old commentary on gadri from pc

[Logical Language Group <lojbab>]

What follows is an extract from an undated commentary by pc of the
draft cmavo dictionary produced by Jeff Taylor.  The draft referred to
by the commentary is said to be that of 10/89.  I have inserted, at the
appropriate places, material from a somewhat later draft dated 6/90;
this material is in the form of double-bracketed paragraphs.
I don't believe the differences are very large.  The Taylor material is in
TeX format, but should be fairly easy to read.

pc writes:

LA/LE: I'm having a lot of trouble with this whole set.  At some point in the
evolution from the L1'75 to Lojban (I haven't looked at L1'89), I thought I
understood where we were going.  In terms of the present list (I think it
was different when I was clear) I had these two principles in mind:
1) each system had three members
lV was a set taken distributively, i.e., as, in effect, universal (or other
as specified) quantifier over the members of the set.
lV'i was the set itself, without reference to its members, having those
properties that sets, but not members, have - size, inclusion, exclusion and
overlap with other sets, and so on.
lVi is the set massified, having the properties which are the logical sum of
the properties of the members of the set, i.e., any property any member has
plus any that any team of members has.  Note: this can be apparently
contradictory.
2) each system had a single V:
a : description by name or predicate used as a name, implicitly restricted
e : nonveridical predicate description, implicitly restricted but also not even
required to be accurate
o : veridical predicate description: accurate and complete (not implicitly
restricted.)

Somewhere this simplicity seems to have gotten lost (if it was ever there
except in my misunderstanding of the situation) and now I don't understand many
of the points about descriptors given here.  For the first, the default
quantifiers don't seem to make sense in many cases.  The simple lV would
naturally default to "all" on the outside, as they do in natural languages.
Of course the name case (and probably le as well) usually goes to a single-
membered set, so the differences collapse, but why would we ever want to make
the most common reference to some one - rather than all - of the set?

Similarly , le sets are guaranteed members (that's why they were invented), so
we cannot get into trouble saying that they implicitly have at least one member.
The same is almost true for la, but not quite, since we can shift realities
around it without shifting reference (names may be rigid designators) and come
to a world where the named one does not exist (there ain't no Sherlock Holmes
in this world in the implicitly restricted sense I mean by la Cerlak Xomz.)
And, of course, any veridically described set may happen to be empty (and most
are.)  It would seem hard, then, to pick out an adequate default value for the
cardinal of these sets.  But then, why do we have to?  The cardinal is not an
essential part of the description in any case, thought it is permitted in all
(with difficult in the case of la class, since it has to be fitted in somehow
without getting lost in the name - or part of the name being taken for it.) so
we can just leave it out of defaults.  Every set exists and has some cardinal -
possibly 0 - so every description works to some extent.  If the cardinal is 0,
we may get mildly surprising results with lV descriptions (just what is up for
some debate at the moment).  But the same result will turn up if we stick in some
dummy cardinal like ro and even worse ones would turn up (I suspect) if we 
stuck in cardinals that didn't apply (indeed, I don't know what the result of
saying that a set with five members has six or four is.)

Thirdly, it is the same set involved in each of the three types of description,
though the involvement of the members of the set is different in each case.
But, since it is the same set, it must have the same size (a theorem, if not a
tautology), so why change the defaults in the different descriptions (assuming
we must have defaults at all)?

On particular items, there are further puzzles:

[[la\word{la}{LA}
``that/those which is/are called \ldots''; non-veridical descriptor marking
the following name or {\loj selbri\/}-description as a name of something
that is used as a {\loj sumti\/}; if a {\loj selbri\/} is used, closed by
{\loj ku\/} (usually elidable).  Implicit quantifier {\loj su'o la ro\/} (at
least one of all those that are called \ldots)]]

la : as noted, the usual reading of this would be pa/ro la pa Name, but surely
     it is everything in the set generally, however large the set may be.

