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Each card has a number on one side and a patch of color on the other. Which card or cards must be turned over to test the idea that if a card shows an even number on one face, then its opposite face is red?

The Wason selection task (or four-card problem) is a logic puzzle devised by Peter Cathcart Wason in 1966.[1][2][3] It is one of the most famous tasks in the study of deductive reasoning.[4] An example of the puzzle is:

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) must 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 is red?

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

The test is of special interest because people have a hard time solving it in most scenarios but can usually solve it correctly in certain contexts. In particular, researchers have found that the puzzle is readily solved when the imagined context is policing a social rule.

## Solution

The correct response is to turn over the 8 card and the brown card.

The rule was "If the card shows an even number on one face, then its opposite face is red." Only a card with both an even number on one face and something other than red on the other face can invalidate this rule:

• If the 3 card is red (or brown), that doesn't violate the rule. The rule makes no claims about odd numbers. (Denying the antecedent)
• If the 8 card is not red, it violates the rule. (Modus ponens)
• If the red card is odd (or even), that doesn't violate the rule. The red color is not exclusive to even numbers. (Affirming the consequent)
• If the brown card is even, it violates the rule. (Modus tollens)

### Use of logic

The interpretation of "if" here is that of the material conditional in classical logic, so this problem can be solved by choosing the cards using modus ponens (all even cards must be checked to ensure they are red) and modus tollens (all non-red cards must be checked to ensure they are non-even).

Alternatively, one might solve the problem by using another reference to zeroth-order logic. In classical propositional logic, the material conditional is false if and only if its antecedent is true and its consequent is false. As an implication of this, two cases need to be inspected in the selection task to check whether we are dealing with a false conditional:

• The case in which the antecedent is true (the even card), to examine whether the consequent is false (the opposite face is not red).
• The case in which the consequent is false (the brown card), to study whether the antecedent is true (the opposite face is even).

## Explanations of performance on the task

In Wason's study, not even 10% of subjects found the correct solution.[5] This result was replicated in 1993.[6]

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.[7][8][9] (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.[10]

This latter comment is also controversial, since it does not explain whether the subjects regarded their previous solution incorrect, or whether they regarded the problem sufficiently vague to have two interpretations.

### Policing social rules

As of 1983, experimenters had identified that success on the Wason selection task was highly context-dependent, but there was no theoretical explanation for which contexts elicited mostly correct responses and which ones elicited mostly incorrect responses.[11]

Each card has an age on one side and a drink on the other. Which card(s) must be turned over to test the idea that if you are drinking alcohol, then you must be over 18?

Evolutionary psychologists Leda Cosmides and John Tooby (1992) identified that the selection task tends to produce the "correct" response when presented in a context of social relations.[11] 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., "16", "drinking beer", "25", "drinking soda", most people have no difficulty in selecting the correct cards ("16” and "drinking beer").[11] In a series of experiments in different contexts, subjects demonstrated consistent superior performance when asked to police a social rule involving a benefit that was only legitimately available to someone who had qualified for that benefit.[11] Cosmides and Tooby argued that experimenters have ruled out alternative explanations, such as that people learn the rules of social exchange through practice and find it easier to apply these familiar rules than less-familiar rules.[11]

According to Cosmides and Tooby, this experimental evidence supports the hypothesis 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. They argued that such a distinction, if empirically borne out, would support the contention of evolutionary psychologists that human reasoning is governed by context-sensitive mechanisms that have evolved, through natural selection, to solve specific problems of social interaction, rather than context-free, general-purpose mechanisms.[11] In this case, the module is described as a specialized cheater-detection module.[11]

#### Evaluation of social relations hypothesis

Davies et al. (1995) have argued that Cosmides and Tooby's argument in favor of context-sensitive, domain-specific reasoning mechanisms as opposed to general-purpose reasoning mechanisms is theoretically incoherent and inferentially unjustified.[12] Von Sydow (2006) has argued that we have to distinguish deontic and descriptive conditionals, but that the logic of testing deontic conditionals is more systematic (see Beller, 2001) and depend on one's goals (see Sperber & Girotto, 2002).[9][13][14] However, in response to Kanazawa (2010),[15] Kaufman et al. (2011) gave 112 subjects a 70-item computerized version of the contextualized Wason card-selection task proposed by Cosmides and Tooby (1992) and found instead that "performance on non-arbitrary, evolutionarily familiar problems is more strongly related to general intelligence than performance on arbitrary, evolutionarily novel problems",[16] and writing for Psychology Today, Kaufman concluded instead that "It seems that general intelligence is very much compatible with evolutionary psychology."[17]

