[From Rick Marken (931022.1000)]
I have been having a little off-line discussion with Martin
about categories. He said I could bring it back to the net
so I am posting Martin's most recent comments and my most
recent reply. I hope we can keep this on the net from now on
(if there is a "from now on" for this topic).
···
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Martin Taylor to Rick Marken (cc to Bill Powers):
I think our apparent disagreement has been largely over the use of
particular words, rather than about the underlying concepts (though
see my response to Bill's provocative posting of yesterday).
The way I've been using the term, "category" is something that occurs
within the hierarchy. Discreteness is the primary issue, though Bill's
long posting of yesterday (to which I responded publicly) makes me see
that I may have overemphasized the notion of a binary value of the perception.
The "category" perception is something I think we all agree, perhaps
with slightly different connotations, exists in the hierarchy.
As I see you using the term, categorization is equivalent to a reduction
in measure. If more than one set of input values to a function results
in the same output value, then that function categorizes. I would prefer
to say that an outside observer can categorize the inputs to the function,
using his/her category-level perception. The perceptual function itself
doesn't categorize unless it IS a category-level function. In most of
the lower-level cases you have brought up, all that the perceptual function
does is to reduce to one the dimensionality of its input. It measures
(in my terms) the amount of its input along the single dimension that
the function defines. I (outside observer) can categorize that measure
by giving a number to it, a number that would be different if the measure
changed by some finite amount greater than epsilon, but not for lesser
changes in the measure.
I hope that describes the effects we are talking about. What remains, if so,
is the words we use. I like the term "category" for the perceptual level
that divides the world into discrete aspects that can be used in logical
and linguistic operations, and I like the term "measure" or "evaluation"
or simply "function" for the effect that happens at every perceptual level
(including category). But I'm not fixated on terminology. The important
thing is to have our discussions be about concepts, and not to wast net
bandwidth when it is only words that are at issue.
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Marken to Martin Taylor (cc to Bill Powers):
As I see you using the term, categorization is equivalent to a reduction
in measure. If more than one set of input values to a function results
in the same output value, then that function categorizes.
Yep.
I would prefer
to say that an outside observer can categorize the inputs to the
function, using his/her category-level perception.
If that's your preference.
The perceptual function itself doesn't categorize unless it IS a
category-level function.
And how do we know that it is a category level function? What is the
difference between a category level function and other perceptual
functions?
In most of
the lower-level cases you have brought up, all that the perceptual function
does is to reduce to one the dimensionality of its input.
All perceptual functions reduce the dimensionality of the input --
to ONE dimension. This would also be true of category level
perceptual functions as well.
It measures
(in my terms) the amount of its input along the single dimension that
the function defines. I (outside observer) can categorize that measure
by giving a number to it, a number that would be different if the measure
changed by some finite amount greater than epsilon, but not for lesser
changes in the measure.
It seems to me that you are saying that categorization involves
discretizing a perceptual signal. And that such a discretized
signal IS a category perception. I think this view misses an
important aspect of the PCT model, viz. the notion that The
SEMANTICS OF PERCEPTION (whether what we experience is a sensation,
transition, configuration, principle OR category) are determined
by the nature of PERCEPTUAL FUNCTIONS, NOT BY THE NATURE OF
PERCEPTUAL SIGNALS.
Maybe you mean that the a category perception is always the result
of a perceptual function that produces a non analog output. This
is a little better, but, still, I think, inadequate. Other, non-
category type perceptual functions could produce discrete (categorical
in your sense) output. It's not the nature of the OUTPUT of the
perceptual function (discrete, analog, time coded, whatever) that
determines what is perceived -- it is the nature of the function
itself. The problem to be answered in this discussion (from the
perspective of the PCT model) is "what is the nature of the
function that produces the perceptual signal that corresponds to
the experience that we (well, Bill) calls "category". This
question can only be answered by research -- as I said, testing
to see what variables are controlled when people control for "category"
or "class membership" or whatever you want to call it -- and modelling.
So if you want to continue thinking of categories as discrete
perceptual signals, that's fine. The only problem with doing
so, I think, is that it keeps you from being able to formulate
any useful research questions (or models, for that matter).
I hope that describes the effects we are talking about.
Obviously, I don't think so.
I like the term "category" for the perceptual level
that divides the world into discrete aspects that can be
used in logical and linguistic operations
That's fine; but this perception must be defined by the possibly
discrete results of a perceptual FUNCTION, not as the result of
simply discretizing a perceptual signal.
Why am I having a tremendous sense of deja vue. Didn't we already
go through this?
Best
Rick