Re: more on logical issues

[Jim Carter <jimc@MATH.UCLA.EDU>]

Steve Hazel <hazel@TURING.CS.STEDWARDS.EDU> writes:

> While the English syntax is not flawed, the logic may be.  The basic question
> here, I think, is whether or not it is logical to say that a nonexistant thing
> or nonexistant things ("even prime numbers greater than three") can be given
> properties ("are multiples of 27").

That's the whole point of the argument (which has been running for several years
on and off): when the speaker says the "all" quantifier, under what
 circumstances
does he claim that the number of quantified items is nonzero?  Certainly in
mathematics it's very common to identify some set, prove two properties for all
its members, then prove that the same item can't have both properties, thereby
proving that the set is empty.

Pragmatically, natural languages were created through the speech of workers,
peasants and soldiers who never took a course in math or logic, and it's common
(if not universal) for them to commingle the claim that a set is nonempty, with
an iteration over all its members, as in "all unicorns drive Chevys": "there
is at least one unicorn" and "unicorn[0] drives a chevy and unicorn[1] drives
a chevy and ..."

My own feeling on the matter is that the pan-iteration implied by the universal
quantifier should be kept separate from any claims about count.  Example:
"All even primes are less than 3" (not by language implying that there are any),
and then, if you care, "... and at least/exactly one of them exists".  That may
not be the historical interpretation of "all"/"omni"/etc. in natural languages,
but Lojban is supposed to be _logical_, and I think we can handle a little
modularity.

James F. Carter        Voice 310 825 2897       FAX 310 206 6673
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