TECH: Properties: what do they mean?

[John Cowan <cowan@SNARK.THYRSUS.COM>]

I will begin at the end, by stating my conclusions.  I believe that the
Loglan/Lojban notion of "property abstractions" is seriously broken.
Loglan had, and has, a syntactic contrivance that covers up this fact.
Lojban's syntax exposes it, but no one has written authoritatively
about properties since the split.  I suspect that properties need to be
reworked in some way.  In passing, I point out that "zmadu", whose x3 place
is supposed to be a property, not only illustrates just how properties are
broken, but turns out to be itself not in working order.

In this document I propose nothing.  I merely exercise the function of the
village idiot, viz. to point at something and say loudly, "BAD!".  I hope
that someone will come to the rescue, either with a proposal, or with an
explanation that will cause my perceived difficulties to melt away.

********

Historically, Loglan/Lojban has always treated the property abstractor, "ka"
("pu" in Old Loglan), as grammatically equivalent to the event abstractor, "nu"
("po" in Old Loglan).  Most of the attention has always gone to events, which
were and are seen as the archetypal abstraction.  For the most part, properties
have been "explained" by pointing to certain English words, typically ending
in "-ness", and saying that "blueness" is  "po/nu blanu".  The only extended
writeup on the subject is JCB's from NB3 (1987).  lojbab has said that he
does not regard this explanation as authoritative, but has not said wherein,
if at all, he disagrees with it.  I quote some of the explanation here,
from pp. 99-100:

The semantic distinction between "po" and "pu", between what we call in English
"events" and what we call "properties", is perhaps the most difficult to
understand in the language.  The difference between these two operations is
clearest in the descriptive context, that is, between the designata of event-
descriptions and those of property-descriptions as abstracted, let us say,
from the same predicated relationships.  Any differences found here should
apply, of course, to the other contexts.  Let us examine, then, both an
event-description and the property-description abstracted from the same
relationship.

"lepo" evidently abstracts a case, state, condition, or event of any
length -- as long as an epoch or as short as a sneeze -- from some predicated
relationship.  "lepu", in its turn, may abstract a property or quality
from the same relationship.  Suppose the predicated relationship is a
motherhood between a mammalian mother X, an offspring Y, and a father Z.
[Note by JC: This reflects JCB's place structure for his version of
Lojban "mamta"; it refers to genetic mothers only.] ... We note that the
thing that "lepo" designates about these 3 individuals is laid out in
space-time.  It has a beginning, a duration, and an end.  And the relevant
segments of each of the three life-lines describe paths through space
as well.

The property description of this same relationship, in contrast, is essentially
time-free.  It is the least set of facts which would establish the truth of
that predicated relationship if it were true.  That Y developed from an ovum
produced by X's ovarian tissue is one of them; that that ovum was fertilized
by a spermatozoon produced by Z's testicular tissue is another one.  Are
there any others?  It would seem not.  These two properties of these three
individuals would, if known, be sufficient to establish X's maternity of
Y by Z in any court of law -- or, more likely, in any laboratory.  And that,
it would appear, is what a property is: it is that lean abstraction from
the richness of the world that is just sufficient to enable us to know the
truth of some matter.

The event-description is, in contrast, a "fat" concept.  The designata of
descriptions like ... "The event-state-condition of X's mammalian motherhood
of Y by father Z" are often rich and complicated segments of the world;
and they have a richer dimensionality than properties do.  The designatum of
... "The property of X's mammalian maternity of Y by father Z" consists, in
contrast, of two very simple but sometimes difficult to establish facts;
and those facts are strangely free of time and other complications.

In sum, designata of po-abstractions are rich, multi-dimensional objects
distinguished by duration; the designata of pu-abstractions are least sets
of sufficient facts.  The designata of zo-abstractions [Lojban "ni"] are
the leanest of all, of course, being simply numbers -- and sometimes
uninteresting numbers at that.  While the amount of heat in this room, and
the amount of blue in that painting, may well be interesting numbers, ... [the
amount of X's mammalian maternity of Y by father Z] is not.  How shall
we measure [it]? ...

[End of excerpt.]

JCB also writes, and I think very significantly, the following on p. 90:

        Notice that the events, properties, or quantities described
        with ... ["le po"/"le pu"/"le zo" descriptions] may be
        particular [see 1] ... or general [see 2] ...

