Sunday, March 06, 2005

Concepts IV: A Second Revolution1

In the first three posts on concepts (here, here, and here), I talked about the three types of theories that have dominated cognitive science for the last several decades. First there was the classical (or definitional) theory, which cognitive scientists inhereted from the ancient Greeks. Then there were the similarity-based theories, the most prominent of which were the prototype and exemplar theories. Recently, there has been somewhat of a revolution in the cognitive scientific study of concepts, and these theories have begun to lose their monopolistic grip on the minds of concept researchers. To understand why things are changing, we first have to understand some of the things that these three ostensibly different theories have in common, other than the fact that they are all seriously flawed in some way. Here's a list of some important and, for many, troublesome commonalities.
  1. Concepts are natural kinds. In fact, they are of one kind. The first assumption is important, because it means that concepts can be studied like any other natural kind, using the empirical methods of science. The second means that we can use the same model to describe all concepts (perhaps tweaking some of the parameters in different contexts). Thus, all concepts are definitions, or prototypes, or collections of individual exemplars.
  2. For reasons that may have more to do with the culture of science than any practical or empirical considerations, in the study of concepts, the focus of both the emipirical research and the theories themselves has been almost exclusively directed at classification. Theories are designed to explain how people classify instances as members of concepts, and experiments use classification tasks to test the theories. Theories about how concepts are represented are designed, implicitly or explicitly, to allow the theories to explain how instances are classified.
  3. Concepts are represented by collections of features. The dominant view of reference in concept research is this: concepts carve the world at its featural joints. Whether these features are represented as necessary and sufficient, or as the dimensions of a multi-dimensional space, they tend to be the only information that is explicitly represented in concepts. Any other information is implicit in the representation of the features themselves.
  4. Concepts are amodal. That is, they can be represented digitally (e.g., in a big-ass matrix that represents a multi-dimensional space), without considering the fact that they are represented in an embodied mind.
What if concepts aren't of one kind, but of multiple kinds? What if classification is not the primary use of concepts, or if other uses significantly influence how they are learned and represented? What if features play a secondary role in many concepts, with relational information being more central? What if concept learning and representation is dependent on the embodied or situated nature of the mind? Changing views of how to answer these questions have led many researchers to approach concepts from directions that are not compatible with the three types of theories I have described so far. In fact, there has been a sort of revolution in the study of concepts, and new theories differ from the classical, prototype, and exemplar theories in that they do not have at least one of the four assumptions above. In this post, I'll describe one type of theory, derived from the "theory theory," which, to some degree, get rid of the first three assumptions.

The "theory theory" of concepts began with an incredibly insightful but intuse paper by Greg Murphy and Doug Medin (M&M), titled "The Role of Theories in Conceptual Coherence."2. Given the influence and insight of this paper, it could deserve a place on the list of the hundred most influential works in cognitive science, were it not for the fact that it has been so difficult to figure out exactly what to do with it. For the most part, the paper, written in 1985, and cited at least 300 times (that was the count a couple years ago), there was virtually no empirical research designed to test its claims until the 2000s. The reason is that it's not really clear what its claims are. The goal of the paper is to show that current theories of categories (i.e., exemplarand prototype theories, along with their hybrid rule-based cousins) can't explain one of the most important aspect of concepts: their coherence. The paper begins with a Biblical example, to present the problem of coherence. M&M write:
A somewhat unusual, but nontheless usefrul example, arises from an old puzzle of biblical scholarship, the dietary rules associated with the abominations of Leviticus, which produce the categories clean animals and unclean animals. Why should camels, ostriches, crocodiles, mice, sharks, and eels be declared unclean, whereas gazelles, frogs, most fish, grasshoppers, and some locusts be clean? What could chameleons, moles, and crocodiles have in common that they should be listed together? That is, what is there about clean and unclean animals that makes these categories sensible or coherent? (p. 289, emphasis in original)
They then argue that it is the fact that the current theories are similarity-based that makes it impossible for them to account for conceptual coherence. Adding:
These approaches are inadequate, in part, because they fail to represent intra- and inter-concept relations andmore general world knowledge. (p. 289)
To address this inadequacy, M&M propose that concepts are interwtined with our theoretical knowledge of how the world works, and that concept-representations are, at least in part, determined by that knowledge3. Thus, this theory differs from its predecessors in important ways. It is not similarity-based, it allows for many different kinds of concepts (they're all based in our knowledge of the world, but different concepts can have very different structures or kinds of representations), the focus is on representational coherence rather that classification, and features fall out of concept-representations embedded in theories, rather than composing them. For M&M, the structure and coherence of a conceptual representation comes both from within the concept itself, in the form features and the relations (causal, thematic, etc.) between them, and from outside the concept, in the general world knowledge within which the concept is embedded.

