Abstract
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.
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Bacon, A. M., Handley, S. J., & Newstead, S. E. (2003). Individual differences in strategies for syllogistic reasoning. Thinking & Reasoning, 9, 133–161.
Barres, P. E., & Johnson-Laird, P. N. (2003). On imagining what is true (and what is false). Thinking & Reasoning, 9, 1–42.
Begg, I., & Harris, G. (1982). On the interpretation of syllogisms. Journal of Verbal Learning & Verbal Behavior, 21, 595–620.
Bucciarelli, M., & Johnson-Laird, P. N. (1999). Strategies in syllogistic reasoning. Cognitive Science, 23, 247–303.
Capon, A., Handley, S. [J.], & Dennis, I. (2003). Working memory and reasoning: An individual differences perspective. Thinking & Reasoning, 9, 203–244.
Ceraso, J., & Provitera, A. (1971). Sources of error in syllogistic reasoning. Cognitive Psychology, 2, 400–410.
Chater, N., & Oaksford, M. (1999). The probability heuristics model of syllogistic reasoning. Cognitive Psychology, 38, 191–258.
Copeland, D. E., & Radvansky, G. A. (2004). Working memory and syllogistic reasoning. Quarterly Journal of Experimental Psychology, 57A, 1437–1457.
Déret, D. (1998). Le syllogisme catégorique: Une réexamination du terme “certains” dans une perspective développementale [The categorical syllogism: A reexamination of the term “some” from a developmental perspective]. Canadian Journal of Experimental Psychology, 52, 174–182.
Evans, J. St. B. T., Barston, J. L., & Pollard, P. (1983). On the conflict between logic and belief in syllogistic reasoning. Memory & Cognition, 11, 295–306.
Evans, J. St. B. T., Handley, S. J., & Harper, C. N. J. (2001). Necessity, possibility and belief: A study of syllogistic reasoning. Quarterly Journal of Experimental Psychology, 54A, 935–958.
Evans, J. St. B. T., Handley, S. J., Harper, C. N. J., & Johnson-Laird, P. N. (1999). Reasoning about necessity and possibility: A test of the mental model theory of deduction. Journal of Experimental Psychology: Learning, Memory, & Cognition, 25, 1495–1513.
Evans, J. St. B. T., Handley, S. J., Perham, N., Over, D. E., & Thompson, V. A. (2000). Frequency versus probability formats in statistical word problems. Cognition, 77, 197–213.
Evans, J. St. B. T., & Thompson, V. A. (2004). Informal reasoning: Theory and method. Canadian Journal of Experimental Psychology, 58, 69–74.
Feeney, A., Scrafton, S., Duckworth, A., & Handley, S. J. (2004). The story of some: Everyday pragmatic inference by children and adults. Canadian Journal of Experimental Psychology, 58, 121–132.
Fisk, J. E., Montgomery, C., Wareing, M., & Murphy, P. N. (2005). Reasoning deficits in ecstasy (MDMA) polydrug users. Psychopharmacology, 181, 550–559.
Fisk, J. E., & Sharp, C. (2002). Syllogistic reasoning and cognitive ageing. Quarterly Journal of Experimental Psychology, 55A, 1273–1293.
Geurts, B. (2003). Reasoning with quantifiers. Cognition, 86, 223–251.
Gilhooly, K. J., Logie, R. H., & Wynn, V. (1999). Syllogistic reasoning tasks, working memory, and skill. European Journal of Cognitive Psychology, 11, 473–498.
Gilinsky, A. S., & Judd, B. B. (1994). Working memory and bias in reasoning across the life span. Psychology & Aging, 9, 356–371.
Girotto, V., & Gonzalez, M. (2001). Solving probabilistic and statistical problems: A matter of information structure and question form. Cognition, 78, 247–276.
