Which of these cards must be turned over to show that if a card shows an even number on one face, then its opposite face shows a primary color?

Devised in 1966 by Peter Cathcart Wason,[1][2] the Wason selection task, one of the most famous tasks in the psychology of reasoning, is a logic puzzle which is formally equivalent to the following question:

You are shown a set of four cards placed on a table each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) should you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face shows a primary color?

A response which identifies a card which need not be inverted, or a response which fails to identify a card which needs to be inverted are both incorrect. Note that the original task dealt with numbers (even, odd) and letters (vowels, consonants).

## Solution

The response Wason considered correct was to turn the cards showing 8 and brown, but no other card. Remember how the question was stated: "If the card shows an even number, then its opposite face shows a primary color." If we turn over the card labelled "3" and find that it is red, this does not invalidate the rule. Likewise, if we turn over the red card and find that it has the label "3", this also does not make the rule false. On the other hand, if the brown card has the label "4", this invalidates the rule: it has an even number, but does not have a primary color. The interpretation of "if" here is that of the material conditional in classical logic.

## Explanations of performance on the task

Some authors have argued that participants do not read "if... then..." as the material conditional, since the natural language conditional is not the material conditional.[3][4] (See also the paradoxes of the material conditional for more information.) However one interesting feature of the task is how participants react when the classical logic solution is explained:

A psychologist, not very well disposed toward logic, once confessed to me that despite all problems in short-term inferences like the Wason Card Task, there was also the undeniable fact that he had never met an experimental subject who did not understand the logical solution when it was explained to him, and then agreed that it was correct.[5]

The selection task tends to produce the "correct" response when presented in a context of social relations. For example, if the rule used is "If you are drinking alcohol then you must be over 18", and the cards have an age on one side and beverage on the other, e.g., "17", "beer", "22", "coke", most people have no difficulty in selecting the correct cards ("17" and "beer").

Adherents of evolutionary psychology have argued that a simple rule distinguishes Wason tasks which people find easy from those that they find difficult. The suggested rule is that a Wason task proves to be easier if the rule to be tested is one of social exchange (in order to receive benefit X you need to fulfill condition Y) and the subject is asked to police the rule, but is more difficult otherwise. If this classification is accepted, then it supports the contention of evolutionary psychologists that certain features of human psychology may be mechanisms that have evolved, through natural selection, to solve specific problems of social interaction, rather than expressions of general intelligence.[6]

## References

1. ^ Wason, P. C. (1966). "Reasoning". in Foss, B. M.. New horizons in psychology. Harmondsworth: Penguin.
2. ^ Wason, P. C. (1971). "Natural and contrived experience in a reasoning problem". Quarterly Journal of Experimental Psychology 23: 63–71. doi:10.1080/00335557143000068.
3. ^ Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101, 608-631.
4. ^ Stenning, K. and van Lambalgen, M. (2004). A little logic goes a long way: basing experiment on semantic theory in the cognitive science of conditional reasoning. Cognitive Science, 28(4):481–530.
5. ^ Johan van Benthem (2008). Logic and reasoning: do the facts matter? Studia Logica, 88(1), 67-84
6. ^ Cosmides, L.; Tooby, J. (1992). Barkow et al.. ed. Cognitive Adaptions for Social Exchange. New York: Oxford University Press.  [[1]]