There is a King in the hand or there is an Ace, or both.Nearly everyone responds 'yes' (Johnson-Laird and Goldvarg 1997). Yet, the response is a fallacy. If there were an Ace in the hand, then two of the assertions would be true, contrary to the rubric that only one of them is true. The illusion arises because individuals' mental models represent what is true for each premise, but not what is false concomitantly for the other two premises. A variety of such illusions occur in all the main domains of reasoning. They can be reduced by making what is false more salient.
There is a Queen in the hand or there is an Ace, or both.
There is a Jack in the hand or there is a Ten, or both.
Is it possible that there is an Ace in the hand?
Craik, K. (1943). The Nature of Explanation. Cambridge: Cambridge University Press.
Ehrlich, K. (1996). Applied mental models in human-computer interaction. In J. Oakhill and A. Garnham (Eds.), Mental Models in Cognitive Science. Mahwah, NJ: Lawrence Erlbaum Associates; Hove, Sussex, UK: Erlbaum (UK) Taylor and Francis.
Garnham, A. and J.V. Oakhill. (1996). The mental models theory of language comprehension. In B.K. Britton and A.C. Graesser (Eds.), Models of Understanding Text. Hillsdale, NJ: Lawrence Erlbaum Associates. pp. 313-339.
Gentner, D. and A.L. Stevens (Eds.). (1983). Mental Models. Hillsdale, NJ: Lawrence Erlbaum Associates.
Halford, G.S. (1993). Children's Understanding: The Development of Mental Models. Hillsdale, NJ: Lawrence Erlbaum Associates.
Halpern, J.Y. and M.Y. Vardi. (1991). Model checking vs. theorem proving: a manifesto. In J.A. Allen, R. Fikes and E. Sandewall (Eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference. San Mateo, CA: Morgan Kaufmann, pp. 325-334.
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.
Johnson-Laird, P.N. and R.M.J. Byrne. (1991). Deduction. Hillsdale, NJ: Lawrence Erlbaum Associates.
Johnson-Laird, P.N. and Y. Goldvarg. (1997). How to make the impossible seem possible. Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society. Stanford, CA. Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 354-357.
Johnson-Laird, P.N. and F. Savary. (1996). Illusory inferences about probabilities. Acta Psychologica 93: 69-90.
Kuipers, B. (1994). Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge. Cambridge, MA: MIT Press.
Marr, D. (1982). Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. San Francisco: W.H. Freeman.
Byrne, R.M.J. (1996). A model theory of imaginary thinking. In J. Oakhill and A. Garnham (Eds.), Mental Models in Cognitive Science. Hove: Erlbaum (UK) Taylor and Francis. pp. 155-174.
Garnham, A. (1987). Mental Models as Representations of Discourse and Text. Chichester: Ellis Horwood.
Glasgow, J.I. (1993). Representation of spatial models for geographic information systems. In N. Pissinou (Ed.), Proceedings of the ACM Workshop on Advances in Geographic Information Systems. Arlington, VA: Association for Computing Machinery, pp. 112-117.
Glenberg, A.M., M. Meyer and K. Lindem. (1987). Mental models contribute to foregrounding during text comprehension. Journal of Memory and Language. 26: 69-83.
Hegarty, M. (1992). Mental animation: inferring motion from static diagrams of mechanical systems. Journal of Experimental Psychology: Learning, Memory, and Cognition 18: 1084-1102.
Johnson-Laird, P.N. (1993). Human and Machine Thinking. Hillsdale, NJ: Lawrence Erlbaum Associates.
Legrenzi, P., V. Girotto and P.N. Johnson-Laird. (1993). Focussing in reasoning and decision making. Cognition. 49: 37-66.
Moray, N. (1990). A lattice theory approach to the structure of mental models. Philosophical Transactions of the Royal Society of London, Series B 327: 577-583.
Polk, T.A. and A. Newell. (1995). Deduction as verbal reasoning. Psychological Review 102: 533-566.
Rogers, Y., A. Rutherford and P.A. Bibby (Eds.). Models in the Mind: Theory, Perspective and Application. London: Academic Press.
Schaeken, W., P.N. Johnson-Laird and G. d'Ydewalle. (1996). Mental models and temporal reasoning. Cognition 60: 205-234.
Schwartz, D. (1996). Analog imagery in mental model reasoning: Depictive models. Cognitive Psychology 30: 154-219.
Stevenson, R.J. (1993). Language, Thought and Representation. New York: Wiley.