Advertisement

Minds and Machines

, Volume 27, Issue 1, pp 11–35 | Cite as

Illusions in Reasoning

  • Sangeet S. Khemlani
  • P. N. Johnson-Laird
Article

Abstract

Some philosophers argue that the principles of human reasoning are impeccable, and that mistakes are no more than momentary lapses in “information processing”. This article makes a case to the contrary. It shows that human reasoners commit systematic fallacies. The theory of mental models predicts these errors. It postulates that individuals construct mental models of the possibilities to which the premises of an inference refer. But, their models usually represent what is true in a possibility, not what is false. This procedure reduces the load on working memory, and for the most part it yields valid inferences. However, as a computer program implementing the theory revealed, it leads to fallacious conclusions for certain inferences—those for which it is crucial to represent what is false in a possibility. Experiments demonstrate the variety of these fallacies and contrast them with control problems, which reasoners tend to get right. The fallacies can be compelling illusions, and they occur in reasoning based on sentential connectives such as “if” and “or”, quantifiers such as “all the artists” and “some of the artists”, on deontic relations such as “permitted” and “obligated”, and causal relations such as “causes” and “allows”. After we have reviewed the principal results, we consider the potential for alternative accounts to explain these illusory inferences. And we show how the illusions illuminate the nature of human rationality.

