Wittgenstein's admonition “don't think, but look” has had the important effect of stimulating psychologists to reconsider their common practice of equating concept formation with the learning of simple definitional rules. In the early 1970s, psychologists like Eleanor Rosch (e.g., Rosch, 1973), responding to the difficulty of identifying necessary and sufficient conditions for membership of all kinds of categories, proposed alternative models of category representation based on clusters of correlated features related to the categories only probabilistically. Without denying the importance and impact of this changed view of concepts (reviewed, e.g., by Smith & Medin, 1981), we think that in certain respects the “don't think, but look” advice may have been taken too literally. There are problems with equating concepts with undifferentiated clusters of properties and with abandoning the idea that category membership may depend on intrinsically important, even if relatively inaccessible, features. For example, on the basis of readily accessible properties that can be seen, people presumably will not judge whales to be very similar to other mammals. However, if they think about the fact that whales are mammals not fish, they will probably acknowledge that with respect to some important, although less accessible property or properties whales are similar to other mammals.

Introduction

Suppose we asked someone how to get to some place in the city we were visiting and received needed instructions in response. Clearly, we would say that this person knew the answer, no matter whether the person knew the place personally or just had to figure out its location on the basis of general knowledge of the city, that is, by conducting inference. We would say this, of course, only if the answer were given to us in a reasonable amount of time.

The above example illustrates a general principle: One knows what one remembers, or what one can infer from what one remembers within a certain time constraint. Thus our knowledge can be viewed as a combination of two components, memorized knowledge and inferential extension, that is, knowledge that can be created from recorded knowledge by conducting inference within a certain time limit.

The main thesis of this chapter is that individual concepts – elementary components of our knowledge – parallel such a two-tiered nature of knowledge. We hypothesize that processes of assigning meaning to individual concepts recognized in a stream of information, or of retrieving them from memory to express an intended meaning are intrinsically inferential and involve, on a smaller scale, the same types of inference – deductive, analogical, and inductive – as processes of applying and constructing knowledge in general. This hypothesis reflects an intuition that the meaning of most concepts cannot, in principle, be defined in a crisp and context-independent fashion.

In our studies of human reasoning (Burstein, 1986; Collins, 1978; Collins & Loftus, 1975; Collins & Michalski, 1989) we have found that the processes of comparison and mapping are central to all forms of human inference. For example, comparison underlies categorization (Smith & Medin, 1981) in that the very act of categorizing involves a comparison between an instance and a concept. Categorization is of use to humans because it allows us to make inferences (mappings) about what properties the categorized instances will have (e.g., they may fly away, they can be turned on, etc.). As the chapters in this volume amply illustrate, analogies and metaphors are also heavily dependent on these processes of comparison and mapping.

The literature on similarity, analogy, and metaphor ranges over many different kinds of comparison and mapping processes. Our goal is to clarify the issues being addressed and the critical distinctions that need to be made. We will attempt to consider the entire territory over which the discussion of comparison and mapping arises, but no doubt we will miss some of the critical distinctions and issues.

Some of the disagreements arise because researchers are talking about different kinds of comparisons or the different contexts in which comparison and mapping processes are used. Indeed, one common confusion is due to the use of the term mapping to describe either a functional correspondence between conceptual entities, the process tjiat establishes such correspondences (which we will refer to as comparison), or the process of transferring properties of one conceptual system to another, “similar” one.

Introduction

Artificial intelligence has a long and continuing interest in analogy (Burstein, 1985; Carbonell, 1985; Evans 1968; Forbus & Gentner, 1983; Kedar-Cabelli, 1985; Winston, 1980). From a computational point of view, more controversy surrounds analogy than any other single topic in the cognitive arena. From the perspective of an outsider, researchers appear to be doing wildly different things, all under the rubric of analogy. Perhaps this is just the natural result of a healthy diversity of thought. On the other hand, it may be a manifestation of the seductive name analogy. Somehow, “analogy” and “intelligence” seem to go hand in hand. The notion of researching analogy conjures up the illusion, at least, that one is directly addressing the problems of thinking and reasoning. Why is this? One possible reason is that analogy truly is central to thought. Several researchers have advanced the claim that thought is primarily metaphorical or analogical. A more cynical view is that analogy is a fuzzy concept that means different things to different people. But so is intelligence. Though researchers do not agree on what either term means, they can concur with abstract claims like “analogical reasoning is a fundamental component of intelligence”. It is perhaps this view that prompted Saul Amarel at the 1983 International Machine Learning Workshop to propose a moratorium on the term analogy in machine learning. Perhaps the field has fallen prey to a seductive term.

