Naive Modus Ponens

In his [2011], Lionel Shapiro proposes a very interesting deflationist conception of logical consequence, according to which the logical-consequence predicate applying to sentences serves as a merely expressive device allowing us to talk in a generalising way about typically non-linguistic entailment facts (just as, according to a deflationist conception of truth, the truth predicate applying to sentences serves as a merely expressive device allowing us to talk in a generalising way about typically non-linguistic facts). Entailment facts are in turn facts expressed using a certain suitably strong conditional (henceforth written as ⇒), just as conjunctive facts are facts expressed using a conjunction operator. (I’ll assume with Shapiro that there are such facts and that we have a workable conception of them; when talking in English, I’ll express them using the canonical construction