 To explicate this notion he defined strict implication, according to which the if-then conditional \(p \fishhook q\) expressing the strict implication of \(q\) by \(p\) is equivalent to \({\sim}\Diamond(p \amp{\sim}q)\), and is true just in case it is not possible that \(p\) is true and \(q\) is false. Strict implication is an intensional notion, and the logic of strict implication is a form of modal logic. The system of strict implication developed in SSL (Lewis 1918) was distinguished from earlier modal logics by its axiomatic presentation in the light of the work of Whitehead and Russell. However, Lewis faced a number of criticisms, including one by Emil Post that one of Lewis’ postulates led to the result that it was indeed impossible that \(p\) just in case it was false that \(p\), so that Lewis’ SSL system reduced to an extensional one. Lewis (Lewis and Langford 1932) eliminated these problems in SL and provided distinct systems of strict implication or modal logic, S1–S5, each stronger than its predecessor (with S3 the system of SSL). S1 contained the following axioms: