Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without sacrificing insight into argument.