A necessity illusion for modal inferences from conditionals

Three experiments examined how people reason about what is possible or necessary when a conditional is true. Participants were asked to indicate whether it was necessary, possible or impossible for a specific instance to conform to one of the truth-table cases (pq, p¬q, ¬pq and ¬p¬q) (¬ = not), given the truth of the conditional. It was found that most participants, inconsistently, judged the pq case as necessary but the ¬pq or ¬p¬q cases as possible. Logically, these two kinds of judgments are contradictory. Moreover, a true conditional doesn’t imply that a specific instance under the conditional must be pq . Therefore, people demonstrate a necessity illusion for pq cases which contradicts their commitment to the possibility of ¬pq or ¬p¬q cases. Existing accounts of conditionals are unable to explain the contradiction and the necessity illusion. We propose an inference dissociation account and explore the theoretical implications of this necessity illusion.