## References

1. ^ Wason, P. C. (1968). "Reasoning about a rule". Quarterly Journal of Experimental Psychology. 20 (3): 273–281. doi:10.1080/14640746808400161. PMID 5683766. S2CID 1212273.
2. ^ Wason, P. C. (1966). "Reasoning". In Foss, B. M. (ed.). New horizons in psychology. Vol. 1. Harmondsworth: Penguin. LCCN 66005291.
3. ^ Wason, P. C.; Shapiro, Diana (1971). "Natural and contrived experience in a reasoning problem". Quarterly Journal of Experimental Psychology. 23: 63–71. doi:10.1080/00335557143000068. S2CID 7903333.
4. ^ Manktelow, K. I. (1999). Reasoning and Thinking. Psychology Press. p. 8. ISBN 978-0-86377-708-0. The Wason selection task has often been claimed to be the single most investigated experimental paradigm in the psychology of reasoning.
5. ^ Wason, P. C. (1977). "Self-contradictions". In Johnson-Laird, P. N.; Wason, P. C. (eds.). Thinking: Readings in cognitive science. Cambridge: Cambridge University Press. ISBN 978-0521217569.
6. ^ Evans, Jonathan St. B. T.; Newstead, Stephen E.; Byrne, Ruth M. J. (1993). Human Reasoning: The Psychology of Deduction. Psychology Press. ISBN 978-0-86377-313-6.
7. ^ Oaksford, M.; Chater, N. (1994). "A rational analysis of the selection task as optimal data selection". Psychological Review. 101 (4): 608–631. CiteSeerX 10.1.1.174.4085. doi:10.1037/0033-295X.101.4.608.
8. ^ Stenning, K.; 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. CiteSeerX 10.1.1.13.1854. doi:10.1016/j.cogsci.2004.02.002.
9. ^ a b von Sydow, M. (2006). Towards a Flexible Bayesian and Deontic Logic of Testing Descriptive and Prescriptive Rules. Göttingen: Göttingen University Press. doi:10.53846/goediss-161. S2CID 246924881.
10. ^ van Benthem, Johan (2008). "Logic and reasoning: do the facts matter?". Studia Logica. 88 (1): 67–84. CiteSeerX 10.1.1.130.4704. doi:10.1007/s11225-008-9101-1. S2CID 11228131.
11. Cosmides, L.; Tooby, J. (1992). "Cognitive Adaptions for Social Exchange" (PDF). In Barkow, J.; Cosmides, L.; Tooby, J. (eds.). The adapted mind: Evolutionary psychology and the generation of culture. New York: Oxford University Press. pp. 163–228. ISBN 978-0-19-506023-2.
12. ^ Davies, Paul Sheldon; Fetzer, James H.; Foster, Thomas R. (1995). "Logical reasoning and domain specificity". Biology and Philosophy. 10 (1): 1–37. doi:10.1007/BF00851985. S2CID 83429932.
13. ^ Beller, S. (2001). "A model theory of deontic reasoning about social norms". In Moore, J. D.; Stenning, K. (eds.). Proceedings of the 23rd Annual Conference of the Cognitive Science Society. Mahwah, NJ: Lawrence Erlbaum. pp. 63–68.
14. ^ Sperber, D.; Girotto, V. (2002). "Use or misuse of the selection task?". Cognition. 85 (3): 277–290. CiteSeerX 10.1.1.207.3101. doi:10.1016/s0010-0277(02)00125-7. PMID 12169412. S2CID 2086414.
15. ^ Kanazawa, Satoshi (May–June 2010). "Evolutionary Psychology and Intelligence Research" (PDF). American Psychologist. 65 (4): 279–289. doi:10.1037/a0019378. PMID 20455621. Retrieved February 16, 2018.
16. ^ Kaufman, Scott Barry; DeYoung, Colin G.; Reis, Deidre L.; Gray, Jeremy R. (May–June 2010). "General intelligence predicts reasoning ability even for evolutionarily familiar content" (PDF). Intelligence. 39 (5): 311–322. doi:10.1016/j.intell.2011.05.002. Retrieved February 16, 2018.
17. ^ Kaufman, Scott Barry (July 2, 2011). "Is General Intelligence Compatible with Evolutionary Psychology?". Psychology Today. Sussex Publishers. Retrieved February 16, 2018.