But what does all of this really mean for concept research? Does it mean that concept representations look like theories? For one, it seems to take us backwards, rather than forwards, in that theories likely specify necessary and sufficient conditions, or at least lead us to believe that they exist. This is actually a benefit, in this case, however, because people actually do believe that concepts have essences, or definitions, though the representational place-holders for these essences tend to be pretty devoid of content4. But what else does it mean? Are concepts represented as theories? But aren't theories composed of concepts? How, then, are theories represented? In the end, M&M give us only a vague answer to the problem of coherence, which serves more as a road sign pointing us down the road that leads away from similarity than as a destination. More questions are raised than answered.

For nearly 15 years after the publication of "The Role of Theories in Conceptual Coherence," people cited it, often enthusiastically, but were unable to really provide any empirical investigation, or even operational characterization, of the theory that it seemed to contain. Fifteen years in the life of a science in its infancy, or of any science in the age of specialization, is a lifetime. Most theories don't make it that far, at least not in a form that is recognizable given their initial characterizations. Yet, the theory theory was thriving despite no real characterization. The bulk of the early work on the theory theory was designed to show that background knowledge plays a role in categorization and concept formation. While this work was very interesting and important, it was not impcompatible with similarity-based (particularly prototype) theories.

There were some early attempts, particularly by Alison Gopnik and her colleagues, to make the theory theory itself more coherent. She treated everyday knowledge as theory-like, composed of our folk theories of various domains. Concepts, then, embodied the causal knowledge contained in those folk theories5. Kinds, of which concepts are the representations, are for us defined by their causal relations.Gopnik has argued that this take on the theory theory provides a very nice explanation for early naming and cancept development. In essence, children learn concepts and their names, at least those that refer to kinds, by developing and revising theor folk theoretical knowledge of the world, and thus developing more and more sophisticated knowledge about the types of causal relations in which particular kinds can participate.

This characterization was made even more viable by recent work on causal reasoning, particularly that by Woo-Kyoung Ahn, in which it has been shown that causal reasoning itself involves a top-down process in which theoretical knowledge about kinds determines our characterization of causal relationships6. This work, in turn, has led to what is perhaps the most sophisticated formulation of the theory theory, the causal-model theory. Under this theory
Knowledge of causal relationships between category features is represented in terms of asymmetric and probabilistic causal mechanisms... [and] objects are classified as category members to the extent they are likely to have been generated or produced by those mechanisms.7 (p. 709)
In other words, concept membership is not determined by overall similarity to a representation, but by adherence to theoretically-derived causal knowledge. In fact, similarity and typicality themselves are determined by causal knowledge. This version of the theory theory allows us to connect concepts and categorization to our broader knowledge of memory, reasoning, and folk knowledge, by making concepts schematic, and thus composed of both features and the (mostly causal) relations between those features.

As evidence for the causal-model theory, Bob Rehder, who has developed the causal-model theory, cites research demonstrating that causal knowledge influences how typical members of a category are8, that violations of category knowledge make instances less likely to be classified as members of a category9, and that coherence built around causal knowledge makes individuals better members of categories10. What's more, with this version of the theory theory, Rehder has been able to test it empirically! To do so, he presented participants with exemplars that either contained the sorts of feature co-occurence relationships that participants' causal knowledge would predict, or did not contain these co-occurence relationships. Participants rated those that did as better members of categories. Rehder then showed that a formal version of the causal-model theory fit the data better than similarity-based models. The causal-model theory looks something like this (From Rehder, 2003):
P(A|E) = LA(E)/[LA(E) + LB(E)]
In this equation, the probability (P) of classifying an instance as a member of category A given the presence of property E is a function of the likelihood (determined through a Bayesian probability calculation) of the presence of E given the causal model of concept A (LA(E)), divided by the likelihood of E given that causal-model and the likelihood of E given an the causal model of an alternative classification, concept B (LB(E)). Thus, the probability of classifying an instance as a member of a concept is determined by the chance that its features are predicted by the our causal knowledge embodied in that concept and the chance that its features are predicted by our causal knowledge embodied in alternative concepts. This model thus captures all of the important features that we ant out of a theory of concepts: it handles typicality, by measuring the extent to which exemplars contain the features predicted by causal relations, the interrelations between features, and the interrelations between concepts, including the role of context in classification. Furthermore, because it is not only focused on classification, it allows us to describe other important aspects of concepts, such as their formation and use in non-classification tasks (e.g., inference).

There is another benefit of the theory theory, which has recently begun to receive the attention of researchers. As some in both philosophy and psychology have recently noted, concepts may not be of a single kind. However, similarity-based theories have always treated them as of a single kind, and have thus been forced to focus almost exclusively on noun or object concepts. It may be that concepts differ in their structural properties, how they are processed, or, given the theory theory, in the types of causal theories that influence their content. Thus, concepts from different domains may be entirely different kinds of things. It would do not good, then, to try to develop a general theory of how concepts are represented, processed, used, and learned.

