lo, transparency

[Gerald Koenig <jlk@NETCOM.COM>]

Some parts to the puzzle are:

Variable predicates:    Equivalent forms are in each column. The
exponent is the number of arguments (sumpti). The subscript is an
identifier for each predicate word. These are the bare predicates
without sumpti and are not sentences. Are we mistakenly using "broda"
for the last, general form?  Do we even have a word for it?
>From the gismu list:

broda rod          predicate var
1                           x1 is the 1st assignable variable
predicate                                                      ad
134    (cf. cmavo list bu'a)


         1        2          5        m            (standard notation
        A        A          A .....  A             for predicates in
         1        2          3        n            predicate calculus)

         broda   brode    brodi    (lojban)
        is_fact  thirsts  goes     (example)
         fatci   taske    klama    (example)

-------------------------------------------------------------------------
Predicate variables:

        x        y        z
        da       de       di         Predicate variables range over
                                     constants. Maybe over full
                                     sentences  in lojban predicates
                                     that call for abstractions in x2.

--------------------------------------------------------------------------------
Logical constants:

        a        b        c
        Andy    Bronwyn  Charles     Names
                 d
        that book on the table       singular description
____________________________________________________________________________
Quantifiers:

        Quantifiers operate on predicate variables, not on variable
        predicates.

        All(x)   For all (x). ro da
        E(x)     There exists at least one x.  su'o da
        N(x)     Number of (x).  i.e. no da.  lojban only?



                                   n
To me, su'o  broda  means  " E(x) A  "    or E(x)P which is an
                                   1


incomplete sentence, or not a wff. It is like saying;  At least one
something exists, such that person. It should read E(x)P(x); At least
one something exists, such that it is a person. .i su'o ti prenu, would
be an example. An assertion, ti prenu, corresponds to P(x).
.i su'o ti broda,   works.  su'o broda seems incomplete.

Following pc, but maybe not with full understanding, "lo broda" means
a/the broda or "one P"   or even "any one P", on first use. Thereafter
it means the same particular one as the first time used.  I  would say
there is also an existence claim for the thing it describes or points
to. So it is doing double duty as a descriptor and a quantifier. The
quantifier is "one", contrary to the current default of su'o, at least
one.

The "one" default could be modifed by saying: lo re broda, or lo su'o
broda etc. The default lo would be specific or singular and the
optional explicit greater-than-one kind would be non-specific or
general. Examples of this usage:

.i mi nitcu lo tanxe             singular, opaque
I need a real box.
.i mi nitcu lo su'o tanxe        general, opaque
I need some real boxes.
.i mi nitcu lo ci tanxe          general, opaque
I need three real boxes.

.i mi pencu lo tanxe             singular, transparant
I touch a real box.
.i mi pencu lo su'o tanxe        general, transparant
I touch some real boxes.
.i mi pencu lo ci tanxe          general, transparant
I touch three real boxes.

These sentences parse. It is a matter of convention what lo tanxe is to
mean.

In declaring all the "nitcu, need" cases opaque I just followed Quine.
But he could be wrong. For instance, in a context of two people looking
at and talking about one box; where, as pc says, the a/the meaning of
lo has progressed to the "the",  " mi nitcu lo tanxe" certainly seems
transparent. What other box would they be talking about?  What is
opaque is still murky to me.  The above is my effort to understand. I
hope it can be helpful.  An affirmation:

We now bring a higher level of clarity and precision to lojban.
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jlk@netcom.com