Grice, H. P. (2002). Logic and conversation. In D. J. Levitin (Ed.), Foundations of cognitive psychology: Core readings (pp. 719–732). Cambridge, MA: MIT Press. (Reprinted from Syntax and semantics 3: Speech acts, pp. 26–40, by P. Cole & J. L. Morgan, Eds., 1975, New York: Academic Press).
Henle, M. (1962). On the relation between logic and thinking. Psychological Review, 69, 366–378.
Klauer, K. C., Musch, J., & Naumer, B. (2000). On belief bias in syllogistic reasoning. Psychological Review, 107, 852–884.
Newstead, S. E. (1989). Interpretational errors in syllogistic reasoning. Journal of Memory & Language, 28, 78–91.
Newstead, S. E. (1995). Gricean implicatures and syllogistic reasoning. Journal of Memory & Language, 34, 644–664.
Newstead, S. E. (2003). Can natural language semantics explain syllogistic reasoning? Cognition, 90, 193–199.
Newstead, S. E., & Griggs, R. A. (1983). Drawing inferences from quantified statements: A study of the square of opposition. Journal of Verbal Learning & Verbal Behavior, 22, 535–546.
Newstead, S. E., & Griggs, R. A. (1999). Premise misinterpretation and syllogistic reasoning. Quarterly Journal of Experimental Psychology, 52A, 1057–1075.
Newstead, S. E., Pollard, P., Evans, J. St. B. T., & Allen, J. L. (1992). The source of belief bias effects in syllogistic reasoning. Cognition, 45, 257–284.
Newstead, S. E., Thompson, V. A., & Handley, S. J. (2002). Generating alternatives: A key component in human reasoning? Memory & Cognition, 30, 129–137.
Politzer, G. (1991). Comparison of deductive abilities across language. Journal of Cross-Cultural Psychology, 22, 389–402.
Polk, T., & Newell, A. (1995). Deduction as verbal reasoning. Psychological Review, 102, 533–566.
Quayle, J. D., & Ball, L. J. (2000). Working memory, metacognitive uncertainty, and belief bias in syllogistic reasoning. Quarterly Journal of Experimental Psychology, 53A, 1202–1223.
Revlis, R. (1975). Two models of syllogistic reasoning: Feature selection and conversion. Journal of Verbal Learning & Verbal Behavior, 14, 180–195.
Roberts, M. J., Newstead, S. E., & Griggs, R. A. (2001). Quantifier interpretation and syllogistic reasoning. Thinking & Reasoning, 7, 173–204.
Rosenthal, D. J. (1980). Logical quantifiers in affirmative and negative contexts. Journal of General Psychology, 102, 99–106.
Sloman, S. A., Over, D., Slovak, L., & Stibel, J. M. (2003). Frequency illusions and other fallacies. Organizational Behavior & Human Decision Processes, 91, 296–309.
Smeets, G., & De Jong, P. J. (2005). Belief bias and symptoms of psychopathology in a non-clinical sample. Cognitive Therapy & Research, 29, 377–386.
Thompson, V. A. (1996). Reasoning from false premises: The role of soundness in making logical deductions. Canadian Journal of Experimental Psychology, 50, 315–319.
Thompson, V. A. (2000). The task-specific nature of domain-general reasoning. Cognition, 76, 209–268.
Thompson, V. A., Striemer, C. L., Reikoff, R., Gunter, R. W., & Campbell, J. I. D. (2003). Syllogistic reasoning time: Disconfirmation disconfirmed. Psychonomic Bulletin & Review, 10, 184–189.
Torrens, D., Thompson, V. A., & Cramer, K. M. (1999). Individual differences and the belief bias effect: Mental models, logical necessity, and abstract reasoning. Thinking & Reasoning, 5, 1–28.
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This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC) to V.A.T. and by an NSERC Undergraduate Student Research Award to J.R.S.
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Schmidt, J.R., Thompson, V.A. “At least one” problem with “some” formal reasoning paradigms. Memory & Cognition 36, 217–229 (2008). https://doi.org/10.3758/MC.36.1.217
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DOI: https://doi.org/10.3758/MC.36.1.217