Memory & Cognition

, Volume 28, Issue 3, pp 452–465 | Cite as

Illusions in quantified reasoning: How to make the impossible seem possible, and vice versa

  • Yingrui YangEmail author
  • P. N. Johnson-LairdEmail author


The mental model theory postulates that reasoners build models of the situations described in premises, and that these models normally represent only what is true. The theory has an unexpected consequence. It predicts the existence ofillusions in inferences. Certain inferences should have compelling but erroneous conclusions. Two experiments corroborated the occurrence of such illusions in inferences about what is possible from disjunctions of quantified assertions, such as, “at least some of the plastic beads are not red.” Experiment 1 showed that participants erroneously inferred that impossible situations were possible, and that possible situations were impossible, but that they performed well with control problems based on the same premises. Experiment 2 corroborated these findings in inferences from assertions based on dyadic relations, such as, “all the boys played with the girls.”


Mental Model Explicit Model Control Inference Mental Model Theory Plastic Bead 
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  1. Begg, I. (1987). Some.Canadian Journal of Psychology,41, 62–73.CrossRefGoogle Scholar
  2. Braine, M. D. S. (1998). Steps towards a mental predicate logic. In M. D. S. Braine & D. P. O’Brien (Eds.),Mental logic (pp. 273–331). Mahwah, NJ: Erlbaum.Google Scholar
  3. Braine, M. D. S., &O’Brien, D. P. (1991). A theory of if: A lexical entry, reasoning program, and pragmatic principles.Psychological Review,98, 182–203.CrossRefGoogle Scholar
  4. Bucciarelli, M., &Johnson-Laird, P. N. (1999). Strategies in syllogistic reasoning.Cognitive Science,23, 247–303.CrossRefGoogle Scholar
  5. Cheng, P. W., &Holyoak, K. J. (1985). Pragmatic reasoning schemas.Cognitive Psychology,17, 391–416.CrossRefPubMedGoogle Scholar
  6. Cosmides, L. (1989). The logic of social exchange: Has natural selection shaped how humans reason?Studies with the Wason selection task. Cognition,31, 187–276.Google Scholar
  7. Cummins, D. D. (1996). Evidence for the innateness of deontic reasoning.Mind & Language,11, 160–190.CrossRefGoogle Scholar
  8. Grice, H. P. (1975). Logic and conversation. In P. Cole & J. L. Morgan (Eds.),Syntax and semantics: Vol. 3. Speech acts (pp. 41–58). New York: Seminar Press.Google Scholar
  9. Henle, M. (1962). On the relation between logic and thinking.Psychological Review,69, 366–378.CrossRefPubMedGoogle Scholar
  10. Jackendoff, R. (1988). Exploring the form of information in the dynamic unconscious. In M. J. Horowitz (Ed.),Psychodynamics and cognition (pp. 3–10). Chicago: University of Chicago Press.Google Scholar
  11. Johnson-Laird, P. N. (1970). The interpretation of quantified sentences. In W. J. M. Levelt & G. B. Flores d’Arcais (Eds.),Advances in psycholinguistics (pp. 347–372). Amsterdam: North-Holland.Google Scholar
  12. Johnson-Laird, P. N. (1983).Mental models: Towards a cognitive science of language, inference and consciousness. Cambridge, MA: Harvard University Press.Google Scholar
  13. Johnson-Laird, P. N., &Byrne, R. M. J. (1991).Deduction. Hillsdale, NJ: Erlbaum.Google Scholar
  14. Johnson-Laird, P. N., &Byrne, R. M. J. (1996). Mental models and syllogisms.Behavioral & Brain Sciences,19, 543–546.Google Scholar
  15. Johnson-Laird, P. N., &Goldvarg, Y. (1997). How to make the impossible seem possible. InProceedings of the Nineteenth Annual Conference of the Cognitive Science Society (pp. 354–357). Mahwah, NJ: Erlbaum.Google Scholar
  16. Johnson-Laird, P. N., &Savary, F. (1996). Illusory inferences about probabilities.Acta Psychologica,93, 69–90.CrossRefGoogle Scholar
  17. Kolodner, J. (1993).Case-based reasoning. San Mateo, CA: Morgan Kaufmann.Google Scholar
  18. Oaksford, M., &Chater, N. (1994). A rational analysis of the selection task as optimal data selection.Psychological Review,101, 608–631.CrossRefGoogle Scholar
  19. Polk, T. A., &Newell, A. (1995). Deduction as verbal reasoning.Psychological Review,102, 533–566.CrossRefGoogle Scholar
  20. Rips, L.J. (1994).The psychology of proof. Cambridge, MA: MIT Press.Google Scholar
  21. Shastri, L., &Ajjanagadde, V. G. (1990). An optimal limited inference system.In Proceedings of the Eighth National Conference on Artificial Intelligence. Cambridge, MA: MIT Press.Google Scholar
  22. Stenning, K., &Yule, P. (1997). Image and language in human reasoning: A syllogistic illustration.Cognitive Psychology,34, 109–59.CrossRefPubMedGoogle Scholar
  23. Tabossi, P., Bell, V., &Johnson-Laird, P. N. (1999). Mental models in deductive, modal, and probabilistic reasoning. In C. Habel & G. Rickheit (Eds.),Mental models in discourse processing. Berlin: John Benjamins.Google Scholar
  24. Yang, Y. (1996).Predicting the difficulty of predicate-logic inference problems: An empirical examination of a predicate-logic model. Unpublished doctoral dissertation, New York University.Google Scholar
  25. Yang, Y., Braine, M. D. S., &O’Brien, D. P. (1998). Some empirical justifications of the mental predicate-logic model. In M. D. S. Braine & D. P. O’Brien (Eds.),Mental logic (pp. 334–365). Mahwah, NJ: Erlbaum.Google Scholar

Copyright information

© Psychonomic Society, Inc. 2000

Authors and Affiliations

  1. 1.Department of PsychologyPrinceton UniversityPrinceton

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