TECH: Properties

[jimc@MATH.UCLA.EDU]

John Cowan puts his finger on it by saying that there is a serious
problem with property abstractions.  Lojbab emphasizes the importance
of a conservative solution to the problem.  Bob Chassell makes a key
point that essence-ist philosophy has a long tradition in the Western
world.  Jerry Koenig points out very clearly the reason that Lojban is
not essence-ist, and thus that John Cowan's reservations about
properties are vacuous -- but vacuous in a way which has to be dealt
with carefully in our use of the language (we're essence-ist, after
all) and in our teaching of it to essence-ist newcomers.

To summarize for anyone who missed the foregoing messages, an
essence-ist philosopher considers important the properties of an object
which are special to it; an archetype of essence-ist study is the
taxonomy of creatures, and determining just what it is that makes one
kind of creature special.

In a predicate language such as Lojban, a selbri is considered to
represent a relation, which means that it represents a long list of
objects which are thus related.  For example, rat1 eats cheese1; rat2
eats cheese1; rat1 eats sandwich2; etc. ad nauseum; and this is the
"true meaning" of the word "eat" rather than some uninterpretable text
string about mouths and swallowing (in which the mouth is defined
circularly as "the organ for eating").  From this point of view,
properties are merely a user's idea of regularities in the meaning
lists (if any there be), and not anything fundamental to the language.

Thus the only difference between "nu" and "ka" is, "ka" signals that
the speaker will be taking an essence-ist posture relative to the
phrase referents.  This, I believe, is what JCB means by "lean" vs.
"fat" events.

So what about ellipsis?  I would say that the blind men are feeling around
the butt end of the elephant.  Consider John's example 4:

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

John says that zmadu x3 (the property) contains an ellipsis, i.e. the
words of the sentence do not signify that a particular person is in x1
of "se prami".  So just who is being loved?  And if multiple places
were ellipsized, which one is abstracted to form the property?  I would
like to suggest a change of interpretation which removes this
confusion.  In a subordinate clause the modified sumti is
auto-replicated into x1 (after conversion) of the clause, e.g.

5)      le mlatu poi xekri
        The cat, The which is black

I request that a similar auto-replication be made with zmadu, namely:

6)      la djan. zmadu la djordj. le nu (ke'a) se prami mi
        John exceeds George in-the-property-of
                ((John, resp. George) is loved by me)

Thus x1 and x2 are successively replicated into x1 (after conversion)
of two copies of x3, with no ellipsis involved, and then the "degree"
of each copy is evaluated and they are compared.  This interpretation
is unambiguous and is easy for a speaker to generate and for a listener
to understand.  It also requires no grammar changes.  Just as in a
subordinate clause, ke'a is optional and is usually omitted unless in
an unusual place.  I have used "nu" instead of "ka" merely because the
resulting abstractions are of a form normally expressed with "nu";
there is no reason John could not choose "ka" to make his user-selected
semantic point.

Everyone cries out, "What's Carter saying?  That's what zmadu *means*,
and so his request is vacuous!"  My point is, Cowan doesn't act as if
zmadu x3 is subject to auto-replication, and replication is nowhere in
any language documentation, and it got dumped on when I brought it up
before in connection with dikyjvo.  I'm bringing it out again now because
the examples now before us show how valuable it is.

zmadu is just about the most complex example you can get for replication,
so let's see a more typical one:

7)      le djacu cu binxo lo nu sligu
        The water becomes solid (freezes).

With all of the various permutations of "binxo-become" there are
problems identifying the exact items which are solid, due to the
interpretation that invisible place occupants are ellipsized.  With
replication the interpretation is clear: replicate x1 into x2,
unambiguously giving

7)      le djacu cu binxo lo nu (ke'a) sligu
        The water becomes (the water is solid)

When you see "lo nu broda", if you replicate the preceeding place of
the containing bridi (ordered before conversion) you will get the
right meaning 80% to 90% of the time, and if some place structures were
straightened out the success rate could be increased.  Nonetheless, some
words like zmadu have exceptional patterns which must be specified word
by word.

There's more you can do with replication: replicate ellipsized places;
replicate sumti referents (e.g. "le binxo lo nu sligu", that which
freezes); retro-replicate buried sumti up to the main level (e.g. "lo
nu le djacu ne le lalxu cu sligu cu se cfari", the lake freezing
begins; what's in cfari x1?).  But let's think about the basic process
before the details.  By interpreting certain buried places as
replicates of containing bridi places, we can:
    1.  Avoid ambiguous interpretation of property-type abstractions
    2.  Do it with no change whatever to either grammar or existing text.

James F. Carter        Voice 310 825 2897       FAX 310 206 6673
UCLA-Mathnet;  6221 MSA; 405 Hilgard Ave.; Los Angeles, CA, USA  90024-1555
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