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The discrete symbolic nature of both logic and natural language (at least in its surface manifestations) has led many to propose discrete semantic models, as described above. If the referents of symbols or words are taken to be in the world, this leads to incompatibilities between the models and how we perceive reality to be. These incompatibilities are reflected in philosophical problems like the question of indiscernibles: ``At sunset, where does the sky change from orange to yellow, yellow to ... to blue, blue to dark?''. Only if one assumes that color is a discrete-valued object property would one expect it to change abruptly from one value to another at a particular place. If one assumes that color is a continuous-valued perceptual property, the question becomes ill-posed.
Another pervasive assumption in the domain of color is that color is a
property of objects in the world, and our visual system perceives that
property. In logical models, this would typically be represented as a
predicate, so that, e.g., is taken to mean that object
has the
property of being red, and in formal semantic models these predicates would
map into sets of red objects. As I discussed in
Section
, color is not a property of objects but a
response of the visual system to certain physical stimuli, and this
response is only indirectly related to certain object properties and can
vary in space and time with unchanging objects. In the semantic model I
propose, a term like ``red'' maps into a region of the perceptual color
space; i.e., redness is a perceptual phenomenon, not a phenomenon in the
outside world. It is then easy to see that a question like ``What is the
color of the sky at night?'' is ill-posed as well. The sky does not have
any color, either during the day or at night.
In logical and philosophical writings on semantics, one often runs into
strange denizens like unicorns and round squares, and these poor creatures
are habitually blamed for the existence of possible worlds, accessibility
relations, objects of thought, and the like. The seldom explicated
assumption underlying all this is that since the words exist and we can
use them in thought or natural language, they must refer to some object
somewhere. But where could unicorns and round squares live, other than in
possible worlds or as mere objects of thought? The assumptions of
traditional model theory, as described above, force one into accepting the
strangest things. I believe we should abandon or review those assumptions,
rather than force the universe to conform to them. Along the lines of what
[Harnad 1990] and others have proposed, I believe that meaning
derives from perception and interaction with the real world, not from
possible worlds or objects of thought. In order to understand what a unicorn
is, we first have to know what horses and horns are. If we want to ponder
round squares, we'll have to know what circles and squares are first. Such
knowledge comes from perception and interaction with the world, and we can
consider the corresponding symbols or words to be ``directly grounded''.
Other symbols or words, like abstracta or ``impossible'' objects, which we
can consider to be ``indirectly grounded'', can only be meaningful by
virtue of being related to directly grounded ones in a systematic way, and
don't have to refer to strange creatures in hypothetical modes of
existence. I therefore consider the most urgent task of KRR to be to
investigate how symbols can be directly grounded in perception and
interaction; we can worry about indirectly grounded ones later. We have to
learn how to crawl before learning how to walk.
The work on color perception and color naming presented in this dissertation is an investigation into the grounding of just a small set of terms, and already the complexities are considerable. Under those circumstances, it is useless to worry about unicorns and round squares, or general purpose KRR and natural language processing, in my opinion. Or as [G. Edelman 1992] puts it while discussing Lakoff's cognitive grammar:
The important thing to grasp is that idealized cognitive models involve conceptual embodiment and that conceptual embodiment occurs through bodily activities prior to language. [p. 246, italics in original]I believe this is essentially true, and in order to arrive at true language competence for an artificial agent, it will have to go through at least some prior stages of conceptual embodiment first.
My work may also shed some light on the empiricism vs. innateness debate
in cognitive science (whether ``primitive'' concepts or meanings are
acquired through experience or inborn), with respect to the origin of
``primitive'' concepts. In my model, (color) concepts are grounded in the
perception of the world, rather than in the world itself, but
perception is causally connected to the world. The mechanisms for
abstracting perceptual data into categories, in our case the
neurophysiology of color vision, are to a considerable extent genetically
determined, i.e. ``innate''. That does not mean that a child is born with
complete color concepts, waiting to be ``activated'' by interaction with
the world, except in a very abstract sense. Since the basic mechanism (the
neuro-anatomy and physiology) is innate, any normal child will develop
the same or comparable color concepts (categories) when interacting with
the same kind of environment (which may include cultural and linguistic
factors). But no matter how innate the basic mechanism is, no concepts
(categories) will actually develop without external stimuli. Also,
different physiology leads to different ``innate'' concepts, so one might
consider cats, for instance, to have different color concepts than we do,
while they live in approximately the same environment, something which
would be hard to explain from a purely empiricist point of view. We can
regard the innate vs. empiricist position as duals; both are right in some
respect, but both also miss a part of the picture as a result of
methodological dogmatism. To caricature the respective positions, one might
say that empiricists have overlooked the fact that human physiology is just
as much part of the world as trees and stones are, and it may (and in fact
does) influence concept formation, too. Nativists, on the other hand, have
failed to recognize that interaction with the world is a prerequisite for
any concept formation at all, and that there is a systematic correspondence
between some properties of the world and some properties of categories,
albeit mediated (and perhaps transformed) by perception.