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Re: [jboske] Transfinites
At 10:56 AM 1/13/03 -0500, John Cowan wrote:
Robert LeChevalier scripsit:
> For uncountable extremely large finite, we have so'a, recalling that
"so'i"
> means "many", and so'e has to be enough larger as to make "many" seem too
> small, and so'a larger still in the same sense. All of the so'V words are
> uncountable numbers with varying degrees of size attached, and the use of
> so'u as a standard quantifier shows that they can convey some important
senses.
This is a different sense of "uncountable" than we are using here. Sets
are called *countable* if it is possible to put their members in 1-1
correspondence with the natural numbers or a subset of them; *uncountable*
otherwise. All finite sets are countable; some infinite sets are countable,
some uncountable.
You are using "uncountable" in the sense of "vague".
I realized when I read Nick's long post to me on transfinites that I had
forgotten about countable/uncountable infinities.
Unfortunately I still remain grounded in a real world where there seems to
be no real infinities, only mathematical ones. USUALLY, Lojban talks about
the real world where the largest proper inner quantifier is a countable
sub-infinity. In discussions of mathematics we need to be able to go into
infinities, but I'm not sure we should be designing the language contrary
to quantum/atomic theory.
We may have situations where metaphysical assumptions are contradictory, in
which case Lojban cannot remain metaphysically neutral - we can at best
have a mark that changes the metaphysics from some standard
assumptions. (Do I sense that we've returned to the x4 of djuno yet
again? Let's not go there.)
lojbab
--
lojbab lojbab@lojban.org
Bob LeChevalier, President, The Logical Language Group, Inc.
2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273
Artificial language Loglan/Lojban: http://www.lojban.org