AAP 2026 CONFERENCE

Trivalent accounts of conditionals imply that an indicative conditional ""if A then C"" gets the value undefined when the antecedent A is false. Due to how they handle negation, these theories appear to wrongly predict that an indicative conditional presupposes the truth of its antecedent. However, as argued by Stalnaker (1975), the utterance of a conditional presupposes something weaker, namely that the antecedent is compatible with the context of utterance.

In the first part of this paper, we use the trivalent framework for indicative conditionals and epistemic modals presented recently by Egré, Rossi and Sprenger (ERS) in ""Trivalent conditionals, Kratzer style'' to resolve this tension and to adequately derive this Stalnakerian presupposition. We derive it from the fact that (i) conditionals and modals are evaluated not merely extensionally, but relative to an information state, and (ii) from a particular instance of Grice's Maxim of Quantity, which we call ""Avoid Void''.

In the second part, we use this principle to restrict some problematic inferences of the connexive logic of conditionals put forward by Cooper (1968) and recast by ERS (2025) as a logic of certainty preservation, like the entailment from ""not A"" to ""if A then C"" (for A, C factual).