Here three
           women are beautiful (out of the set of four that I
           happen to have in mind) and the same three are seen.
      1b.  mi viska ci le vo ninmu noi ke'a melbi  Here three are
           seen and four are beautiful.
      2a.  mi viska ci le ninmu noi xai melbi  Here three women
           are seen (as always) and the same three are beautiful
           (out of the set of all that I have in mind).
      2b.  mi viska ci le ninmu noi ke'a melbi  Here all of the
           women are beautiful, and three of the same are seen.
      3.   (skipped)
      4a.  mi viska ci ninmu noi xai melbi  Here three are seen,
           and three are beautiful, and we avoid the problem of
           having to call the whole lot beautiful!
      4b.  mi viska ci ninmu noi ke'a melbi  Here three are seen,
           and the members of the set of all women are beautiful.

      Another possibility has come to my mind, and the grammar may
very well specify exactly this, but I'll call it to your attention
anyway.  What it involves is the quantification of ke'a itself.  If
we allow ke'a to refer to all of I, then we can echo the quantific-
ation of I or S to show the one to which we are referring, and thus
we won't need two cmavo.  If this seems rather hazy, the following
examples should clear it up:

      1.   mi viska ci le vo ninmu noi ci ke'a melbi  Here we
           know that three of the women are beautiful, because
           the S quantification is echoed with ke'a.  (Remember
           that ke'a is always quantified as "all of I", so ci
           ke'a means "three of the four", and the rule would
           state that these three must be S.)
      2.   mi viska ci le vo ninmu noi ro ke'a melbi  Here four
           women are beautiful.
      3.   mi viska ci le vo ninmu noi ke'a melbi  Here we don't
           know whether three or four are beautiful, and only
           context will help us.
      4.   mi viska ci le vo ninmu noi paboi ci ke'a melbi  "I
           see three of the four women, of which one of the three
           (of all four) is beautiful."  And this woman is a
           member of S.
      5.   mi viska ci le vo ninmu noi paboi ro ke'a melbi  "I
           see three of the four women, of which one of the four
           is beautiful."  And not necessarily any of S.
      6.   mi viska ci le vo ninmu noi su'oboi ci ke'a melbi  "I
           see three of the four women, of whom at least one of
           the three is beautiful."  Etc.

      I frankly don't know which one of these systems (two cmavo or
one with special quantification rules) will work best, but I am
partial to the latter method.  Our intuition will still be of great
help to us when deciphering relative clauses -- as shown by the fact
that, so far as I know, no one has noticed this problem before -- so
it will still often be possible to omit the relative pronoun.
      One last possibility would be that noi clauses always refer to
S and poi clauses always to I, but that will run into some problems,
as you may already see.
      What does the baselined grammar say about all this?  I'd love
to know.

Greg Higley