 Critics objected that strict implication posed its own alleged paradoxes. Within Lewis’ systems S2–S5, a necessarily true proposition is strictly implied by any proposition whatsoever, and a necessarily false proposition strictly implies any proposition whatsoever. However, Lewis (Lewis and Langford 1932) replied in SL that these alleged paradoxes are simply the result of entirely natural assumptions about valid deductive inference and entailment quite apart from the systems of strict implication, and thus are not a problem for the claim that strict implication provides an explication of deducibility and entailment. (The presentation in this and the previous two paragraphs owes much to the excellent account and discussion of Lewis’ systems of strict implication in Hughes and Cresswell (1968, Chapters 12–13).)