The paper first proves the completeness of the (non-modal) first-order predicate logic presented in Carnap’s 1946 article ‘Modalities and quantification’. By contrast the modal logic defined by the semantics Carnap produces is unaxiomatisable. One can though adapt Carnap’s semantics so that a standard completeness proof for a Carnapian version of predicate S5 turns out to be available./
