This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council (ERC CoG), grant number 681404.A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.Publisher PDFPeer reviewe