Re: A couple of questions

[ucleaar <ucleaar@ucl.ac.uk>]

Dave Matuszek:
> Whether universal quantification has existential import has been
> argued extensively by philosophers and logicians, a lot of it during
> the Middle Ages when Aristotle reigned supreme.  There is no "correct"
> answer.  The standard interpretation in modern formal logic is that it
> does not have existential import; only the explicit existential
> quantifier has that.  Again this is not "correct," merely what
> logicians have decided is convenient.

Aha. And in English they do tend to imply existence. (E.g. for "I
read every book" we need "Ex [x is a book & I read x] & Ax [x is
a book] -> I read x".)

The lojbanic solution in such cases is usually to invent ways to
express both meanings (& to make both expressions "Zipfean" - i.e.
verbose in proportion to their infrequency). So I conclude that
we need:
  (1) all, not implying existence
  (2) all, implying existence
  (3) some-but-not-necessarily-all, not implying existence
      [This is the ">0%" I've advocated.]
  (4) some-but-not-necessarily-all, implying existence
(1) is "ro" & (4) is "lo" & "da". It would be nice to have a convenient
expression for (2) & (3).

---
And