A Contradiction between Necessity and Possibility Inferences from General Conditionals

The author investigated the relationship between possibility and necessity inferences from general conditionals (e.g., If a card is red, then it is round). An experiment examined how people reason about what cases are possible or necessary under a general conditional. Participants were asked to infer whether each truth-table cases (pq, p¬q, ¬pq and ¬p¬q) (¬ = not) must be in the set of cases under a true general conditional, and whether the combinatorial sets of the four truth-table cases are possible under the conditional. The test order of necessity and possibility questions was varied with the NP (necessity/possibility questions) and PN (possibility/necessity questions) group. The findings are as follows. The test order did not affect the relationship between possibility and necessity inferences for each of p¬q, ¬pq and ¬p¬q cases. It affected the relationship between necessity inferences for pq cases and possibility inferences for the sets including only ¬pq or ¬p¬q cases. The NP group more often showed the contradiction between these two inferences than the PN group. The existing main accounts of conditionals are unable to explain the contradiction. Alternatively, the author proposes an inference dissociation account for it.