[From Bill Powers (931023.0930 MDT)]
Martin Taylor (931022.1840) --
It seems to me that you argue against yourself. Take the last
point first. If there exists a category-level PIF that answers
yeah or nay to "tying a bow knot", and another that answers to
"eating an ice-cream cone," neither should have any influence
on the other, and the perceptual output of one should not be
expected to be related to the perceptual output of the other.
Logically, you're right. I hope I'm not arguing against myself --
how could I tell if I lost the argument? A logic-level conflict
is a self-contradiction, isn't it?
So far, what you paraphrase above is what I meant to say: at the
category level, perception of different categories is
independent.
Only at some logic level to which these feed might there be a
relationship that enforced an exclusive-or. The facts of the
world might mean that both were never 1 at the same time, but
nothing at the category level would be expected to do so. In
terms of the linguistic discussion that started this thread,
there is no "contrast" between these two categories.
Yes. Only at the logic level could the exclusive-or rule be
imposed, although it might exist because of properties of the
world (a fact unappreciated at the category level).
Now let's go backwards in your posting. It is true that
anything that is not within a category boundary is outside it.
Only from the standpoint of the logic level. At the category
level, either a category is present or it's not. From within any
one category-perceiver, nothing is known about what is "outside"
the category. To speak of "anything that is ..." is to posit a
thing which can be in one "place" or another, but which has
continued existence independently of its place. That implies a
point of view from which it can be seen wherever it is. That has
to be a level higher than the category level.
But what if there are no rulers being perceived?
Then no PIF for "ruler" category will be giving any output, and
presumably the logic level that is testing this relationship
will be cut off in some way (we haven't discussed the
mechanisms of logic levels yet, so I don't think I am begging
the question).
The logic level won't be cut off, because both presence and
absence of a signal are signals (i.e., have specific perceptual
consequences) at the logic level. At the logic level, an element
of a learned perception is a place-holder, a variable with a
single persistent identity and only two possible magnitudes, both
meaningful. This could lead to contradictions: that is, a
category signal indicating x >= y and another independent
category signal indicating x < y could both be zero. If the logic
level is set up to perceive _both_ conditions separately, it
would then (or could -- there is no standard structure of logic
at the logic level and we can miss seeing paradoxes) detect a
logically impossible condition. However, that could be converted
to a proposition, "it is not the case that (x >= y AND x < y)."
This proposition would then simply take on the value FALSE.
Problems of this sort, I believe, are typically handled by
including the necessary premises as explicit conditions: "IF
there are two rulers of fixed length ...". If there are not two
rulers, or they are not of fixed length, then "it is not the case
that (x >= y AND x < y)" is just irrelevant because the IF clause
is false.
I think you are confusing an outsider's view of "A vs not-A,"
which defines the location of the boundary of the category's
acceptance region in the space of its inputs, with the category
PIF's "view," which is that it provides a significant output
when it has appropriate input and not otherwise.
In your discussion, you're trying to argue me into the point of
view that I already have. It must feel good to be on the giving
end for a change.
It's that outsider's view that I am arguing against; actually, a
view from the logic level that imputes logical properties to
category perceptions.
What I'm arguing against is the idea that a category splits the
universe of existent things into two parts, the category and its
complement. At the category level of perception, that is not
true. If one had no logic level, it would not even seem to be
true. Categories would simply be present or not present, quite
independently of each other. Categories which are logically
contradictory -- chair and person -- could coexist at the
category level, where it is not true that a thing cannot be both
a chair and a person (which is a not-chair). Only at the logic
level do we think of a "thing" that is existent regardless of its
truth-value, so that it exists just as much in its absence as in
its presence. The very concept of a variable originates at the
logic level (which I am probably misnaming, but you get the
idea). Only at the logic level could we say "let x = 0" and still
have a perception of x to manipulate. If we say "Let John = 0" at
the category level, then there is simply no John. There isn't any
not-John. There isn't any "person" variable which must be either
John or not-John.
... the question is ill-posed, because it presumes that there
must always be a positive category (and seems to presume that
there is always exactly one).
Yes, exactly. That is what I mean by "existent." I think that
many discussions of categories (that I have seen) involve ill-
posed questions that confuse the logic level with the category
level. Much of what is said about categories is said from the
logic level, which means that the discussion _reveals_ the
operation of logical processes, while _imputing_ them to the
categorization process. For example,
It is true that anything that is not within a category boundary
is outside it.
All this helps, I think, in clarifying what the category level
must do, as well as helping to distinguish it from the logic
level which manipulates signals standing for categories. At the
logic level, the place where those signals come in creates
variables, which continue to exist in thought even when the value
of the signal is 0. So this helps us toward understanding some
philosophical problems, like the quality of existence of
imaginary creatures. If you create a category perceiver called a
"unicorn detector", it will never provide a signal except through
imagination or art -- yet it can be reasoned about even if there
is no category signal. You can conclude "there are no unicorns,"
simultaneously accepting existence of a variable called "unicorn"
and asserting that its value is zero.
We do get led into some interesting byways, don't we?
···
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Note to Bruce Nevin
I said that phonemes don't have to be categories. However, it
occurs to me that when we TALK about phonemes, assigning symbols
to them, we make categories of them for purposes of linguistic
discussions. The actual process of word-event recognition,
however, doesn't have to involve categories.
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Best to all,
Bill P.