 At one extreme, we might want the operators to generate as many plausible truth values as possible in order to validate as many classically valid formulas as we can. At the other, one might arrange things so that all empty-termed formulas are truth-valueless, which would produce a very weak logic (Lehman 2001). But however we choose, many formulas that are valid in both classical predicate logic and the usual forms of free logic—indeed, even in propositional logic—will become invalid. The law of noncontradiction, for example: