 The proof above is simpler than the original proof of Montague (1963) and directly mimicks the reasoning underlying the paradox of the knower. Montague’s theorem shows that in the setting of first-order arithmetic we cannot have a theory of knowledge or knowability satisfying even the basic principles A1–A4. Montague’s theorem is a generalisation of Tarski’s theorem. If a predicate symbol \(K\) satisfies Tarski’s schema \(T\) then it is easy to see that it will also satisfy axiom schemas A1–A4. Thus axiom schemas A1–A4 constitute a weakening of the \(T\)-schema, and Montague’s theorem shows that even this much weaker version of the \(T\)-schema is sufficient to produce inconsistency.