With this in mind, researchers have begun to develop theories about kinds of concepts that deviate, in certain ways, from the noun or object concepts that have been studied by adherents of the similarity-based views. One interesting example of a proposed kind of concept is the role-governed category11. These concepts also embody our theoretical knowledge of the world, but instead of doing so through the representation of causal relations, they do so in the form of the roles (causal or otherwise) in which the concepts can participate. Motivated by the insights of theory theory, as well as those of Wittgenstein, Markman and Stilwell (2001) argue that some concepts are defined (yes, defined) by their roles in the larger relational systems that compose our general or theoretical knowledge of the world. Take an oversimplified example, from the M&S paper, that of GAME (used, presumably, because of its discussion by Wittgenstein). According to them, GAME cannot be defined by a set of features, and is thus not a feature-based concept like those discussed by the similarity-based models. Instead, it is defined by its role in the relation PLAYS(X,Y), where X is the PLAYER (defined by its role in the relation) and Y is the GAME. This concept is contrasted with another, which has a similar structure, but participates in a different relation, namely JOB, which is defined by its role in the relation WORK. This theory also requires the creation of a third type of concept, relational concepts, which are usually represented by verbs (e.g., PLAY and WORK). Thus, using a theory theory approach to concepts, we can develop at least two potential new types of concepts, which differ in their content and structure from traditional object concepts.

So far, the theory theory looks like a very promising alternative to similarity-based approaches, but because serious research on versions of it has only recently begun, it's too early to tell how well it will fair. As the discussions of the classical, prototype, and exemplar theories of concepts has shown, once you develop a theory of concepts, concepts will come around behind you and bite you in your theoretical ass. New problems will inevitably arise. However, I think it's safe to say that any subsequent theory of concepts will have to take seriously the findings that background knowledge, particularly causal knowledge and folk theoretical knowledge in general, play an important role in our learning, representation, and use of concepts. For this reason, we will not be able to focus exclusively on features in concept representations, or on classification in our tests of theories. We may also have to abandon for good the belief that concepts can be characterized as a single kind of thing.

In the next post, I'll talk about another theory, born of neuroscientific research, which posits types of concepts. After that, I'll try to get into some modal theories of concepts. Then maybe I can leave concepts alone for a while.

1In the interest of full disclosure, I should say that I am an adherent of the theory theory described in this post, that I have written about it, and find it generally superior to all of the previous theories I have described. I will try to be fair in describing it, but it won't be easy.
2 Murphy, G., & Medin, D. (1985). The role of theories in conceptual coherence. Psychological Review, 92(3), 289-316.
3 This may remind the philosophers in the audience of Quine's paper "Natural Kinds," in which he argues that primitive concept-representations (those of primitive societies and children) are similarity-based, but more advanced (modern and adult) concepts are parts of theoretical systems, such as those of the sciences.
4 Medin, D., & Ortony, A. (1989). Psychological essentialism. Similarity and Analogical Reasoning. S. Vosniadou & A. Ortony (eds.), Cambridge University Press: New York, pp. 179-195.
5 See e.g., Gopnik, A. & Wellman, H.M. (1994). The theory theory. In L.A. Hirschfeld and S.A. Gelman (eds.), Mapping the mind: domain specificity in cognition and culture. New York: Cambridge University Press, pp. 257-293; and Gopnik, A., & Nazzi, T. (2003). Words, kinds and causal powers: A theory theory perspective on early naming and categorization. In D. Rakison, & L. Oakes (eds.) Early Categorization. Oxford: Oxford University Press.
6 Ahn, W. & Kalish, C.W. (2000). The role of mechanism beliefs in causal reasoning. In F.C. Keil & R.A. Wilson (eds.) Explanation and Cognition, MIT Press, pp. 199-225.
7 Rehder, B. (2003). Categorization as causal reasoning. Cognitive Science, 27, 709-748.
8 Malt, B. C., & Smith, E. E. (1984). Correlated properties in natural categories. Journal of Verbal Learning and Verbal Behavior, 23, 250–269.
9 Rehder, B. (2003). A causal-model theory of conceptual representation and categorization. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 1141-59.
10 Rehder, B., & Ross, B. H. (2001). Abstract coherent categories. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27, 1261–1275, and Wisniewski, E. J. (1995). Prior knowledge and functionally relevant features in concept learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21, 449–468.
11 Markman, A.B., & Stilwell, C.H. (2001). Role-governed categories.
Journal of Experimental and Theoretical Artificial Intelligence, 13(4), 329-358.

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