Which alternatives matter? The role of the Question Under Discussion and speaker knowledge in conditionals

Abstract

Conditional perfection (CP) is often analyzed as a quantity implicature that arises when “if p, q” is strengthened by excluding relevant alternatives to p. If this analysis is correct, CP should not arise in contexts that do not license exhaustification, such as when the Question Under Discussion (QUD) does not make alternative antecedents salient, or when the speaker cannot be assumed to know them. To date, experimental studies on CP have revealed limited or inconclusive evidence in support of these typical signatures of quantity implicatures. In two experiments, we demonstrate robust support for both signatures: Experiment 1 found that CP arose only when the conditional answered an antecedent-focused QUD; consequent-focused and neutral QUDs did not lead to perfection. Experiment 2 showed that CP was further constrained by the speaker’s epistemic access: listeners computed a perfected reading only when the speaker appeared to know the full set of relevant antecedents. Our findings provide robust evidence that both QUD and the speaker’s knowledge state influence the interpretation of conditional statements and that CP is indeed a quantity implicature.