Keywords

Illusory inferences Mental models Deduction Rationality 

References

  1. Adams, E. W. (1998). A primer of probability logic. Stanford, CA: Center for the Study of Language and Information.zbMATHGoogle Scholar
  2. Baratgin, J., Douven, I., Evans, J. S. B. T., Oaksford, M., Over, D., Politzer, G., et al. (2015). The new paradigm and mental models. Trends in Cognitive Sciences, 19, 547–548.CrossRefGoogle Scholar
  3. Bauer, M. I., & Johnson-Laird, P. N. (1993). How diagrams can improve reasoning. Psychological Science, 4, 372–378.CrossRefGoogle Scholar
  4. Bell, V., & Johnson-Laird, P. N. (1998). A model theory of modal reasoning. Cognitive Science, 22, 25–51.CrossRefGoogle Scholar
  5. Boolos, G., & Jeffrey, R. (1989). Computability and logic (3rd ed.). Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  6. Bucciarelli, M., & Johnson-Laird, P. N. (1999). Strategies in syllogistic reasoning. Cognitive Science, 23, 247–303.CrossRefGoogle Scholar
  7. Bucciarelli, M., & Johnson-Laird, P. N. (2005). Naïve deontics: A theory of meaning, representation, and reasoning. Cognitive Psychology, 50, 159–193.CrossRefGoogle Scholar
  8. Byrne, R. M., Espino, O., & Santamaria, C. (1999). Counterexamples and the suppression of inferences. Journal of Memory and Language, 40, 347–373.CrossRefGoogle Scholar
  9. Cohen, L. J. (1981). Can human irrationality be experimentally demonstrated? Behavioral and Brain Sciences, 4, 317–331.CrossRefGoogle Scholar
  10. Cook, S. A. (1971). The complexity of theorem proving procedures. In Proceedings of the third annual association of computing machinery symposium on the theory of computing, pp. 151–158.Google Scholar
  11. Craik, K. (1943). The nature of explanation. Cambridge: Cambridge University Press.Google Scholar
  12. De Neys, W., Schaeken, W., & D’Ydewalle, G. (2003). Inference suppression and semantic memory retrieval: Every counterexample counts. Memory & Cognition, 31, 581–595.CrossRefGoogle Scholar
  13. Evans, J. S. B. T. (2008). Dual-processing accounts of reasoning, judgment, and social cognition. Annual Review of Psychology, 59, 255–278.CrossRefGoogle Scholar
  14. García-Madruga, J. A., Moreno, S., Carriedo, N., Gutiérrez, F., & Johnson-Laird, P. N. (2001). Are conjunctive inferences easier than disjunctive inferences? A comparison of rules and models. Quarterly Journal of Experimental Psychology, 54A, 613–632.CrossRefGoogle Scholar
  15. Gentner, D., & Stevens, A. L. (Eds.). (1983). Mental models. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  16. Goldvarg, Y., & Johnson-Laird, P. N. (2000). Illusions in modal reasoning. Memory & Cognition, 28, 282–294.CrossRefGoogle Scholar
  17. Goldvarg, Y., & Johnson-Laird, P. N. (2001). Naïve causality: A mental model theory of causal meaning and reasoning. Cognitive Science, 25, 565–610.CrossRefGoogle Scholar
  18. Goodwin, G., & Johnson-Laird, P. N. (2010). Conceptual illusions. Cognition, 114, 253–265.CrossRefGoogle Scholar
  19. Hegarty, M. (1992). Mental animation: Inferring motion from static diagrams of mechanical systems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18, 1084–1102.Google Scholar
  20. Henle, M. (1978). Foreword to R. Revlin & R. E. Mayer (Eds.), Human reasoning. Washington, DC: Winston.Google Scholar
  21. Hinterecker, T., Knauff, M., & Johnson-Laird, P. N. (2016). Modality, probability, and mental models. Journal of Experimental Psychology: Learning, Memory, and Cognition, 42, 1606–1620.Google Scholar
  22. Jeffrey, R. (1981). Formal logic: Its scope and limits (2nd ed.). New York: McGraw-Hill.zbMATHGoogle Scholar
  23. Johnson-Laird, P. N. (1983). Mental models: Towards a cognitive science of language, inference, and consciousness. Cambridge: Cambridge University Press; Cambridge, MA: Harvard University Press.Google Scholar
  24. Johnson-Laird, P. N. (2006). How we reason. New York: Oxford University Press.Google Scholar
  25. Johnson-Laird, P. N., & Byrne, R. M. J. (1991). Deduction. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  26. Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: A theory of meaning, pragmatics, and inference. Psychological Review, 109, 646–678.CrossRefGoogle Scholar
  27. Johnson-Laird, P. N., Byrne, R. M. J., & Schaeken, W. (1992). Propositional reasoning by model. Psychological Review, 109, 646–678.CrossRefGoogle Scholar
  28. Johnson-Laird, P. N., Girotto, V., & Legrenzi, P. (2004). Reasoning from inconsistency to consistency. Psychological Review, 111, 640–661.CrossRefGoogle Scholar
  29. Johnson-Laird, P. N., & Hasson, U. (2003). Counterexamples in sentential reasoning. Memory & Cognition, 31, 1105–1113.CrossRefGoogle Scholar
  30. Johnson-Laird, P. N., Khemlani, S. S., & Goodwin, G. P. (2015a). Logic, probability, and human reasoning. Trends in Cognitive Sciences, 19, 201–214.CrossRefGoogle Scholar
  31. Johnson-Laird, P. N., Khemlani, S. S., & Goodwin, G. P. (2015b). Response to Baratgin et al.: Mental models integrate probability and deduction. Trends in Cognitive Sciences, 19, 548–549.CrossRefGoogle Scholar
  32. Johnson-Laird, P. N., Legrenzi, P., Girotto, P., & Legrenzi, M. S. (2000). Illusions in reasoning about consistency. Science, 288, 531–532.CrossRefGoogle Scholar
  33. Johnson-Laird, P. N., Legrenzi, P., Girotto, V., Legrenzi, M., & Caverni, J.-P. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88.CrossRefGoogle Scholar
  34. Johnson-Laird, P. N., Lotstein, M., & Byrne, R. M. J. (2012). The consistency of disjunctive assertions. Memory & Cognition, 40, 769–778.CrossRefGoogle Scholar
  35. Johnson-Laird, P. N., & Savary, F. (1996). Illusory inferences about probabilities. Acta Psychologica, 93, 69–90.CrossRefGoogle Scholar
  36. Johnson-Laird, P. N., & Savary, F. (1999). Illusory inferences: A novel class of erroneous deductions. Cognition, 71, 191–229.CrossRefGoogle Scholar
