 Notice that it was Lewis’s search for a system apt to express strict implication that made Quine reject modal systems as based on a use-mention confusion insofar as such systems were formulated to express at the object level proof-theoretic or semantic notions like consistency, implication, derivability and theoremhood (in fact, whenever \(p\rightarrow q\) is a propositional theorem, system S1, and so all the other stronger Lewis systems too, can prove \(p\Rightarrow q\) (Parry 1939: 143)).