 It is worth mentioning that the foregoing argument may seem to depend crucially on a somewhat contested feature of classical propositional logic. The argument appeals to the principle that if \(A \lor B\) logically entails \(C\), then \(B\) alone logically entails \(C\). But this in turn rests on the principle that \(B\) alone logically entails \(A \lor B\), for any \(A\), and this principle is rejected by so-called containment logics (for which see  §3.1 of the entry on connexive logic).  However, it is possible to revise Church’s argument so that it is compatible with containment-logical principles. So in fact Church’s argument is not in this way beholden to classical logic.