Re: Some thoughts on Lojban gadri

[Logical Language Group <lojbab>]

la .and. cusku di'e

> > I understand "loi" to involve a kind of denial of differentiation
> > between members of a category, not so that they all merge together
> > in a porridgey blob, but so that we cannot tell the difference
> > between one instance of Mr Broda and another instance.
> >
> > But if I have this right, a default of "pisuho loi" doesn't make
> > much sense.

la xorxes. cusku di'e

> Exactly. Also the porridgey blob is very useful, especially in the
> case of {lei}.
> 
> (And if you want to consider the body as a "mass" of cells, another
> of the favoured examples, you better allow for differences among the
> members.)

Ah, I think I see the trouble here.  Jorge is correct, Lojban masses are
"porridgey blobs", or more precisely they are wholes characterized by
parts, where the parts are not precisely differentiated (unlike the members
of a set, which are distinct).

The "I see Mr. Rabbit" bit means not that we have perceived an instance of
the class "lo'i ractu", but rather that we have perceived a component of the
rabbity-blob.  What is blurred is not the distinctions between individual
rabbits, but the separating lines between one rabbit and the next.

There was an incident (details in the >Oxford Collection of Literary Anecdotes<)
in which a number of people observed an arm removing pieces of paper from a
pile, writing on each at full speed, and moving each to a second pile.  The
owner of the arm remained in shadow, or perhaps out of sight in some
other way.  It turned out to be Walter Scott's arm, which is why the OCLA
has the story.

The bystanders saw "Mr. Scott", although actually only {pisu'o} Mr. Scott
was visible.  Similarly, when we see a rabbit, or even a rabbit ear,
we see {pisu'o} Mr. Rabbit, where Mr. Rabbit is the whole rabbity-blob.
So when And says that "loi ractu" is unique, he is part right and part wrong.
"piro loi ractu" is certainly unique, but there are various "pisu'o loi ractu"s,
and we may talk about "re lo pisu'o loi ractu" if we like: two different
submasses of the rabbity-blob.  Or, if we want to be specific, "le re lo pisu'o
loi ractu" does the job.

(There is the point, mentioned briefly in the sumti paper, that the same
components may be massified with different structures; the mass of rabbits
taking all ears, eyes, legs, tails together is somewhat different from the
mass of all rabbits taking each (biological) individual together.  But this
distinction can normally be ignored.)

What remains doubtful in my mind is the extent to which component properties
can be attributed to various portions of the mass which are not grouped
componentwise.  On a straightforward reading, the number of legs that
"pisu'o loi ractu" has can be anything from zero to 4 * N, where there are
N rabbits in the universe, since "loi" is -specific and simply asserts that
>some< portion of the rabbity-blob has a given number of legs.  Maybe
there is really no property inheritance from parts to wholes at all, and
the belief that there was came from the insufficiently appreciated
non-specificness of "loi".

But if so, then the quantifier "piro" proposed by Jorge for "lei" won't
work in the way we expect.  "lei re prenu", viz. "la alis. joi la djordj."
has four legs, and the notion that if Alice is small and George is big, then
the mass is both small and big, breaks down.  Alice-joi-George would have
to be compared to other masses-of-two-persons, not to individual properties
of individual persons.

The fact that "lei" is +specific doesn't affect what its outside quantifier
is, since (as I said before), the outside quantifiers of masses aren't
true logical quantifiers: the true quantifier in the sense of predicate
logic is always "pa".  The apparent quantifier is really a fractionator:
we massify some number of components, determined by the inside quantifier
(really a set cardinal, as pc says), get some fraction of it, specific or
non-specific as the gadri tells us, and then use that as a singular term.

So as usual, I end up being (in Smullyan's phrase) dogmatic about what I
know, and skeptical about what I don't.

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