[Martin Taylor 960927 13:15]
Bill Powers (960927.0945 MDT)
The problem is in where to apply the "not" to a statement that refers to
more than one thing. Does "not seeing X" mean (not seeing) X, or seeing
(Not-X)? In the first case, not-seeing can be accomplished by not looking,
whether or not X is present. In the second case, you are looking and seeing
that X is not there (or that something else is where X would be if it were
present).
Yes, that's an aspect of the problem. "Not" is a word very strangely used
in English. We usually apply it to the verb in a clause, regardless of
whether it is the relationship implied by the verb that is negated, or
one of the arguments of the relationship. That's the aspect you are
addressing.
An example I have often used is "John did not give Mary the book."
What happened? Nothing? (As with (not seeing) X). Did John give the book
to Judy? Was it a ring that John gave to Mary? Did John sell Mary the book?
Was it Bob who gave Mary the book? Why don't we say "John gave the not-book
to Mary" when that's what is meant?
It's that "not-book" aspect that I want to question. In the case of the
fly-eating frog that induced me to ask the question, it was proposed that
the frog had a reference for not-seeing flies. Is that the same as a
reference level of zero for number of flies seen? If so, what happens
when a fly goes by just outside the reach of the tongue? What is the
perception of "not-fly"? Is it the same as not the perception of "fly"?
Is the anti-goal of "not seeing a fly" achieved through a positive
feedback system with a perceptual signal whose value is number of flies
seen and a reference level of many flies, or through a negative feedback
system with a reference level of zero flies? Those are quite different
kinds of mechanism, and it seems to me that perceptual control of a
perception of not-X can quite generally be achieved by a positive
feedback loop with a non-zero reference value for X. It matters not
what you perceive, so long as it is far from X. And that's quite different
from having a specific value (zero) for a reference for X.
This may be easier to see in a specific case. Suppose that the 1200 block
of X street has a very bad reputation. I don't want to perceive myself
in that block, but the 200 block and the 2200 block are both acceptable
places to be. I have a reference to perceive "not 1200" in the street
numbers. I don't have a reference to perceive 200, or a reference to
perceive 2200. It looks to me as if I would have a positive feedback
system with a reference value of 1200 for the perception of street number,
which would cause me to get-the-hell-out if I found myself in that
neighbourhood.
In my argument to which I referred, I claim that a belief in "not-X" (where
X is a proposition to which a truth value could be assigned) is different
from not-a-belief in "X". This is in a communicative context, where sometimes
the issue may be to determine what _is_ the case, and sometimes it is to
be assured that X is not the case. If John did not give Mary the book, it
may not matter which of the alternative possibilities is true--John is not
liable for any damages that might arise had he in fact given her the book.
But then again it might matter, and have greatly different consequences
if John sold Mary the book, rather than Bob having given it to her.
In logic, there is no difference between believing not-X and disbelieving X.
In communication, there is--or so it seems to me.
Does "not seeing X" mean (not seeing) X, or seeing (Not-X)?
That's the kind of issue, and, like you, I claim they are very different,
though the possibilities of the first include the second.
Martin