Reasoning from shared structure

Reasoning from shared structure Sergey Victor Blok (s-blok@northwestern.edu) Dedre Gentner (gentner@northwestern.edu) Department of Psychology, Northwestern University, Evanston, Illinois Abstract Two experiments contrasted the predictions of the simi- larity-coverage model of category-based induction with those of a structure-based account. We focused on the two theories’ ability to account for the paradoxical fact that both monotonicities (increases in argument strength with the addition of premises) and non- monotonicities (decreases in argument strength with addition of premises) occur in human reasoning. The results are mainly in accord with the structure-based account and are inconsistent with the similarity- coverage account. Introduction Monotonicity and Induction Humans routinely make inductive inferences, and the principles that guide these inferences have received a great deal of empirical attention (Lopez, 1995; McDon- ald, Samuels & Rispoli, 1996; Osherson, Smith, Wilkie Lopez & Shafir, 1990; Sloman, 1993). One principle that has both intuitive and empirical support is monotonicity – the principle that confidence in an inductive inference should increase with the number of supporting premises. For example, Osherson et al. showed that adults preferred Argument B over Argument A. A. All FOXES have sesamoid bones, All PIGS have sesamoid bones, Therefore, all GORILLAS have sesamoid bones B. All FOXES have sesamoid bones, All PIGS have sesamoid bones, All WOLVES have sesamoid bones Therefore, all GORILLAS have sesamoid bones. However, robust nonmonotonicities have also been documented. Osherson et al.’s participants chose Argu- ment C over D. C. All FLIES have sesamoid bones, Therefore, all BEES have sesamoid bones. Sloman (1993) and McDonald et al. (1996) have also documented nonmonotonic responding in adults. Even more strikingly, Lopez, Gelman, Gutheil & Smith (1992) showed nonmonotonicity effects very early in develop- ment; in fact, nonmonotonicity effects were reliably ob- tained earlier than monotonicity effects. People appear to believe that more premises make for a stronger argument, except when more premises make for a weaker argument. How can we reconcile these apparently contradictory phenomena? Similarity-Coverage Model A pioneering theory of argument strength is the Simi- larity-coverage model (SCM) of Osherson et al. (1990). The two components of SCM are similarity -- the extent of feature overlap between premise and conclusion cate- gories -- and coverage -- the average similarity of the premises and the instances of the lowest level taxonomic category that includes both the premises and the conclu- sion. The similarity-coverage model predicts monotonic- ity when the additional premise is a member of the same lowest level superordinate category as the initial premises and the conclusion. It predicts nonmonotonicity when the additional premise is not a member of the lowest level superordinate category. Thus nonmonotonicity can be seen as a kind of dilution effect, as illustrated by Osher- son et al’s (1990) data in (1) and (2), respectively. (1) a. ROBINS, SPARROWS / SEAGULLS > b. ROBINS / SEAGULLS 1 (2) a. ROBINS, RABBITS / SEAGULLS < b. ROBINS / SEAGULLS Argument (1) is monotonic; adding the extra premise SPARROW in (1a) adds an additional piece of premise support without diluting the category coverage, because it fits within the lowest-level category (BIRDS) that applies in the single premise case (1b). In contrast, the additional premise RABBITS in (2a) raises the lowest-level common category to ANIMALS, thus diluting the category cover- age. Thus the SCM can successfully predict some in- stances of monotonicity. D. All FLIES have sesamoid bones, All ORANGUTANGS have sesamoid bones, Therefore, all BEES have sesamoid bones. Research in this area typically uses so called “blank” or opaque properties – such as ‘has sesamoid bones’ to ensure that belief in the conclusion is derived from the premise statements, rather than from prior beliefs about the truth of the conclusion. We will omit property names from further examples.