Absence Makes the Thought Grow Stronger: Reducing Structural Overlap Can Increase Inductive Strength

Absence Makes the Thought Grow Stronger: Reducing Structural Overlap Can Increase Inductive Strength Hee Seung Lee (heeseung@ucla.edu) Department of Psychology, University of California, Los Angeles Los Angeles, CA 90095 USA Keith J. Holyoak (holyoak@lifesci.ucla.edu) Department of Psychology, University of California, Los Angeles Los Angeles, CA 90095 USA status by virtue of the fact that causes actually produce (or sometimes prevent) their effects (e.g., Bartha, in press; Hesse, 1966; Winston, 1980), or whether causal relations simply operate as special cases of higher-order relations, defined by the formal properties of predicate-argument structures. Holyoak (1985) emphasized that causal knowledge is the basis for pragmatic rather than just structural constraints on analogical inference. Using complex stories, Spellman and Holyoak (1996) showed that when the source-target mapping was ambiguous by structural criteria, those relations causally-relevant to the reasoner’s goal determined the preferred mapping and inferences about the target. Lassaline (1996) demonstrated that people make stronger inferences on the basis of the higher-order relation “cause” than on the basis of a non- causal relation, “temporally prior to”, which appears to have the same formal structure. Thus the same syntactic “order” of relations does not always yield the same degree of inductive strength about the target property to be inferred. There is no doubt that causal relations play an important role in analogical inference. However, very little effort has been devoted to incorporating basic elements of causal models (Griffiths & Tenenbaum, 2005; Waldmann & Holyoak, 1992), such as the distinction between generative and preventive causes (Cheng, 1997; Lu et al., 2007), into models of analogy. Recently, Lee and Holyoak (2007) examined the role of causal models in analogical inference by testing a hypothesis proposed by Bartha (in press). Bartha distinguished between contributing causes (generative) and counteracting causes (preventive) in evaluating the strength of analogical arguments. He pointed out that eliminating from the target a counteracting cause present in the source might actually strengthen an argument from analogy. For example, iron deposits are still present on earth despite the fact that humans have been extracting iron ore in mining operations for centuries. Taking the earth as a source analog for the moon, the fact that no mining operations have so far been conducted on the moon (a mismatch with a property of the source) seems to strengthen the analogical inference that iron deposits remain to be found on the moon. To test this hypothesis, Lee and Holyoak examined use of causal models by adapting a paradigm introduced by Lassaline (1996). Participants read a description of two Abstract Computational models of analogy have assumed that the strength of an inductive inference about the target is based directly on similarity of the analogs, and in particular on shared higher-order relations. However, in Experiment 1 we show that reducing analogical overlap by eliminating a higher-order causal relation (a preventive cause present in the source) from the target increased inductive strength even though it decreased similarity of the analogs. In Experiment 2 we extend these findings to cross-domain analogical inferences based on correspondences between higher-order causal relations. Analogical inference appears to be mediated by building and then “running” a causal model. We discuss the implications of the present findings for theories of both analogy and causal inference. Keywords: analogical inference; causal model; similarity; inductive strength; preventive cause; generative cause. Introduction When people face uncertainty, they often make analogical inferences about an unfamiliar target situation based on a similar but better understood source situation. However, people do not draw inferences from the source about all the missing target properties. For example, consider the earth as a source analog for inferring properties of the moon. It seems more likely the resulting analogy will lead to the inference that the moon may contain iron deposits than that the moon has a system of freeways, even though the earth contains iron deposits and also has freeways. In general, inductive inferences seem to be guided by certain general constraints that allow people to make analogical inferences selectively (Holyoak, 1985). Inductive constraints: Are causal relations special? People are more likely to draw confident analogical inferences when they perceive a source and target to be similar, particularly if they overlap in their relational structure. According to Gentner’s (1983) systematicity principle, higher-order relations are especially important in promoting analogical inferences. The canonical example of a higher-order relation is “cause”; however, the “order” of a relation is defined syntactically (a relation that takes another relation as an argument), rather than by meaning. A central issue in understanding constraints on analogical inference is whether causal relations have some special