Mike, Eugene:
In some languages, a double negative is an affirmative (e.g. the
Chinese
hit song "Bushi Wo Bumingbai", which means "It's not that I don't
understand"). In other languages, a double negative is a negative
(e.g.
French, which uses the "ne pas" construction and shows a fondness for
intensifying rather than negating double negatives in lots of other
ways).
As the bastard tongue of bastards, English is somewhere in between.
In my
examples, I deliberately cut out the following sequence:
a) It's worth nothing.
b) It's NOT worth nothing.
c) It ain't wort' nuttin'.
You can see that a) is a simple negative and b) is a CHINESE style
double
negative, but c) is a FRENCH double negative.
Now, if we go any further (e.g. the kinds of triple and quadruple
negatives
you get in something like "Nothin' ain't worth nothin' hon if it ain't
free") then we see that natural language (in numbers of negators
over two
and even just with two negators) tends to use negation as an adverbial
intensifier and not really as a mathematical or logical operator.
Language is what it is because it does what it does. There is an
expansion
of the Arab proverb which I well remember from my days on the
street in
Algeria: "Me against my brother, me and my brother against my
cousin, and
me, by brother and my cousin against you, you kafir (Kabyle, Jew,
communist,
Tunisian, etc.)!"
You can see that here the negation of the negation actually creates
HIGHER
forms of solidarity rather than simply reversing the lower forms.
You can
also see that none of them are particularly high. One can actually
begin to
sympathize with Wolff-Michael's assertion, that Derek Melser claims
not to
be able to see, to the effect that labor movements create
solidarity by
fencing out rather than fencing in.
(I think what Wolff-Michael denies by this assertion is precisely
that the
working class has historic tasks that are capable of uniting all the
oppressed and fencing out precisely those who might open the gates
to the
oppressors. This is a fairly common form of denial, particularly among
academics, who are not always that careful about closing the
political fence
gate after themselves.)
In order to get to the idea of negation as a reversible operator
rather
than negation as an adverbial intensifier, we need a refined, more
abstract,
more scientific model. This is why linguistic models really will
muddle up
our mathematical understandings at some point, Mike, though I agree
that
they are "bonnes a penser" at lower levels (and of course I am a
hopeless
slave of language in the way I think about mathematics myself).
You know the hoary old linguist's joke about negation (and if you
don't I
retell it mercilessly in my "Commentary" in the current MCA). A
linguistics
professor explaining negation to a sleepy room of undergraduates:
"A double
negation is a negation in French, but it's an affirmation in
English. This
makes us rather doubtful of Chomsky's claim that language is based on
cognitive universals. However," he continued brightly, "there is no
known
language in which a double affirmation is a negation!"
"Yeah," said someone in the back of the room. "Right."
David Kellogg
Seoul National University of Education