 The linguistic expression of negation, its interaction with the phenomena of negative polarity, concord, and scope, and the mapping between negative form and negative meaning all present complex and important problems for syntax, semantics, and pragmatics. (Recent perspectives on a range of issues involved are provided in Atlas 2012, Horn 2018, and work cited therein.)  But perhaps the most striking feature of negation is the mismatch between the formal and distributional complexity of negative elements in natural languages and the simplex character of the one-place negative operator of propositional logic. Yet here too the apparent simplicity is deceiving once we undertake a systematic investigation of the logic of negation. It is to that task that we now turn.