Academic journal article Memory & Cognition

# "At Least One" Problem with "Some" Formal Reasoning Paradigms

Academic journal article Memory & Cognition

# "At Least One" Problem with "Some" Formal Reasoning Paradigms

## Article excerpt

In formal reasoning, the quantifier "some" means "at least one and possibly all." In contrast, reasoners often pragmatically interpret "some" to mean "some, but not all" on both immediate-inference and Euler circle tasks. It is still unclear whether pragmatic interpretations can explain the high rates of errors normally observed on syllogistic reasoning tasks. To address this issue, we presented participants (reasoners) in the present experiments either standard quantifiers or clarified quantifiers designed to precisely articulate the quantifiers' logical interpretations. In Experiment 1, reasoners made significantly more logical responses and significantly fewer pragmatic responses on an immediate-inference task when presented with logically clarified as opposed to standard quantifiers. In Experiment 2, this finding was extended to a variant of the immediate-inference task in which reasoners were asked to deduce what followed from premises they were to assume to be false. In Experiment 3, we used a syllogistic reasoning task and observed that logically clarified premises reduced pragmatic and increased logical responses relative to standard ones, providing strong evidence that pragmatic responses can explain some aspects of the errors made in the syllogistic reasoning task. These findings suggest that standard quantifiers should be replaced with logically clarified quantifiers in teaching and in future research.

Syllogistic reasoning is a widely used measure of formal, deductive reasoning. In this task, reasoners are presented with two premise statements (e.g., "Some of the As are Bs" and "All of the Bs are Cs") and are then asked to decide whether a given conclusion statement logically follows from the premises (e.g., "Some of the As are Cs," which is a valid conclusion). Syllogistic reasoning is used as a vehicle to investigate such disparate phenomena as belief bias (Evans, Barston, & Pollard, 1983; Klauer, Musch, & Naumer, 2000; Newstead, Pollard, Evans, & Alien, 1992; Thompson, Striemer, Reikoff, Gunter, & Campbell, 2003), the role of working memory in reasoning (Capon, Handley, & Dennis, 2003; Copeland & Radvansky, 2004; Gilhooly, Logie, & Wynn, 1999; Quayle & Ball, 2000), strategies in reasoning (Bacon, Handley, & Newstead, 2003; Bucciarelli & Johnson-Laird, 1999; Chater & Oaksford, 1999), and disruptions to reasoning performance caused by age (Fisk & Sharp, 2002; Gilinsky & Judd, 1994) and other factors (Fisk, Montgomery, Wareing, & Murphy, 2005; Smeets & De Jong, 2005).

Although often taken as a measure of logical or analytic reasoning, it is almost certainly the case that performance on this task also encompasses a number of nonanalytic processes. For example, it is well known that the believability of both the premises and the conclusion have a large effect on the inferences that reasoners are willing to endorse (e.g., Evans et al., 1983; Klauer et al., 2000; Newstead et al., 1992; Thompson, 1996; Thompson et al., 2003). Even when the believability of the material is not an issue (i.e., premises and conclusions describe arbitrary or abstract relations), the reasoner must still interpret the task, the instructions, and the meaning of the quantifiers used in the problems. Poor performance, therefore, may not necessarily represent poor logical reasoning, but, instead, may reflect differences between the reasoner's and the experimenter's interpretation of the task requirements. For example, reasoners may conflate the concepts of logical possibility with logical necessity (e.g., Evans, Handley, & Harper, 2001; Evans, Handley, Harper, & JohnsonLaird, 1999; Newstead, Thompson, & Handley, 2002) and employ heuristic, rather than logical, strategies (Chater & Oaksford, 1999). Consequently, it is difficult to attribute contributions of analytic processes to performance in the absence of a well-articulated model of interpretation (Evans & Thompson, 2004; Thompson, 2000). …

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