Ciardelli, Zhang, and Champollion (2018b) adopt the framework of inquisitive semantics to provide a novel semantics for counterfactuals. They argue in favour of adopting inquisitive semantics based on experimental evidence that De Morgan’s law, which fails in inquisitive semantics, is invalid in counterfactual antecedents. We show that a unique feature of inquisitive semantics—the fact that its meanings are downward closed—undermines Ciardelli et al.’s semantic account of their data. The scenarios we consider suggest either adopting a semantic framework other than inquisitive semantics, or developing a non-semantic explanation of the phenomena Ciardelli et al. (2018b) seek to explain.