Logic

Why is C.I. Lewis' strict implication not taken seriously in this day and age? Clarence Irving Lewis was known for criticizing material implication and for instead proposing strict implication. Why is he, his criticisms, and his proposed strict implication not taken seriously today? Many contemporary logic, philosophy, and mathematical texts refer to material implication rather than strict implication.

Comments

I'd say that C. I. Lewis's strict implication is very much alive in contemporary philosophy, although often called by different names, such as "logical entailment" or "logical implication." Philosophers frequently claim (or deny) that some proposition "entails" another, by which they very often seem to mean "strictly implies."

Material implication, unlike strict implication, is a truth-functional relation between propositions: given only the classical truth-values of two propositions, you can tell which one materially implies the other (material implication will run in at least one direction between them, if not both). By contrast, strict implication isn't truth-functional: it requires asking about the truth-values that propositions take in worlds other than the actual world, which invites philosophical controversy. As a result, strict implication is a less clear-cut relation than material implication. So despite its unintuitive features (which, as you say, Lewis criticized), material implication is far more often taught in contemporary logic and math courses: the logical theory of material implication is more straightforward. But, again, philosophers often want to express an implication relation that's stronger than material implication, and in those cases strict implication is commonly what they use. Counterfactual (or subjunctive) implication is another such relation, but it's even less clear-cut, and even more controversial, than strict implication.

It should also be said that there is nowadays a lot of formal, logical work that is devoted to various forms of implication, like strict implication. Part of this is done within so-called "modal" logic; part of it is done in theories of conditionals generally; some of it concerns non-classical logics like relevant logic.

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