A plea for multilateralism

In their terrific book Reasons for Logic, Logic for Reasons, Ulf Hlobil and Robert Brandom defend a normative-pragmatic interpretation of implication and incompatibility cashed out in bilateral terms. Using epistemic modal cases, I argue that Hlobil and Brandom's normative-pragmatic interpretation of implication fails to account for the force of consequence and to provide an extensionally adequate characterization of implication. I also show that the same cases cause trouble for Hlobil and Brandom's condition relating negation to incompatibility. I argue, however, that these problems can be avoided by switching from a bilateral to a multilateral setting.