Differences in Interpretation of Implication
Guy Politzer · The American Journal of Psychology · 1981
In a study in which 242 adults interpreted implicative statements by making .judgments of compatibility between sentences and pictures, three patterns of interpretation were found: conjunctive, equivalent, and implicative. There were marked differences across situations (binary or nonbinary) described by the sentences and across groups of subjects (arts or science students). From a learning viewpoint, the three patterns were hierarchically organized in the above order. Subjects gave significantly fewer conjunctive and more implicative interpretations in a transfer task. The presence of conjunctive and implicative patterns may be attributed to implicit conventions of logic and the natural languages. It is generally agreed that among the logical connectives, implication is the one that carries the most problems. Indeed, despite the number of studies that have been devoted to it, most questions remain unanswered. Braine (1978) has presented a formalization of the natural logic in which the status of the connective if . . . plays a central role; in his system, if . . . is the interpretation (in the axiomatic sense) of the inference line that is one of the primitive symbols of the system. According to Braine, it follows from this identification that for ordinary users (that is, nonlogicians) sentences of the form if p then should be construed as irrelevant when p is not true because the inference just cannot be applied. This category of interpretation had been suggested earlier by Wason (1966), and its existence was later partly (Wason, 1968) or completely (Johnson-Laird & Tagart, 1969; Legrenzi, 1970) confirmed. When p and q are true the sentence is evaluated as true, and when p is true and q false it is evaluated as false. Therefore, this interpretation makes use of the three truth values (true, false, irrelevant), which is why Wason called it defective in reference to the two-valued truth tables of propositional logic. By deriving an inferential scheme, Braine showed that in his system if p then has the same truth value as the material implica