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Critical Thinking mini-lesson 3
One of the nicer features of the James Randi Educational Foundation's Amazing Meeting earlier this year was the time set aside for mini-talks by those responding to a call for papers. One of those talks was given by Dr. Jeff Corey, who teaches experimental psychology at C. W. Post College. His talk was on "The Wason Card Problem" and its role in teaching critical thinking skills. Four cards are presented: A, B, 4, and 7. There is a letter on one side of each card and a number on the other side. Which card(s) must you turn over to determine whether the following statement is false? "If a card has a vowel on one side, then it has an even number on the other side."
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(I suggest you spend a few minutes trying to solve the problem before continuing.)
(I hope you have been able to restrain yourself from jumping ahead and have worked out your solution to the problem. Before continuing, try to solve the following alternative version: Let the cards show "beer," "cola," "16 years," and "22 years." On one side of each card is the name of a drink; on the other side is the age of the drinker. What card(s) must be turned over to determine if the following statement is false? If a person is drinking beer, then the person is over 19-years-old.)
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I gave the Wason Card Problem to 100 students last semester and only seven got it right, which was about what was expected. There are various explanations for these results. One of the more common explanations is in terms of confirmation bias. This explanation is based on the fact that the majority of people think you must turn over cards A and 4, the vowel card and the even-number card. It is thought that those who would turn over these cards are thinking "I must turn over A to see if there is an even number on the other side and I must turn over the 4 to see if there is a vowel on the other side." Such thinking supposedly indicates that one is trying to confirm the statement If a card has a vowel on one side, then it has an even number on the other side. Presumably, one is thinking that if the statement cannot be confirmed, it must be false. This explanation then leads to the question: Why do most people try to confirm a statement, when the task is to determine if it is false? One explanation is that people tend to try to fit individual cases into patterns or rules. The problem with this explanation is that in this case we are instructed to find cases that don't fit the rule. Is there some sort of inherent resistance to such an activity? Are we so driven to fit individual cases to a rule that we can't even follow a simple instruction to find cases that don't fit the rule? Or, are we so driven that we tend to think that the best way to determine whether an instance does not fit a rule is to try to confirm it and if it can't be confirmed then, and only then, do we consider that the rule might be wrong?
Corey noted that when the problem is changed from abstract items, such as numbers and letters, and put in concrete terms, such as drinks and the age of the drinker, the success rate significantly increases (see the example described above). One would think that confirmation bias would lead most people to say they must turn over the beer card and the 22 card, but they don't. Most people see that the cola and 22 cards are irrelevant to solving the problem. If I remember correctly, Corey explained the difference in performance between the abstract and concrete versions of the problem in terms of evolutionary psychology: Humans are hardwired to solve practical, concrete problems, not abstract ones. To support his point, he says he simplified the abstract test to include only two cards (showing 1 and 2) with equally poor results.
I had discussed confirmation bias, but not conditional statements, with my classes before giving them the Wason problem. The majority seemed to understand confirmation bias; so, if the reason so many do so poorly on this problem is confirmation bias, then just knowing about confirmation bias is not much help in overcoming it as a hindrance to critical thinking. This is consistent with what I teach. Recognition of a hindrance is a necessary but not a sufficient condition for overcoming that hindrance. However, next semester I'm going to give my students the Wason test after I discuss determining the truth-value of conditional statements. The reason for doing so is that anyone who has studied the logic of conditional statements should know that a conditional statement is false if and only if the antecedent is true and the consequent is false. (The antecedent is the if statement; the consequent is the then statement.) So, the statement If a card has a vowel on one side, then it has an even number on the other side can only be false if the statement a card has a vowel on one side is true and the statement it has an even number on the other side is false. I must look at the card with the vowel showing to find out what is on the other side because it could be an odd number and thus would show me that the statement is false. I must also look at the card with the odd number to find out what is on the other side because it could be a vowel and thus would show me that the statement is false. I don't need to look at the card with the consonant because the statement I am testing has nothing to do with consonants. Nor do I need to look at the card with the even number showing because whether the other side has a vowel or a consonant will not help me determine whether the statement is false.
There is a possibility that the reason many think that the even-numbered card must be turned over is that they mistakenly think that the statement they are testing implies that if a card has an even number on one side then it cannot have a consonant on the other. In other words, it is possible that the high error rate is due to misunderstanding logical implication rather than confirmation bias. In the concrete version of the problem, perhaps it is much easier to see that the statement If a person is drinking beer, then the person is over 19-years-old does not imply that if a person is over 19 then they cannot be drinking cola. If this is the case, then an explanation in terms of the difference between contextual implication and logical implication might be better than one in terms of confirmation bias. Perhaps it is the context of drinking and age of the drinker that indicates to many people that a person can be over 19 and not drink beer without falsifying the statement being tested, i.e., that simply because if you're drinking beer you are over 19 doesn't imply that if you're over 19 you can't be drinking cola. That is, in the concrete case people may not have any better understanding of logical implication than they do in the abstract case and neither case may have anything to do with confirmation bias.
On the other hand, some might reason that if I turn over the even card and find a vowel, then I have confirmed the statement, which is in effect the same as showing that the statement is not false, but true. This would be classic confirmation bias. Finding an instance that confirms the rule does not prove the rule is true. But, finding one instance that disproves the rule shows that the rule is false.
lesson 4: Wason Problem continued
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