| THE ROLE OF SIMILARITY IN CONCEPT FORMATION |
Peter Gärdenfors
Lund University Cognitive Science
Kungshuset
S-222 22 Lund, Sweden
Telephone and fax: +46-46-2224817
e-mail:
Peter.Gardenfors@fil.lu.se
http:
//lucs.fil.lu.se/Staff/Peter.Gardenfors/
One of the most fundamental notions in the study of concept formation is that of similarity. In essence, concepts group together things which are similar. However, the notion of similarity is also central for many other aspects of cognition like learning, memory and perceptual organization. One may go as far as claiming that representation is representation of similarities. In other words, representations need no be similar to the objects they represents - what is important is that the representations preseve the similarity relations between the objects they represent. In this lecture, I will focus on the question of what role similarity plays in concept formation and categorization. The ultimate goal of the work is to show how a theory of similarity can be used to explain why people and animals form the kind of concepts that they do.
Goodman (1972) challenges the very meaningfulness of the notion of similarity. The main point of Goodman's argument is that there is nothing like overall similarity that can be universally measured, but we always have to say in what respects two things are similar. Similarity judgments will thus become crucially dependent on the context in which they occur. My interpretation of this point is that the degree of similarity between two things must always be determined relative to a particular domain (or dimension) Things are similar with respect to color or with respect to size, or with respect to any other domain, but they are not similar tout court. In my work on conceptual spaces I have developed a theory of domains that is useful here. For many basic concepts, perceptual domains are more prominent than others. However, even for more advanced concepts the perceptually grounded similarity can be transferred to abstract domains by metaphoric mappings.
A fundamental question concerning similarity that is often neglected is: What kind of quantity is similarity? Among the few who address the question, one can distinguish three major positions:
- Realism: Similarity is something that exists objectively in the world, independently of any perceptual or other cognitive processes.
- Conceptualism, empirical entity: Similarity is a cognitive magnitude that can be measured directly in subjects.
- Conceptualism, theoretical entity: Similarity is a cognitive magnitude that is used as a theoretical entity in models of categorization, concept formation etc. On this view, similarity cannot be measured directly, but only determined by applying a theoretical model.
The position adopted here is that similarity is best understood as a theoretical entity used in cognitive models. According to position 3, any measurement of similarity, direct or indirect, will be based on some assumptions concerning the properties of a similarity relation. Such assumptions come from a, more or less explicit, theoretical model. The cognitive models that are studied are based on conceptual spaces. It will be assumed that similarity can be modelled by using the distance measures in the conceptual spaces. In order words, I will assume that similarity is a function of distance (and possibly some other factors) in a conceptual space.
On the approach taken here, similarity and distances in conceptual spaces are intimately connected. There is, however, an contrary view of the relationship between concepts and similarity. I will argue that seeing properties and concepts as more primitive than similarity leads to severe problems. A fundamental task for such an approach is to determine exactly what could count as a property. The problem is pressing because given only a moderate generosity, any two objects can be shown to share an infinite number of properties. If it is the number of shared properties that determines the similarity of objects, then any two objects will be arbitrarily similar. In order to avoid this quandrum, one must be extremely careful in defining which properties to allow in a comparison and which to exclude. I know of no theory of properties that furnishes a satisfactory solution to this problem. Consequently, I see no way of defining similarity in terms of the number of shared properties.
The assumption that similarity can be modelled by using distances in conceptual spaces has been heavily criticized by Tversky and his collaborators. Since this is a crucial assumption for my theory, I must consider the criticism. The symmetry assumption has been the main focus of Tversky's attack against spatial models of similarity. As an alternative to spatial models of similarity, Tversky proposed a set-theoretic model based on property matching or feature matching which can account for the violations of the distance axioms. However, such a model is open to the criticism above, since it assumes that similarity can be defined in terms of shared properties.
It seems to me that the experimental results can be better explained by instead considering the cognitive process underlying the similarity judgments. The prominence of different dimensions play an important role. For example, when Tel Aviv is compared to New York, other dimensions will be prominent than when New York is compared to Tel Aviv. The different dimensions and their weighting in a comparison are determined by considering the properties of the domain that is in focus of the comparison and the conceptual space is "stretched" along the prominent dimensions of the comparison.
e-mail: hmp@ipvvis.unipv.it