Five Empirical Phenomena

Psychological investigations have established five principal phenomena of deductive reasoning. The first phenomenon is that the more possibilities that reason-ers have to envisage to draw an inference, the more difficult the inference—it takes them longer, and they are more likely to make a mistake. A simple example is that inferences based on a disjunction are more difficult when the disjunction is inclusive, as in the preceding example, than when it is exclusive and allows only two possibilities: "The switches are on or the brakes are on, but not both.'' The same effect of number of possibilities occurs in reasoning with other sentential connectives, in reasoning about spatial and temporal relations, and in reasoning with premises containing quantifiers, such as "all," "some," and "none."

The second phenomenon is that reasoners use counterexamples to establish invalidity. When reason-ers draw conclusions for themselves, they may not consider counterexamples. However, when they reject a conclusion, they can do so by constructing a counterexample—that is, they envisage a possibility that satisfies the premises but refutes the conclusion. One experiment, for example, used problems, such as

More than half of the people in the room speak French.

More than half of the people in the room speak English.

Does it follow that more than half of the people in the room speak both French and English?

Most people responded correctly, "no," and they typically reported having envisaged a situation analogous to the one represented in Fig. 1. They drew such diagrams when they were allowed paper and pencil.

French speaking

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