Reasoning Experiments

In this section, we describe two experiments about deductive reasoning.

The Wason Selection Task

The first experiment, known as the Wason Selection Task, was devised in 1966 by the psychologist Peter Wason. This experiment had a profound effect on the study of the psychology of reasoning. It has generated a lot of discussion among philosophers and psychologists, and has inspired many follow-up experiments.

In the original experiment, people are presented with the following task:

You are shown a set of four cards, each of which has a number on one side and a letter on the other side. Also below is a rule which applies only to the four cards. Your task is to decide which if any of these four cards you must turn in order to decide if the rule is true. Don't turn unnecessary cards.

Rule: If there is a vowel on one side, then there is an even number on the other side.

(if you click on a card, you will see an explanation using propositional logic about whether you should/should not turn over the card.)

A

K

2

5

If the rule is interpreted as a conditional statement in propositional logic, then the correct answer is to flip both the A and 5 cards (and do not flip the K and 2 cards). In Wason's original experiment, very few people (less than 10%) chose to flip only the A and 5 cards. This outcome seems to suggest that human reasoning is very different than what is found in propositional logic. However, further experiments have shown that the responses that people provide are very sensitive to many features of the task.

For example, people tend to choose both the A and 5 card when asked to evaluate the following variation of the rule from Wason's original experiment:

Rule 2: If there is a vowel on one side, then there is not an odd number on the other side.

The different responses in these two variations of the task is very interesting since "the number on the card is not odd" is equivalent to "the number on the card is even".

A second variant of the Wason selection task in which people's responses tend to match what is predicted by propositional logic is the following:

Suppose that you're working as a security executive in a bar (you're a bouncer). It's your job to ensure that the rule governing the consumption of alcohol is strictly enforced. It states:

Rule: If a person drinks an alcoholic drink, then they must be over the age of 21 years old.

Please indicate which card or cards you definitely need to turn over, and only that or those cards, in order to determine whether the rule is broken in the case of each of the four customers.

Even though the logical form of this task is the same as Wason's original task, most people choose both the Beer and 17 card (this is analogous to choosing both the A and 5 card in Wason's original task).

Suppression Task

A second experiment about deductive reasoning, known as the Suppression Task, was devised in 1989 by the psychologist Ruth M. J. Byrne. In the experiment, three groups of people were asked to derive conclusions given a set of premises. The first group was given the following two premises:

1. If she has an essay to finish, then she will study late in the library.
2. She has an essay to finish.

The people in the first group were asked which of the sentences necessarily follows assuming that the above two premises are true.

1. She will study late in the library.
2. She will not study late in the library.
3. She may or may not study late in the library.

This task is asking participants to apply the Modus Ponens inference rule. The two premises have the logical form "$E\rightarrow S$" and "$E$" where $E$ means "she has an essay to finish" and $S$ means "she will study late in the library". According to Modus Ponens, the first answer ($S$) follows from $E\rightarrow S$ and $E$. This is the answer that was chosen by almost all the participants in the first group. The same answer was chosen by almost all the participants in a second group that were provided with the following three premises:

1. If she has an essay to finish, then she will study late in the library.
2. If she has a textbook to read, then she will study late in the library.
3. She has an essay to finish.

Interestingly, the participants in a third group did not choose the same answer when provided the following three premises:

1. If she has an essay to finish, then she will study late in the library.
2. If the library stays open, then she will study late in the library.
3. She has an essay to finish.

In Byrne's experiment, about 96% of the participants in groups 1 and 2 conclude that "she will study late in the library" while only 38% of the participants in group 3 came to the same conclusion. In the third group, the presence of the second premise suppressed the application of Modus Ponens. These responses are not what is predicted by propositional logic. Since the order of the premises does not matter and valid inference satisfies the monotonicity property (see the discussion in the chapter on Valid and Invalid Inference Rules): For all formulas $X$, $Y$ and $Z$:

If $X\rightarrow Y, X\models Y$, then $X\rightarrow Y, Z, X\models Y$.

The Suppression Task concerns situations in which there are some statements $Z$ that suppress the valid inference $X\rightarrow Y,X\models Y$.

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The Wason Selection Task, the Suppression Task and related experiments do highlight ways that human reasoning deviates from the strict patterns of inference found in propositional logic. But this is just the beginning of the story about logic and human reasoning. Inspired in part by these experiments, modern research in logic highlights both weaker forms of rules of inference and the important role that representation plays in reasoning tasks.