Introduction to Cognitive Science


The correct answer is...

There is NO King in the hand !!

Here's why:

Consider the following statements about a hand of cards:

  1. If there is a Jack in the hand, then there is a King in the hand, or else if there's no Jack in the hand, then there is a King in the hand.

  2. There is a Jack in the hand.

These 2 sentences can be represented in propositional logic as follows:

  1. [(J -> K) v (~J -> K)] & ~[(J -> K) & (~J -> K)]

    (i.e., Either: if there's a Jack, then there's a King,
                or: If there's no Jack, then there's a King,
                      but not both.

  2. J
On Johnson-Laird's mental-models theory, the situation would be represented instead as follows:


But if you do a truth-table analysis of (1) and (2) (just assign "true" or "false" to J and K--there are 4 possible combinations--then compute the truth values of (1) and (2)), you will see that:

Consequently, only 2 situations are really possible, and in both, K is false. Moreover, neither of the possible situations are represented in the mental-model theory.

For more information, see:

  1. Laird-Johnson, P.N.; Girotto, Vittorio; & Legrenzi, Paolo (1998), "Mental Models: A Gentle Guide for Outsiders"

  2. Selmer Bringsjord, Ron Noel, Elizabeth Bringsjord (1998), "In Defense of Logical Minds"

  3. Johnson-Laird, Philip N. (1983), Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness (Cambridge, MA: Harvard University Press).

  4. Rips, Lance J. (1994), The Psychology of Proof: Deductive Reasoning in Human Thinking (Cambridge, MA: MIT Press).

  5. Johnson-Laird, Philip N. (1997), "Rules and Illusions: A Critical Study of Rips's The Psychology of Proof", Minds and Machines 7(3): 387-407.

  6. Rips, Lance J. (1997), "Goals for a Theory of Deduction: Reply to Johnson-Laird", Minds and Machines 7(3): 409-424.

  7. Johnson-Laird, Philip N. (1997), "An End to the Controversy? A Reply to Rips", Minds and Machines 7(3): 425-432.

  8. Fetzer, James H. (1999), "Deduction and Mental Models", Minds and Machines 9(1): 105-110.

  9. Johnson-Laird, Philip N., & Byrne, Ruth M.J. (1999), "Models Rule, OK? A Reply to Fetzer", Minds and Machines 9(1): 111-118.

  10. Fetzer, James H. (1999), "Mental Models: Reasoning without Rules", Minds and Machines 9(1): 119-126.

Copyright © 2001 by William J. Rapaport (
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