The power of human intelligence depends on the growth of knowledge through experience, coupled with flexibility in accessing and exploiting prior knowledge to deal with novel situations. These global characteristics of intelligence must be reflected in theoretical models of the human cognitive system (Holland, Holyoak, Nisbett, & Thagard, 1986). The core of a cognitive architecture (i.e., a theory of the basic components of human cognition) consists of three subsystems: a problem-solving system, capable of drawing inferences to construct plans for attaining goals; a memory system, which can be searched in an efficient manner to identify information relevant to the current problem; and an inductive system, which generates new knowledge structures to be stored in memory so as to increase the subsequent effectiveness of the problem-solving system.

These three subsystems are, of course, highly interdependent; consequently, the best proving ground for theories of cognition will be the analysis of skills that reflect the interactions among problem solving, memory, and induction. One such skill is analogical problem solving – the use of a solution to a known source problem to develop a solution to a novel target problem. At the most general level, analogical problem solving involves three steps, each of which raises difficult theoretical problems (Holyoak, 1984, 1985). The first step involves accessing a plausibly useful analog in memory. It is particularly difficult to identify candidate analogs when they are concealed in a large memory system, and when the source and target were encountered in different contexts and have many salient dissimilarities. These theoretical issues are closely related to those raised in Schank's (1982) discussion of “reminding.”

A central goal of cognitive science is to characterize the knowledge that underlies human intelligence. Many investigators have expended much effort toward this aim and in the process have proposed a variety of knowledge structures as the basic units of human knowledge, including definitions, prototypes, exemplars, frames, schemata, scripts, and mental models. An implicit assumption in much of this work is that knowledge structures are stable: Knowledge structures are stored in long-term memory as discrete and relatively static sets of information; they are retrieved intact when relevant to current processing; different members of a population use the same basic structures; and a given individual uses the same structures across contexts. These intuitions of stability are often compelling, and it is sometimes hard to imagine how we could communicate or perform other intelligent behaviors without stable knowledge structures.

But perhaps it is important to consider the issue of stability more explicitly. Are there stable knowledge structures in long-term memory? If so, are they retrieved as static units when relevant to current processing? Do different individuals represent a given category in the same way? Does a given individual represent a category the same way across contexts? Whatever conclusions we reach should have important implications for theories of human cognition and for attempts to implement increasingly powerful forms of machine intelligence.

Introduction

This chapter discusses the issues of similarity and analogy in development, learning, and instruction as represented in the chapters by John Bransford, Jeffery Franks, Nancy Vye, and Robert Sherwood; Ann Brown; Brian Ross; Rand Spiro, Paul Feltovich, Richard Coulson, and Daniel Anderson; and Stella Vosniadou. The following anecdote illustrates many of the themes that appear in the discussion of these chapters.

I was in a seminar recently where we were trying to set up an overhead projector for the first time. There was no screen in the room, and the one patch of wall of reasonable size was crossed with pipes. So I said to one of the other faculty members, “Let's try aiming the projector at the blackboard.” This individual said, “No, that's crazy.” I immediately gave in and began helping to aim the projector toward the wall. Then I said, “Wait, let's try the blackboard – I think it will work”. We did try the blackboard, and it did work reasonably well.

What was going on here? First, why did the other person immediately reject my original suggestion, and why did I give in? I think it is clear that the other person had a causal model for light which included the assumption that black surfaces absorb all the light that falls on them. As applied to the example at hand, this meant that it would be stupid to try to project the overhead on the blackboard, since no light would reflect off it and we would not be able to see the transparencies.

Introduction

We compare objects to each other in a variety of ways. We experience our world in terms of a complex system of distinct kinds of perceptual similarities. We judge objects to be similar or different. We also judge objects to be similar and different in part – to be, for example, similar in color and different in size. We categorize objects by their attributes and in so doing judge them to be similar; for example, we categorize objects as red, as blue, as big, as small. We compare objects in terms of their direction of difference – judging, for example, one object to be smaller than another. This variety of kinds of judgments clearly indicates that perceptual similarity is not one thing but is of many interrelated kinds. In brief, we seem to possess a complex system of perceptual relations, a complex system of kinds of similarity. The concern of this chapter is with the development of a system of knowledge about such relations.

The evidence suggests that an understanding of perceptual relations develops quite slowly during the preschool years. Indeed, working out a system of perceptual dimensions, a system of kinds of similarities, may be one of the major intellectual achievements of early childhood. The evidence for an emerging dimensional competence is widespread – and includes developments in Piagetian conservation tasks (e.g., Piaget, 1929), in seriation and transitive inference tasks, in classification tasks (e.g., Inhelder & Piaget, 1958, 1964), in transposition learning (e.g., Keunne, 1946) and discriminative learning tasks (e.g., Kendler, 1979).

