Which Possibility is Necessaryfor Basic Conditionals?

A current dispute in the psychology of conditionals is which possibility is necessary for basic conditionals such as if p then q. There are three accounts with different predictions about the question. The original model theory predicts that if p then q means the disjunction of three possibilities: possibly pq or possibly ¬pq or possibly ¬p¬q ( ¬ = “not”), in which each is unnecessary. The revised model theory predicts that it means the conjunction of the three possibilities, in which each is necessary. The suppositional theory predicts that people interpret it as a hypothetical test based on the conditional probability of p given q, in which only the pq possibility is necessary. Two experiments investigated possibility and truth judgments about basic conditionals given sets that consist of one or more of the four truth table cases of basic conditionals. The results demonstrate that both judgments approximate to the prediction of the suppositional theory rather than the original and revised model theory, and so people show the suppositional interpretation of basic conditionals, in which only the pq possibility is necessary for basic conditionals. Only the pq possibility is necessary for judging a basic conditional true. A true basic conditional mentally implies that only the pq possibility is necessary. These findings support the suppositional theory, but not the original and revised model theory.