I will use Lojban equivalents of JCB's Institute Loglan examples:

1)      leni ko'a pu limna
        the amount that X swam

2)      le nu limna
        the event of swimming
        swimming

Now in events, there is indeed a clear distinction between the particular
and the general, and it corresponds to the usual mechanisms of Lojban
ellipsis.  "The event-of swimming" is the event of zo'e swimming; perhaps
the event of John swimming, or of Alice swimming.  But "the property-of
swimming", which may also be glossed "the property-of being-a-swimmer",
is all one whether it is John's or Alice's.  It is not the property of
"zo'e limna", but more like the property of "da limna".

Consider that old standby, the comparison sentence.  We have:

3)      la djan. zmadu la djordj. le ka darno mi
        John exceeds George in-the property-of farness from-me.

Here the x1 of the "ka" bridi is ellipsized, and we understand that
we are to look at "la djan. darno mi" and "la djordj. darno mi" and see
which is "zmadu".  But what about:

4)      la djan. zmadu la djordj. le ka se prami mi
        John exceeds George in-the property-of being-loved-by me

This differs from:

5)      la djan. zmadu la djordj. le ka mi prami

not at all, and from:

6)      la djan. zmadu la djordj. le ka prami mi

only in what is ellipsized.  But this difference of Ellipsis between 4)
or its equivalent 5 on the one hand, and 6 on the other, makes a vast
semantic difference.  4 and 5 mean that I love John more than I love George,
whereas 6 means that John loves me more than George loves me.  This
distinction hangs only on ellipsis of x1 vs. ellipsis of x2.  In fact,
ellipsis is being used to show which place has been made "open" in converting
the bridi to a property.  This is not a difference of specificity vs.
generality, but of two different properties altogether, viz.
the property of loving me and the property of being loved by me.

Those familiar with Lisp, or with the lambda calculus, will
recognize "ka prami mi" and "ka se prami mi" as

        (lambda (x) (prami x mi))

and

        (lambda (x) (prami mi x))

The notation "(lambda (x) ...)" may be read as "the function defined by
the rule "...", where "x" is the variable name used by the argument.  Thus

        (lambda (x) (+ x 1))

is the name of the function which produces the successor to a number.
In effect, "ka <sentence>" is a predicate which is true of certain abstract
objects, namely those which can be applied to certain sumti to produce
a truth value.  "le ka <sentence>" is one of those abstract objects.
I believe this is what JCB means by "a least set of sufficient facts".

So far, so satisfactory.  The difficulty is seen when we consider the
role of ellipsis.  Suppose I speak of "le ka binxo lo bitmu", the
rather odd property of "becoming a wall".  We know that this property
is a property of that which changes, rather than of that which is
change into, because x1 is ellipsized and x2 is not.  However, x3
(the conditions) is also ellipsized!  How are we to know that this "le ka"
phrase does not refer to the property of being a set of conditions under
which something unspecified becomes a wall?  Ellipsis in ka-sentences
serves both to indicate the variables in the lambda abstraction, and also
the normal zo'e places which are to be understood.  (The nit-picking objection
that "le ka" covers a multitude of sins because "le" is not veridical
breaks down when we consider the less familiar "lo ka", that which really
is a property.

Finally, let me point out the problem that "zmadu" (as well as "mleca") has.
One way to avoid the semantic messiness of 3 is to say:

7)      le ni la djan. darno mi cu zmadu le ni la djordj. darno mi
        The amount-of John being-far-from me exceeds the amount-of George
                being far-from me.

It has always been supposed that this formulation is quite precise, since
"ni"-abstractions are numbers, and that this has the same rigor as:

8)      li vo zmadu li ci
        The-number four is-greater-than the-number three.
        4 > 3

But in fact, neither 7 nor 8 is precise, since the third place of zmadu
has gotten lost.  Just what is the property by which four exceeds three?
Number-greaterness (ka namcu zmadu)?  Hardly, as this circularly drags
in "zmadu" again?  We gave up the separate cmavo for "<" and ">" as predicates,
believing that "zmadu" and "mleca" would do the work.  But with what x3
place?  If we are to reduce comparison of things (by some property) to
comparison of numbers (ni-abstractions), by what property do we compare
those numbers?

I hope that someone can clear up all these difficulties, because the
abstraction paper I am now trying to write depends heavily on a decent
explication of non-event properties; it will be the first full-length
explication that the Loglan Project has ever had.  I have talked to pc,
and at the time he agreed that there was a problem, so one of the
standard avenues is closed off.  Does anyone know the Right Thing?

--
John Cowan      cowan@snark.thyrsus.com         ...!uunet!lock60!snark!cowan
                        e'osai ko sarji la lojban.