[[\word{la'i}{LA}
``the set of those called \ldots''; descriptor of the mass of the all those
called by the name.  Implicit quantifier {\loj piro la'i su'o\/} (all of the
non-empty set of those called \ldots)]]

la'i line 2: is the set of things ..., not the mass.  I suppose these are the
     same object in some parsimonious ontology, but the effect that the members
     have on the sentence as a whole is very different.  Again there is no
     guarantee that the set has members (and the empty set causes the fewest
     problems here, since empty sets exist, unlike their members).  "The whole
     of the set" is better than "all of the set", which sounds like it is about
     the members again.

[[\word{lai}{LA}
``part of the mass of those called \ldots''; descriptor of the mass of all
those called by the name.  Implicit quantifier {\loj pisu'o lai ro\/} (some
non-zero part of the mass of all those called \ldots)]]

lai  : Why only a part of the mass?  Are you sure?  If a part has a property,
     the whole does but not always conversely - it takes a whole team to win
     a game, for example, even though some players' contributions may be small.
     I'd stick with the safe stuff.  We don't want to get into a lie by
     default, without even thinking about it.

[[\word{le}{LE} ``that/those which I describe as \ldots'', ``the \ldots'';
non-veridical descriptor marking the following {\loj selbri\/} as a
description-{\loj bridi\/} for something the speaker has in mind, the first
place of which is to be the {\loj sumti\/}; closed by {\loj ku\/} (usually
elidable).  Implicit quantifier {\loj su'o le ro\/} (at least one of all
those that I describe as \ldots)]]

le : again, "the men walked in" doesn't mean some of them, it means all of
     them, and I don't see why Lojban is different.  Of course, in Lojban, le
     is guaranteed a referent so we could use internal su'o, but why bother?

[[\word{le'i}{LE}
``the set of those I am describing as \ldots'', non-veridical descriptor
indicating the set of all things that I have in mind relating to the tail of
the {\loj sumti}.  Parallels {\loj le}, and is likewise non-veridical.  A
speaker referring to the set of ``Americans'' might have in mind only
citizens of the USA, as opposed to all residents of the Western
Hemisphere---another interpretation of ``Americans''.  Implicit quantifier
{\loj piro le'i su'o\/} (all of the non-empty set of those that I am
describing as \ldots)]]

le'i : The speaker might also mean any whiteskinned person in the room even if
     they came from Kishinev (Moldavian SSR - I like the sound of both
     places), there is no limit to how unveridical the predicate might be.  It
     might mean (as "little green men" may very well) certain nonparadigmatic
     electrical activity in the cerebral cortex.  You've only shown "implicitly
     restricted" here.  Discussion might be better at le anyhow.

[[\word{lei}{LE}
``part of the mass of individuals I am describing as \ldots, being treated
as a whole''; non-veridical like {\loj le\/} in that it discusses those the
speaker wishes to refer to, which may not exist.  {\loj lei\/} can refer to
a specific mass that the speaker has in mind.  The classic example is ``the
two men jointly carried the log,'' which is {\loj piro lei re nanmu}.  Since
the speaker has in mind a particular pair of individuals, who are certainly
not all men (and may not actually be men), this massified expression is
non-veridical.  {\loj lei\/} can also be used to refer to massified things
not claimed to exist, such as ``little green men''.  Implicit quantifier
{\loj pisu'o lei ro\/} (some non-zero part of the entire mass of those I am
describing as \ldots)]]

lei : what the speaker wishes to refer to be lie must exist, by the nature of
     the description.  BUT they need not be anything like the [sic] what the
     description suggests.  le cmalo vegri nanmu (how many languages mangled
     here?) may not be any of them small or green or men or even hominoid or
     even physical objects.  And lei doesn't refer to the mass the speaker has
     in mind but the mass of the things the speaker has in mind; the
     reference is always primary with le-class.  And of course, we wouldn't
     say piro lei re nanmu since that would be redundant, even if we wanted to
     stress that both did a fair share (since this does not say that); we say
     just lei re nanmu, just as in English (less the ambiguity).

