STRICT IMPLICATION, ENTAILMENT, AND MODAL ITERATION (1955)

Ever since C. I. Lewis offered the concept of “strict implication,” defined explicitly in terms of logical possibility (p−3 q ≡_df ~◊(p.~q)) and implicitly by the axioms of his system of strict implication, as corresponding to what is ordinarily meant by “deducibility” or “entailment,” there have been analytic philosophers who denied this correspondence. They denied it specifically because of the paradoxes of strict implication: that a necessary proposition is strictly implied by any proposition and an impossible proposition strictly implies any proposition. These theorems, it is maintained, do not hold for the logical relation ordinarily associated, both in science and in conversational language, with the word “entailment.” It is my aim in this paper to show that it is extremely difficult, if not downright hopeless, to maintain this distinction. I shall refer specifically to a subtle paper by C. Lewy (Lewy 1950), which deals with the intriguing problem of modal iteration, and which emphatically endorses the distinction here to be scrutinized.