The category inclusion rule specifies that categories inherit the properties of their superordinates. For example, given that all metals are pentavalent, it can be concluded that all iron is pentavalent. Sloman (1998) showed that people do not fully endorse conclusions that follow from the category inclusion rule. He claims that people rely on the similarity between the premise and the conclusion categories (metals and iron), rather than applying the category inclusion rule. By allowing reasoners to rate their certainty for category relations (e.g., iron is metal), as well as for conclusions, the present study shows that similarity has only an indirect effect on the certainty of conclusions: Reasoners are more certain that similar categories have a category inclusion relation, and this in turn affects the certainty of conclusions based on this relation.
It is generally believed that similarity plays an important role in cognition (e.g., Sloman & Rips, 1998), although there is no consensus on why certain concepts are considered similar (e.g., Tversky, 1977; Wallach, 1958). Some examples of the importance of similarity in cognition have come from research on categorization (e.g., Goldstone, 1994), induction (e.g., Osherson, Smith, Wilkie, Lopez, & Shafir, 1990), hypothesis testing (e.g., Kincannon & Spellman, 2003), and analogical reasoning (e.g., Markman, 1997). Sloman (1998) suggested that similarity also plays a role in deductive reasoning, despite the fact that prominent theories of deduction, such as mental logic (Braine & O'Brien, 1998) and mental models (JohnsonLaird & Byrne, 1991), preclude any use of similarity. In the present study, we examine the role of similarity in deductive categorical inference and address the findings of Sloman (1998).
Sloman (1998) had participants rate the probability of a conclusion's truth from a given fact. He found that probability ratings were less than certain and that they varied with the similarity between the category in the conclusion and the category in the fact. He claims that it is the similarities between these categories that make some arguments appear stronger than others. We test an alternate interpretation here-namely, that the reasoners' decisions follow a rational procedure, in which similarity plays only a minor role.
Before we explain our approach, we will describe the structure of the reasoning task and will review the findings of Sloman (1998). The reasoner sees two statements: a premise presented as a fact and a conclusion to be evaluated, as shown below:
(1) Fact: All metals are pentavalent.
Conclusion: All iron is pentavalent.
If the fact entails the conclusion, the probability of the fact should not be greater than the probability of the conclusion (e.g., Edgington, 1995). Therefore, if reasoners treat the fact as a certain truth and the conclusion follows from the fact, they should endorse the conclusion with certainty. However, in the problem above, the conclusion does not follow from the fact; it can be derived from the fact only if the tacit premise (All iron is metal) is made explicit. Arguments with a missing premise are known as enthymemes1 (e.g., Madden, 1952) and are common in mathematical proofs (Fallis, 2003), advertising (Areni, 2002), language understanding (Revlin & Hegarty, 1999), and everyday reasoning (Levi, 1995).
Sloman ( 1998) presented participants with enthymemes containing familiar categories, but with properties that were intended to be unfamiliar to the participants (henceforth, blank predicates), so that the participants could not rely on knowledge of the conclusion (as illustrated in Enthymeme 1). Sloman (1998) found that the participants did not fully endorse these conclusions, despite having previously affirmed the tacit premise (e.g., iron is a metal). He asked the participants in a separate questionnaire whether the category in the conclusion (iron) was an instance of the category in the fact (metal) and analyzed the conclusion ratings only for trials in which the participants affirmed this category inclusion relation. …