[[\word{lo}{LE} ``at least one individual in the set of all those satisfying
\ldots (the tail of the {\loj sumti\/})'', ``a \ldots'', ``some \ldots'';
descriptor referring to individuals in the set of those actually having the
property referred to by the {\loj sumti\/} tail; closed by {\loj ku\/}
(usually elidable).  Implicit quantifier {\loj su'o lo ro\/} (at least one
of all members of the set that satisfies \ldots).  Usage: an indefinite,
quantified {\loj sumti}, such as {\loj ze mensi}, is equivalent to {\loj ze
le ro mensi\/}: seven of a set of all those that satisfy a claim of being
sisters.  {\loj pimu nanmu\/} (= {\loj pimu lo ro nanmu\/}) means 1/2 of a
man, not 1/2 of all men.  {\loj pimu loi nanmu\/} or {\loj ropimu loi
nanmu\/} would be used for the latter (= 1/2 of, or each of 1/2 of the mass
individual of men)]]

lo : Again, why su'o rather than ro?  Is it the case that ze mensi is ze le
     mensi and, if so, which is this discussion under lo?  Is the mensi
     veridical?  If so, there must be another source and why not use ze da poi
     mensi instead.  I suspect it typically is not veridical and so the
     suggested source is right, so this discussion - if it belongs in this list
     at all, belongs at le.  Similarly, the fractional quantifiers discussion
     applies equally to all the lV and lVi descriptors.   The discussion does
     not compute, however.  pimu loi nanmu is going to be a set (otherwise
     unspecified) which is included in the set of men and has a cardinality one
     half that of the full set.  It is not a set of halves of men or of half men,
     nor is it its members distributively - it remains loi, not lo.  It
     may be that ropimu loi nanmu drops back down to members, but I would think
     it more natural (and I think this is the original usage) to use this
     special quantifier with lo (and le and la), which are already about
     members.  After all, ropimu le n broda is just n/2 le n broda, when we
     know all the numbers involved.

[[\word{lo'i}{LE}
``the set of those which satisfy \ldots''; this is the set for which {\loj
lo\/} is used to refer to the individual members, and is likewise veridical.
Implicit quantifier {\loj piro lo'i su'o\/} (all of the non-empty set that
satisfies \ldots)]]

[John Cowan's note: pc wrote no commentary on lo'i.]

[[\word{loi}{LE} ``part of the mass individual consisting of all of those
satisfying \ldots, being treated as a whole''; massified descriptor that the
thing(s) referred to really has/have the property expressed in the
description, and that they exist, at least conceptually, to be massified;
{\loj loi cinfo\/} refers to all lions (those for which the statement {\loj
ti cinfo\/} would be true), not just those the speaker has in mind.  (One of
the {\lex GOI\/} lexemes could be used to restrictively reduce the range of
the set).  Implicit quantifier {\loj pisu'o loi ro\/} (some non-zero part of
the mass of all those satisfying \ldots)
\rafsi {\rm use} gunma]]

loi lines 5-6: "and that they exist, at least conceptually, to be massified"
     redundant and misleading: if they have the property mentioned, the exist
     and do so in whatever way is appropriate to that property.  For example,
     if something is a unicorn, then it exists and exists as an animate
     physical object.  But note also that nothing about using loi guarantees
     that there is anything which does have the property in question.

[[\word{lo'e}{LE}
``the typical \ldots''; descriptor labelling the {\loj sumti\/} as the
typical/average/stereotypical member of the set satisfying the description
tail.  Very similar to {\loj loi}, this treats the set of those meeting the
description tail as a mass individual.  The claim is more specific than {\loj
loi}, since {\loj loi\/} is satisfied if any part of the mass meets the
description; {\loj lo'e\/} claims that a particular portion---that portion
(if it exists) which is ``typical'', ``average'', or ``characteristic'' of
the mass.  Implicit quantifier {\loj pisu'ono lo'e ro\/} (any portion which
is typical of the mass of all those satisfying \ldots)]]

lo'e : I suppose that lo'e is a bit like loi in the way suggested, but in
     fact it is more summary than loi, since it is always presented as a
     single individual of the type of the set, so the external quantifiers
     would whack off pieces of it.  But it need not be an actual individual
     of the set, so we don't have to go treating it as reached by quantifying
     either lo or loi.

Or so it seems to me and has for a long time now.  And, as I said, I don't get
a coherent picture of these other notions, while this one does cohere.

-- 
John Cowan		sharing account <lojbab@access.digex.net> for now
		e'osai ko sarji la lojban.