Here is a simple and appealing idea about the way people decide whether an object belongs to a category: The object is a member of the category if it is sufficiently similar to known category members. To put this in more cognitive terms, if you want to know whether an object is a category member, start with a representation of the object and a representation of the potential category. Then determine the similarity of the object representation to the category representation. If this similarity value is high enough, then the object belongs to the category; otherwise, it does not. For example, suppose you come across a white three-dimensional object with an elliptical profile; or suppose you read or hear a description like the one I just gave you. You can calculate a measure of the similarity between your mental representation of this object and your prior representation of categories it might fit into. Depending on the outcome of this calculation, you might decide that similarity warrants calling the object an egg, perhaps, or a turnip or a Christmas ornament.

This simple picture of categorizing seems intuitively right, especially in the context of pattern recognition. A specific egg – one you have never seen before – looks a lot like other eggs. It certainly looks more like eggs than it looks like members of most other categories. And so it is hard to escape the conclusion that something about this resemblance makes it an egg or, at least, makes us think it's one.

The subtitle of this chapter is borrowed from an article published in 1940 by Charles L. Cragg. He begins with the following quotation from Balzac:

So he had grown rich at last, and thought to transmit to his only son all the cut-and-dried experience which he himself had purchased at the price of his lost illusions; a noble last illusion of age.

Except for the part about growing rich, we find that Balzac's ideas fit our experiences quite well. In our roles as parents, friends, supervisors, and professional educators we frequently attempt to prepare people for the future by imparting the wisdom gleaned from our own experiences. Sometimes our efforts are rewarded, but we are often less successful than we would like to be and we need to understand why.

Our goal in this chapter is to examine the task of preparing people for the future by exploring the notion that wisdom can't be told. Our arguments are divided into four parts.

First, we consider in more detail the notion that wisdom cannot be told. The argument is not that people are unable to learn from being shown or told. Clearly, we can remind people of important sets of information and tell them new information, and they can often tell it back to us. However, this provides no guarantee that people will develop the kinds of sensitivities necessary to use relevant information in new situations.

It is widely accepted that similarity is a key determinant of transfer. In this chapter I suggest that both of these venerable terms – similarity and transfer – refer to complex notions that require further differentiation. I approach the problem by a double decomposition: decomposing similarity into finer subclasses and decomposing learning by similarity and analogy into a set of component subprocesses.

One thing reminds us of another. Mental experience is full of moments in which a current situation reminds us of some prior experience stored in memory. Sometimes such remindings lead to a change in the way we think about one or both of the situations. Here is an example reported by Dan Slobin (personal communication, April 1986). His daughter, Heida, had traveled quite a bit by the age of 3. One day in Turkey she heard a dog barking and remarked, “Dogs in Turkey make the same sound as dogs in America.… Maybe all dogs do. Do dogs in India sound the same?” Where did this question come from? According to Slobin's notebook, “She apparently noticed that while the people sounded different from country to country, the dogs did not.” The fact that only humans speak different languages may seem obvious to an adult, but for Heida to arrive at it by observation must have required a series of insights. She had to compare people from different countries and note that they typically sound different.

Introduction

Analogies are tools for thought and explanation. The realization that a problematical domain (the target) is analogous to another more familiar domain (the source) can enable a thinker to reach a better understanding of the target domain by transporting knowledge from the source domain. A scientific problem can be illuminated by the discovery of a profound analogy. A mundane problem can similarly be solved by the retrieval of the solution to an analogous problem. An analogy can also serve a helpful role in exposition: A speaker attempting to explain a difficult notion can appeal to the listener's existing knowledge by the use of an analogy. A psychological theory of analogies must accordingly account for three principal phenomena: (a) the discovery or retrieval of analogies of various sorts from the profound to the superficial, (b) the success or failure of analogies in the processes of thinking and learning, and (c) the interpretation of analogies that are used in explanations.

My main purpose in this chapter is to establish that psychological theories of analogy have so far failed to take the measure of the problem. The processes underlying the discovery of profound analogies are much harder to elucidate than is generally realized. Indeed, I shall argue that they cannot be guaranteed by any computationally tractable algorithm. But my goals are not entirely negative; I want to try to establish a taxonomy of analogies and to show that there are some forms of analogy that can be retrieved by tractable procedures. I shall begin with an area that has undergone considerable psychological investigation: the role of analogies in problem solving.

