On the conflict between logic and belief in syllogistic reasoning

Abstract

Three experiments are reported that investigate the weighting attached to logic and belief in syllogistic reasoning. Substantial belief biases were observed despite controls for possible conversions of the premises. Equally substantial effects of logic were observed despite controls for two possible response biases. A consistent interaction between belief and logic was also recorded; belief bias was more marked on invalid than on valid syllogisms. In all experiments, verbal protocols were recorded and analyzed. These protocols are interpreted in some cases as providing rationalizations for prejudiced decisions and, in other cases, as reflecting a genuine process of premise to conclusion reasoning. In the latter cases, belief bias was minimal but still present. Similarly, even subjects who focus primarily on the conclusion are influenced to an extent by the logic. Thus a conflict between logic and belief is observed throughout, but at several levels of extent.An important debate in cognitive psychology surrounds the notion of rationality with respect to human inference (see Cohen, 1981, and associated commentaries). Recent reviews by Evans (1982) and Nisbett and Ross (1980) have stressed the role of apparently irrational processes in the study of inductive and deductive inference, respectively (see also Pollard, 1982). However, theories favoring a rationalist interpretation of inferential behavior still hold a dominant position in the recent literature (see, for example, the collections of papers edited by Falmagne, 1975, andMayer, 1978).In the case of deductive reasoning, much of the argument centers on the use by subjects of a system of logic, whether of the philosopher's variety (cf. Henle, 1962) or of an alternative "natural" type (e.g., Braine, 1978).The nonlogical or antirational position is sometimes misinterpreted as denigrating man's proven intelligence. What is in fact suggested is an alternative conception of that intelligence. The "rationalist" position entails the supposition that the reasoner proceeds by forming an abstract representation of problem information and applying a general set of inferential rules to its logical structure, regardless of its content. This notion is clearly embodied, for example, in Piaget's theory of formal operations (cf. Inhelder & Piaget, 1958). The alternative argument stressed here is that specific features of problem content, and their semantic associations, constitute the dominant influence on thought (see Evans, 1982, for extended discussion).

Assessing the belief bias effect with ROCs: It's a response bias effect.

“…The interaction effect described by Evans et al (1983) can thus be estimated by a contrast of contrasts. This measure, often referred to as the interaction index, has provided the basic datum for a substantial number of studies that have investigated the Belief ϫ Logic interaction (e.g., Ball, Phillips, Wade, & Quayle, 2006;Evans et al, 1983;Evans & Curtis-Holmes, 2005;Evans, Newstead, Allen, & Pollard, 1994;Morley, Evans, & Handley, 2004;Newstead, Pollard, Evans, & Allen, 1992;Quayle & Ball, 2000;Roberts & Sykes, 2003;Shynkaruk & Thompson, 2006;Stupple & Ball, 2008;Thompson, Striemer, Reikoff, Gunter, & Campbell, 2003). Rewriting the index, we can denote P("Valid"|Valid) as H (the hit rate), and P("Valid"|Invalid) as F (the false-alarm rate).…”

“…Evans, Barston, and Pollard (1983), in an important early study of belief bias, showed that the believability of a given syllogistic conclusion can have drastic effects on the probability that subjects will endorse it. In three experiments, subjects were asked to evaluate the validity of four types of syllogisms, which resulted from crossing the logical status and believability of the conclusions.…”

“…(For the data in Evans et al (1983) has focused on explaining the Belief ϫ Logic interaction, the importance of measuring the effect accurately should not be underestimated. In what follows, we review several theoretical accounts of belief bias, all of which attempt to explain the interaction observed in contrasts of H and F. We discuss problems arising from assumptions about the relationship between response bias and accuracy that are inherent in the interaction index.…”

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A belief bias effect in syllogistic reasoning (Evans, Barston, & Pollard, 1983) is observed when subjects accept more valid than invalid arguments and more believable than unbelievable conclusions and show greater overall accuracy in judging arguments with unbelievable conclusions. The effect is measured with a contrast of contrasts, comparing the acceptance rates for valid and invalid arguments with believable and unbelievable conclusions.

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Matching Traffic Safety Strategies to Youth Characteristics: A Literature Review of Cognitive Development

“…One problem is that people, especially children (Ward & Overton, 1990), have a tendency to confuse truth with validity and reason based upon what they want to believe rather than using rules of logic (e.g., Evans, Barston, & Pollard, 1983;Henle & Michael, 1956;Wilkins, 1928). A second problem is that the context of the syllogism topic influences how people judge its validity (e.g., Braine, 1978;Evans, 1989;Ward & Overton, 1990); for example, a syllogism of the same form may be judged differently depending on whether the topic is safety belts or high school parties.…”