The Spontaneous Use of Propositional Connectives

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Abstract
We extend the model theory of reasoning to the understanding and use of propositional connectives, such as and, or, and if. We use a novel paraphrase paradigm to compare the model theory to an alternative one based on rules of inference. In Experiment 1, subjects paraphrased pairs of conditionals. Their general knowledge guided their combination of the antecedents: they used disjunctive descriptions to combine antecedents that were each sufficient to bring about the outcome, and they used conjunctive descriptions to combine antecedents that were both necessary to bring about the outcome. They expressed their combinations using simple connectives such as and or or, as the model theory predicts, rather than hypothetical connectives, such as and if or or if, as the rule theory predicts. Experiment 2 demonstrated the phenomenon in the less constrained task of combining three assertions in a single conditional. Conjunctions and disjunctions are easy to elicit; conditionals have proved far more difficult. The model theory proposes that individuals represent a conditional situation by keeping in mind the described events, but they also keep in mind that there may be alternatives to the events. Therefore, they should use conditionals when they are aware that the events may or may not occur. Experiment 3 corroborated this prediction: subjects used conditionals to combine assertions (with no restrictions on the connective they should use) when the clause describing the outcome contained a modal verb that suggested that the outcome might or might not occur.

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