How do people reason? The view that I learned at my mother's knee was that they rely on logic. During the 1960s and 1970s when the study of thinking had become respectable again after the Dark Ages of Behaviorism, psychologists – including the present author – took this view for granted. The idea that logic provided the norms of reasoning can be traced back to the rise of modern logic, and was defended in the nineteenth century by both Boole (1854) and Mill (1874). In the twentieth century, the Swiss psychologist, Jean Piaget, and his colleagues argued that the construction of a formal logic in the mind was the last great step in children's intellectual development, and that it occurred at about the age of twelve (see, e.g., Inhelder and Piaget, 1958). And so thirty years ago the task for psychologists appeared to be to determine which particular formal logic was laid down in the mind and which particular rules of inference were used in its mental formulation. That, at least, was how several like-minded authors conceived their research (see, e.g., Osherson 1974–1976; Johnson-Laird 1975; Braine 1978; Rips 1983). In the parallel “universe” of artificial intelligence, researchers were similarly developing computer programs that proved theorems relying on formal rules of inference (e.g., Bledsoe 1977). The main skeptics were those engaged in trying to analyze everyday arguments. They discovered that it was extraordinarily difficult to translate such arguments into formal logic.
Let us begin with three problems that call for you to reason:
Suppose that you are on the jury of a murder trial, and that two propositions are established beyond a reasonable doubt: The stabbing occurred on an Amtrak train to Washington, and the suspect was in a cinema at the time of the stabbing. What conclusion would you draw? You may want to take a pencil and paper, and record your answer to this problem and the two that follow.
Suppose that you have the following information: Either Omar is in Kandahar or at least he is in Afghanistan. In fact, he is not in Afghanistan. Is he in Kandahar: “yes,” “no,” or “don't know”?
You park your car in London on a double yellow line drawn at the side of the road. When you return, you car has been wheel-clamped, and a note on the windshield tells you where to pay the fine to get the wheel released. What offense have you committed?
Nearly everyone responds to problem (1): the suspect is innocent. They respond to problem (2): no, he is not in Kandahar. And they respond to problem (3): the offense was to park in a “no parking” zone. Our ability to reason is perhaps our preeminent cognitive skill. Without it, as these examples show, daily life would be impoverished, and there would be no science or mathematics, no legal systems or social conventions.
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.
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