 Hintikka’s criterion could be reformulated by saying that a logic is of first order, if any play of a semantic game associated with a formula of this logic only involves (in addition to choices interpreting conjunctions and disjunctions) choices of individuals, as opposed to choices of higher-order entities. By this criterion \(\mathbf{IFL}\) (and even \(\mathbf{EIFL})\) are first-order logics, but the logic of generalized quantifiers such as \(Q_{\ge \kappa}\) is  not.[71]  Feferman (2006: 461) anticipates the possibility of such a reply, but finds it unconvincing.