This paper presents novel empirical observations showing that
counterfactuals and conditionals involving a contrast between events
generate the implicature that their consequent is false, in addition to the
well-known implicature that the antecedent is false. I show that existing
compositional theories which predict the falsity of the antecedent do not
predict the falsity of the consequent, and propose an extension of Starr's
unified semantics (Starr, 2014) to capture it. I also examine the effect of
this new implicature on minimal model generation for conditionals,
providing algorithms for generating minimal models capturing the falsity of
the antecedent for counterfactuals, the consistency of presuppositions with
the actual world (Ippolito, 2003; Starr, 2014) for indicative and future
subjunctive conditionals, and this newly observed falsity of the consequent.