Message-Id: <m0r3uv7-00005bC@xiron.pc.helsinki.fi>
Date:         Sat, 5 Nov 1994 18:26:12 EST
Reply-To:     jorge@PHYAST.PITT.EDU
Sender:       Lojban list <LOJBAN%CUVMB.bitnet@FINHUTC.hut.fi>
From:         jorge@PHYAST.PITT.EDU
Subject:      Re: lo, transparency
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 7675
Lines: 209

la djer cusku di'e

> 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.

In lojban, a bare predicate can be a sentence. The arguments are taken
to be "the obvious ones from context". Very ambiguous, but it works.
That's why you don't need to fill all the places with sumti to get
a sentence, you can fill from none to all.

> 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)

That may be an old list. It doesn't really make sense to have 5 predicates
defined like "x1 is a variable predicate". The definition I have is:

>> broda rod          predicate var 1
>> 1st assignable variable predicate (context determines place structure)
>>                           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.

In some sense you could say that {lo broda} is a predicate variable that has
already some restrictions. Whereas {da} is "at least one something", {lo gerku}
is "at least one dog".
>
>
 -------------------------------------------------------------------------------
 -
> Logical constants:
>
>         a        b        c
>         Andy    Bronwyn  Charles     Names
>                  d
>         that book on the table       singular description

In Lojban, I guess these would be {ko'a}, {ko'e}, etc, as well as all {le broda}
and all names.

> ____________________________________________________________________________
> 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.

I'm not sure what wff means, but you are right that {su'o broda} is not
a complete sentence. The grammar allows you to omit {lo} when using a
PA to form a sumti, so {su'o broda} is exactly the same as {su'o lo broda},
which in turn is the same as {lo broda} because {su'o} is {lo}'s default
quantifier. {su'o broda} is a sumti.

> 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.

{su'o ti prenu} means "at least one of these is a person", where "these"
is whatever you are pointing at.

> An assertion, ti prenu, corresponds to P(x).

Rather, it would be P(a) in your notation, because {ti} has a specific
referent.

> .i su'o ti broda,   works.  su'o broda seems incomplete.

That's because it is incomplete. A sentence with a selbri would be
for example {su'o broda cu brode} = "at least one broda is such that
it brodes".

> 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.

"At least one P", exactly the same thing {su'o broda} means.

> Thereafter
> it means the same particular one as the first time used.

It can't, because of its default quantification. Someone (Iain?) said that
{le broda} will mean the at least one broda that satisfied whatever
was claimed for {lo broda}, but this is not very clear to me.

> 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.

Yes! That's right.

> The
> quantifier is "one", contrary to the current default of su'o, at least
> one.

That's not how things are, and I doubt it will be changed to it. Even if
it did mean "one of the things that are broda", it would still be
nonspecific.

> The "one" default could be modifed by saying: lo re broda, or lo su'o
> broda etc.

Don't confuse inside and outside quantifiers.

lo broda = su'o lo ro broda = at least one of all things that broda
le broda = ro le su'o broda = each of the thing(s) I'm calling broda

lo re broda = at least one of the only two things that really are broda
le re broda = each of the two things that I'm calling broda

pa lo re broda = one of the two things that really are broda
pa le re broda = one of the two things that I'm calling broda

> 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.

Notice that in your translations you have implicitly an outside quantifier
{ro}, not {pa}. For example, you say that {mi pencu lo ci tanxe} means
{mi pencu ro lo ci tanxe} = "I touch each of the three boxes", and not
what you proposed as a default quantifier {mi pencu pa lo ci tanxe} =
"I touch one of the three boxes".

What it means in standard Lojban is {mi pencu su'o lo ci tanxe} =
"I touch at least one of the only three things that are real boxes".

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

Certainly, but there already is a convention. You can read more about this
in the grammar paper about sumti, I think.

> In declaring all the "nitcu, need" cases opaque I just followed Quine.

I don't think we can do that in Lojban, to have different rules for different
predicates. If {mi pencu lo tanxe} means "there exists a box such that
I touch it", then {mi nitcu lo tanxe} means "there exists a box such that
I need it", i.e., the transparent interpretation.

> 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.

I don't think {lo} has this {a/the} meaning. It's not reconcilable with
the {su'o} quantifier.

> 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.

Hopefully. :)


Jorge