Re: [loglanists] Sets

[John Cowan <cowan@ccil.org>]

John W. Kennedy scripsit:

> This seems to involve the
> late-19th-century dispute over whether "all" statements and "some"
> statements have existential import. Classicists claimed they did. 
> Modernists claimed they did not.

Nobody has ever claimed that existential ("some") statements did not
have existential import. The whole point of saying "Some swans are
white" is to assert that there *are*, indeed, swans that are white.

The question is about universal statements and how to map them.
Traditionally, "All swans are white" (used by Aristotle, but now known
to be empirically false) was read as having existential import, as
you say.

Modernists mapped this to "For all X, if X is a swan then X is white"
which does not have existential import about swans (it has existential
import about X, but that is no problem unless we are considering a
purely empty universe, which can be dismissed). It merely says that
*if* there are any swans then they are white.

This clash can be resolved in one of two ways: decide that "All swans
are white" has no existential import either, or decide that "For all X
etc." is not a fully adequate mapping of "All swans etc."
Lojban takes the second view, since both forms can be expressed:
one using number + predicate directly (= "All swans"), the other
using a bound variable and a relative clause ("All X such that").

> Lewis Carroll, as I recall, tried to
> compromise by giving existential import to "some" statements, but not to
> "all" statements (so that, by his scheme, "All unicorns are white" is
> acceptable, but "Some unicorns have halitosis" is not).

Carroll took the traditional view: both have existential import.

-- 
John Cowan http://www.ccil.org/~cowan cowan@ccil.org
To say that Bilbo's breath was taken away is no description at all. There
are no words left to express his staggerment, since Men changed the language
that they learned of elves in the days when all the world was wonderful.
--_The Hobbit_