 Hintikka suggests that \(\mathbf{IFL}\) is, substantially speaking, a first-order logic: the entities its quantified variables range over are individuals, and so are all entities with which the players of the semantic games operate. (See Subsect. 5.1 for a discussion of this idea.) A part of the interest of the intertranslatability theorem lies in the fact that if Hintikka’s controversial claim is accepted, this would mean that the expressive power of \(\mathbf{ESO}\) can actually be achieved on the first-order level.