  37. Juhos, C., Quelhas, A. C., & Byrne, R. M. J. (2015). Reasoning about intentions: Counterexamples to reasons for actions. Journal of Experimental Psychology: Learning, Memory, and Cognition, 41, 55–76.Google Scholar
  38. Juhos, C., Quelhas, A. C., & Johnson-Laird, P. N. (2012). Temporal and spatial relations in sentential reasoning. Cognition, 122, 393–404.CrossRefGoogle Scholar
  39. Khemlani, S. (2016). Automating human inference. In U. Furbach & C. Shon (Eds.), Proceedings of the 2nd IJCAI Workshop on bridging the gap between human and automated reasoning (pp. 1–4). CEUR Workshop Proceedings.Google Scholar
  40. Khemlani, S., & Johnson-Laird, P. N. (2009). Disjunctive illusory inferences and how to eliminate them. Memory & Cognition, 37, 615–623.CrossRefGoogle Scholar
  41. Khemlani, S., & Johnson-Laird, P. N. (2012). Theories of the syllogism: A meta-analysis. Psychological Bulletin, 138, 427–457.CrossRefGoogle Scholar
  42. Khemlani, S. S., Mackiewicz, R., Bucciarelli, M., & Johnson-Laird, P. N. (2013). Kinematic mental simulations in abduction and deduction. Proceedings of the National Academy of Sciences, 110, 16766–16771.CrossRefGoogle Scholar
  43. Khemlani, S., Orenes, I., & Johnson-Laird, P. N. (2012). Negation: A theory of its meaning, representation, and use. Journal of Cognitive Psychology, 24, 541–559.CrossRefGoogle Scholar
  44. Khemlani, S., Orenes, I., & Johnson-Laird, P. N. (2014). The negations of conjunctions, conditionals, and disjunctions. Acta Psychologica, 151, 1–7.CrossRefGoogle Scholar
  45. Knauff, M., Fangmeier, T., Ruff, C. C., & Johnson-Laird, P. N. (2003). Reasoning, models, and images: Behavioral measures and cortical activity. Journal of Cognitive Neuroscience, 4, 559–573.CrossRefGoogle Scholar
  46. Koralus, P., & Mascarenhas, S. (2013). The erotetic theory of reasoning: Bridges between formal semantics and the psychology of deductive inference. Philosophical Perspectives, 27, 312–365.MathSciNetCrossRefGoogle Scholar
  47. Kunze, N., Khemlani, S., Lotstein, M., & Johnson-Laird, P. N. (2010). Illusions of consistency in quantified assertions. In S. Ohlsson & R. Catrambone (Eds.), Proceedings of the 32nd annual conference of the cognitive science society. Austin, TX: Cognitive Science Society.Google Scholar
  48. Legrenzi, P., Girotto, V., & Johnson-Laird, P. N. (2003). Models of consistency. Psychological Science, 14, 131–137.CrossRefGoogle Scholar
  49. Mackiewicz, R., & Johnson-Laird, P. N. (2012). Reasoning from connectives and relations between entities. Memory & Cognition, 40, 266–279.CrossRefGoogle Scholar
  50. Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. San Francisco: W.H. Freeman.Google Scholar
  51. Metzler, J., & Shepard, R. N. (1982). Transformational studies of the internal representations of three-dimensional objects. In R. N. Shepard & L. A. Cooper (Eds.), Mental images and their transformations (pp. 25–71). Cambridge, MA: MIT Press.Google Scholar
  52. Newsome, M. R., & Johnson-Laird, P. N. (2006). How falsity dispels fallacies. Thinking & Reasoning, 12, 214–234.CrossRefGoogle Scholar
  53. Oaksford, M., & Stenning, K. (1992). Reasoning with conditionals containing negated constituents. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18, 835–854.Google Scholar
  54. Polk, T. A., & Newell, A. (1995). Deduction as verbal reasoning. Psychological Review, 102, 533–566.CrossRefGoogle Scholar
  55. Quelhas, A. C., Johnson-Laird, P. N., & Juhos, C. (2010). The modulation of conditional assertions and its effects on reasoning. Quarterly Journal of Experimental Psychology, 63, 1716–1739.CrossRefGoogle Scholar
  56. Quine, W. V. O. (1953). Two dogmas of empiricism. In From a logical point of view (pp. 20–46). Cambridge, MA. Harvard University Press.Google Scholar
  57. Ragni, M., Sonntag, T., & Johnson-Laird, P. N. (2016). Spatial conditionals and illusory inferences. Journal of Cognitive Psychology, 28(3), 348–365.CrossRefGoogle Scholar
  58. Rips, L. J. (1994). The psychology of proof. Cambridge, MA: MIT Press.zbMATHGoogle Scholar
  59. Santamaria, C., & Johnson-Laird, P. N. (2000). An antidote to illusory inferences. Thinking & Reasoning, 6, 313–333.CrossRefGoogle Scholar
  60. Schwartz, D., & Black, J. (1996). Analog imagery in mental model reasoning: Depictive models. Cognitive Psychology, 30, 154–219.CrossRefGoogle Scholar
  61. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701–703.CrossRefGoogle Scholar
  62. Sloutsky, V. M., & Johnson-Laird, P. N. (1999). Problem representations and illusions in reasoning. In Proceedings of the twenty first annual conference of the cognitive science society, pp. 701–705.Google Scholar
  63. Stanovich, K. E. (1999). Who is rational? Studies of individual differences in reasoning. Mahwah, NJ: Erlbaum.Google Scholar
  64. Stenning, K., & van Lambalgen, M. (2008). Human reasoning and cognitive science. Cambridge, MA: MIT Press.Google Scholar
  65. Tabossi, P., Bell, V. A., & Johnson-Laird, P. N. (1998). Mental models in deductive, modal, and probabilistic reasoning. In C. Habel & G. Rickheit (Eds.), Mental models in discourse processing and reasoning (pp. 299–331). Berlin: Elsevier Science.Google Scholar
  66. Walsh, C., & Johnson-Laird, P. N. (2004). Co-reference and reasoning. Memory & Cognition, 32, 96–106.CrossRefGoogle Scholar
  67. Yang, Y., & Johnson-Laird, P. N. (2000a). Illusory inferences in quantified reasoning: How to make the impossible seem possible, and vice versa. Memory & Cognition, 28, 452–465.CrossRefGoogle Scholar
  68. Yang, Y., & Johnson-Laird, P. N. (2000b). How to eliminate illusions in quantified reasoning. Memory & Cognition, 28, 1050–1059.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017 2017

Authors and Affiliations

  1. 1.Naval Research LaboratoryNavy Center for Applied Research in Artificial IntelligenceWashingtonUSA
  2. 2.Naval Research LaboratoryPrinceton UniversityPrincetonUSA
  3. 3.Department of PsychologyNew York UniversityNew YorkUSA

Personalised recommendations