upright=1.35|right|thumb|Each card has a number on one side and 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 blue? <!-- BE CAREFUL ABOUT CHANGING THIS CAPTION. The whole point of the Wason task is to demonstrate that people make mistakes when thinking about this stuff; several past version of the caption have... made mistakes in thinking about this stuff.-->

In psychology, the Wason selection task (or four-card problem) is a logic puzzle devised by Peter Cathcart Wason in 1966. It is one of the most famous tasks in the study of deductive reasoning. An example of the puzzle is:

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 red card.

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

  • If the 3 card is blue (or red), that doesn't violate the rule. The rule makes no claims about odd numbers. (Denying the antecedent)
  • If the 8 card is not blue, it violates the rule. (Modus ponens)
  • If the blue card is odd (or even), that doesn't violate the rule. The blue color is not exclusive to even numbers. (Affirming the consequent)
  • If the red 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 blue) and modus tollens (all non-blue cards must be checked to ensure they are non-even).

One experiment revolving around the Wason four card problem found many influences on people's selection in this task experiment that were not based on logic. The non-logical inferences made by the participants from this experiment demonstrate the possibility and structure of extra-logical reasoning mechanisms.

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 blue).
  • The case in which the consequent is false (the red 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, which for the specific criteria of this problem, would be the 8 card and the red card. This result was replicated in 1993. The poor success rate of this selection experiment may be explained by its lack of relevant significance. If this task was reframed, however, empirical evidence has shown an increase in logical responses.

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.

Wason also ascribes participants' errors on this selection task due to confirmation bias. Confirmation bias compels people to seek the cards which confirm the rule; meanwhile, they overlook the main purpose of the experiment, which is to purposefully choose the cards that potentially disconfirm the rule.

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. In this case, the module is described as a specialized cheater-detection module. 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). However, in response to Kanazawa (2010), 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", and writing for Psychology Today, Kaufman concluded instead that "It seems that general intelligence is very much compatible with evolutionary psychology."

See also

  • Cognition
  • Cognitive reflection test
  • Confirmation bias
  • Evolution of human intelligence
  • Logic
  • Necessary and sufficient conditions
  • Psychology of reasoning

References