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Semantics, Grounding, and Truth

Meaning derives from embodiment and function, understanding arises when concepts are meaningful in this sense and truth is considered to arise when the understanding of a statement fits one's understanding of a situation closely enough for one's own purposes. Thus, there is no absolute truth or God's-eye view. Our view of what exists (metaphysics) is not independent of how we know it (epistemology). [G. Edelman 1992][p. 250]

We now return to the subject of Chapter , discussing some of these issues in the light of the model of color perception and color naming we have presented.

I consider the model of color perception and color naming as presented in this dissertation to be a true referential semantic model in the domain of (basic) color names. It is true in the sense that it is well-defined and computable, and enables certain behaviors that require a semantic model to bridge the gap between the external world and internal symbols, and referential in the sense that it expresses the meaning of color terms in terms of a mapping to/from another domain. The referents of the color terms are not directly objects or properties in the world, however, but certain areas in an internally represented color space. But the color space itself is causally connected to the outside world, which I consider a necessary property for any referential semantic model, or at least for the models that constitute the ``direct grounding'' for some set of terms. Other terms may derive their meaning from being systematically related to directly grounded ones, but without such a core set of directly grounded terms, I believe no meaning or understanding is possible. To put it succinctly: no amount of semantics will ever allow a robot to relate its internal symbols to its environment without some set of directly grounded terms. The algorithm for determining compound color names as presented in Section may be regarded as a primitive compositional semantic characterization of such terms, which are indirectly grounded in the meanings of (characteristic functions of) the set of basic color terms. I therefore do not agree with an extreme solipsistic view of semantics that would hold that the world is permanently ``out of reach'' of cognition, and that it therefore does not matter how we choose to characterize the meanings of concepts, as long as this characterization is internally consistent. Meaning is a function of at least two variables: what is ``out there'', and what is ``in here''. The world and the cognitive mechanisms both have a necessary role in meaning and understanding. An agent equipped with an arm can actually reach out and touch the things out there that in its internal representation correspond to the referents of some of its internal symbols, and while one may contend that the referent of its symbols is really part of its internal representation and not part of the external world, the difference is not relevant for most practical purposes. One might consider the internal thing to be the ``direct referent'' and the external thing the ``indirect referent'', and in most cases they will be causally related. It is possible, however, to uncouple this ``alignment'' (see Appendix ) under certain circumstances, and in this case we might speak of ``being deceived by one's senses'' (as in optical illusions) or of ``perceptual defects'' (as in blindness).

A ubiquitous red herring in writings about semantics is truth. Truth, of the metaphysical God's-eye variety, has very little to do with meaning, in my opinion. The Edelman quote above expresses this sentiment quite well. The often-found Tarskian statement that ``snow is white if and only if snow is white'', where x denotes the referent of x (an object or relation over objects) is of no use if those referents are assumed to be in the world, and one is supposed to verify the metaphysical, God's-eye truthfulness of the description of the state of affairs, without the intervention of any perceptual or cognitive mechanism. The most one can say is ``I believe snow is white if and only if '', where is a point in color space corresponding to a sample of an image of something belonging to the perceptual class ``snow''. Usually, though not always, this will be the case when one has the appropriate white and cold stuff in one's field of view. It is futile to torture oneself with existential doubt as to whether what one is beholding is ``really'' snow, or merely a very good imitation of it. The duck test applies.

With our concrete model of basic color term semantics before us, it is also easy to see what makes a symbolic representation symbolic. The labels in equations are the (names of the) symbols we use for the perceptual categories that they are paired (associated) with. They carry meaning only by virtue of being associated with those categories, but there is nothing intrinsic about them that makes them mean what they mean. The association is arbitrary, and can easily be changed without changing anything fundamental about our understanding of color. A rose would look just as red by any other color name, so to speak. What is not arbitrary is the perceptual model, however, since changing any parameters in there will literally make us see the world differently. The perceptual categories might thus be considered analog or iconic in nature, as opposed to symbolic. This also sheds some light on how translation is possible. Without any perceptual underpinnings, the knowledge that ``red'' = ``rood'' does not mean much at all. While it may allow us to syntactically substitute one for the other, it would not help us much if we were to move to Flanders. But in the presence of the perceptual category, knowing that ``red'' = ``rood'' allows us to move to Flanders and understand what people mean when they talk about ``rood'' things, and pick out the referents in the world without any further learning. I contend that without a more or less common set of perceptual categories (and hence directly grounded terms), learning a foreign language would not be possible - indeed it would not be possible to understand what anyone else is talking about, and probably it would not be possible to learn any language at all.

Some related issues are brought up in [Davidoff \& Concar 1993], where the authors discuss the ``memory palette'' for colors, or the ``internal color space'' which functions as a link between the mental worlds of color vision and color language. They report that children have difficulty learning color names: red, green, yellow, and blue are learned first, in no particular order, and only when all four of these are learned can they use any of them correctly. These colors have been called ``landmark colors''. They are easy to name, form associations with, and children prefer to point to examples of them. They play a central role in learning to name other regions of the color space. Categorization is reported to be not necessarily hardwired, and to some extent alterable by experience. It can be impaired while color vision itself is intact. These findings support the two-stage model of a color space with a separate set of categorization functions defined on that space, and the ``looseness'' of the coupling between perceptual color categories and color names. Some similar views can be found in [G. Edelman 1989], who mentions research in pre-verbal concepts and complains that concepts and their names are usually tied together in computational models, which is not the case in our model of course. As will have become obvious by now, I share the view of cognition as being based in perception.

With respect to Knowledge Representation and Reasoning issues, the color model can be seen as providing the direct grounding for a set of atomic concepts (base nodes in SNePS terminology, cf. [Shapiro \& Rapaport 1987]). These may in turn take part in reasoning about color or about colored objects, but I believe that to be relevant, such reasoning must take the semantics of these terms (the perceptual model) into account, for instance in determining the meaning of compound color names based on the meanings of their constituent terms, as was hinted at in Section . In other words, meaningful reasoning requires meaningful terms. Such meaning must derive directly or indirectly from grounding through perception and action (see Appendix ), and cannot be based on imaginary worlds or descriptive semantics in manuals.