The contributions included in Part II focus on the psychological processes involved in analogical reasoning and discuss how and whether these processes can be captured in computer models. In her chapter, Dedre Gentner outlines a structure-mapping theory of analogy and discusses how this theory can be extended to model other subprocesses in analogical reasoning. John Anderson and Ross Thompson describe a mechanism for doing analogy in problem solving within a production system architecture, and Keith Holyoak and Paul Thagard describe a model of analogical problem solving embedded within a larger computational program of problem solving called PI (for “processes of induction”). In his contribution, David Rumelhart discusses how analogical reasoning might be handled within a parallel distributed processing system. Finally, Philip Johnson-Laird argues that current psychological theories of analogy have underestimated the complexity of analogical phenomena and raises the possibility that profoundly original analogies may depend on classes of algorithms that are not computationally tractable.

There are two discussions of the contributions in Part II. Stephen Palmer offers a critique of the papers by Gentner, Holyoak and Thagard, and Rumelhart, in the context of the Palmer and Kimchi metatheoretical framework for levels of description within informationprocessing psychologv. Gerald Dejong's commentary takes an artificial intelligence perspective, and therefore also includes some reactions to the chapter by Ryszard Michalski in Part I.

Interest in analogy has been generated to a large extent by a recognition of the role that analogy can play in the acquisition of new knowledge. Although our models of learning have stressed the importance of.prior knowledge in thinking, remembering, and learning, they have remained mainly silent on the processes whereby new knowledge is acquired. One mechanism that has been recognized by scientists, philosophers, and psychologists alike as having the potential of bringing prior knowledge to bear on the acquisition of, sometimes, radically new information is analogy.

My purpose in this chapter is to examine analogical reasoning, paying particular attention to the role it plays in knowledge acquisition. This question will be approached from a developmental point of view.

The chapters by Dedre Gentner, Keith Holyoak and Paul Thagard, and David Rumelhart in this volume present a broad spectrum of approaches to understanding the nature of analogical thought processes. Gentner spends a good deal of effort on formulating just what an analogy is; Holyoak and Thagard use production systems and spreading activation to simulate analogical processing in a problemsolving task; and Rumelhart explores the potential importance of connectionism for understanding analogies in the context of other “higher mental processes.” How are we to integrate this enormous diversity in tackling the same underlying problem? Is one right and the others wrong? Which proposals actually conflict, and which ones are compatible? What have we learned from each one about analogical thought?

I plan to approach these questions within a broad metatheoretical framework that spans the unique as well as the common aspects of the three presentations. The framework I have in mind is closely related to David Marr's (1982) well-known distinction among three levels of analysis of an information-processing (IP) system: the computational level, the algorithmic level, and the implementational level. My own view of the situation is slightly different from Marr's in that I see IP theories as spanning a single continuum of possible theoretical levels defined at the “upper” end of the spectrum by informational (or task) constraints, at the “lower” end by hardware constraints, and in between by behavioral constraints.

Our goal is to extend certain theoretical notions about similarity – particularly notions about similarity to prototypes – to studies of decision making and choice. For the past decade, the psychology of decision making has been dominated by the brilliant research of Daniel Kahneman and Amos Tversky. Although Kahneman and Tversky (hereafter K & T) have contributed greatly to this area, their research seems to be swimming against the strongest current in contemporary psychology in that it is not primarily concerned with issues of representation and process. We think that this neglect of a computational perspective has limited the generalizations that K & T and their followers have drawn from studies of decision making. We will support our position by showing that an explicit model of similarity and decision making promotes new generalizations and suggests new insights about some of K & T's best-known studies.

In particular, such a model will allow us to specify the factors that control the phenomena that K & T have uncovered, thereby permitting us to determine the conditions under which the reasoning illusions they describe will arise. This is in contrast to K & T's approach of simply demonstrating the phenomena, with no attempt to delineate boundary conditions. Our approach should also enable us to connect the areas of decision and choice to recent advances in the theory of knowledge representation.

The contributions included in Part I have something to say either about similarity itself or about how people's conceptual representations affect similarity judgments. The papers by Lance Rips and by Edward Smith and Daniel Osherson look at similarity from the point of view of the role it plays in other psychological processes, like categorization and decision making. Rips argues that, although similarity may provide some cues to an object's category identity, it fails to provide an adequate explanation of people's category judgments. In contrast, Smith and Osherson believe that similarity plays an important role in decision making. They propose an explicit model wherein a person estimates the probability that an object belongs to a certain class by relying on the similarity the object bears to a prototype of the class. Linda Smith discusses the issue of how the complex system of similarity kinds that people use may develop.

Lawrence Barsalou's chapter deals with the question of instability (or flexibility) in people's conceptual representations and its implications for a theory of similarity. The contribution by Ryszard Michalski has been placed in Part I because it extends some of Barsalou's arguments about the flexibility of conceptual representations and offers a method for achieving such flexibility in a computer model of induction. Finally, Douglas Medin and Andrew Ortony discuss the contributions to Part I and also present their own views about similarity and, particularly, about the role that similarity might play in categorization.