What is an inconsistent truth table? Do truth tables---the ordinary sort that we use to teach and explain basic propositional logic---require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim: that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than any one logic being privileged, then, on this count partisans from all parts of the logical spectrum are in relatively similar dialectical positions. Joint work with Guillermo Badia (Otago) and Patrick Girard (Auckland).