 In “The Calculus of Strict Implication” (1914) Lewis suggests two possible alternatives to the extensional system of Whitehead and Russell’s Principia Mathematica. One way of introducing a system of strict implication consists in eliminating from the system those theorems that, like (1) and (2) above, are true only for material implication but not for strict implication, thereby obtaining a sound system for both material and strict implication, though in neither case complete. The second, more fruitful alternative consists in introducing a new system of strict implication, still modeled on the Whitehead and Russell system of material implication, that will contain (all or a part of) extensional propositional logic as a proper part, but aspiring to completeness for at least strict implication. This second option is further developed in A Survey of Symbolic Logic (1918). There Lewis introduces a first system meant to capture the ordinary, strict sense of implication, guided by the idea that: 