Kinds

["And Rosta" <a.rosta@lycos.co.uk>]

Intensional contexts that can give rise to opaque readings
can be handled by propositionalism, but only by using
predicates that take propositional arguments. As English
shows us, a not-mutually-exclusive alternative is to use
Kinds.

Consider (1).

1. The branches are shaped like a snake.

This has three readings:

2a. The branches are shaped like Mr Snake (= Snake as a kind).
2b. The branches are shaped like the same (kind of) snake.
= There is a kind of snake
2c. The branches are shaped like a possibly different (kind 
of) snake.
For each branch there is a kind of snake that the branch
is shaped like.

Talking about Kinds is not restricted to intensional contexts:

3a. We each ate the same meal.
3b. We each ate a possibly different meals.

On readings where a meal is a menu item rather than a physical
plate, these can be rendered as:

4a. There is a kind of meal that we each ate.
4b. Each x of us is such that there is a kind of meal that x ate.

Kinds involve a fundamentally different ontology from ordinary
predicate logic:

i. To every property there corresponds one Kind. (I'm not sure
whether relations also have corresponding Kinds.) A Kind is
the embodiment of the property.
ii. Every x can be construed as a Kind corresponding to property
{me x}.
iii. All kinds exist. 
iv. A Kind exists in more than one world.
v. One Kind can be a kind-of another.

For property P, the corresponding Kind could be defined thus:

x such that for every y, if P(y) then y is a kind of x
and if y is a kind of x then either P(y) or for me'i ro
z such that P(z), z is a kind of y.

To implement this in Lojban we need a selbri meaning "is a kind
of", and some sort of gadrioid for expressing the kind corresponding 
to a property. Assuming we are dealing with BF-style revisions
to SL, then options for the gadrioid are:

A. One Kind o-gadri:
lo-kind broda = lo-kind cmima be lo'i broda
lo-kind cmima be le'i broda
lo-kind cmima be la'i broda

B. One Kind gadrow:
lo-kind broda
le-kind broda
la-kind broda

C. One Kind LAhE:
LAhE-kind lo'i broda
LAhE-kind le'i broda
LAhE-kind la'i broda

In AL, I follow xorxes in opining that lo/le/la when not preceded
by an explicit PA should mean lo/le/la-kind. This solution seems
so overwhelming superior to A/B/C that the BF ought to consider
it.

As for "is a kind of", this can either be a selbri (typically
taking as x2 a sumti of type A/B/C), or a NU working like
{poi'i}, or (by stipulation) LE + ro + A/B/C.

--And.