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Some Pseudo-Philosophical Notes

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]

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.