 Hintikka’s position leads to a puzzle. If \(\phi\) is a sentence of \(\mathbf{IFL}\) not truth equivalent to any \(\mathbf{FO}\) sentence, the truth-condition of the sentence \(\neg \phi\) of \(\mathbf{EIFL}\) cannot be formulated without recourse to the set of all strategies of player 2: \(\neg \phi\) is true in model \(M\) iff for all strategies of player 2 in game \(G(\phi , M)\), there is a sequence of moves by player 1 such that player 1 wins the resulting play. The set of all strategies of player 2 is undeniably a higher-order entity. How can commitment to entities other than individuals be said to have been avoided here? Can the meaning of the sentence \(\neg \phi\) be well understood without presupposing the genuinely second-order idea of all strategies of a given  player?[74]  Rather than being nominalistic, Hintikka’s position appears to be a variant of universalia in rebus. While rules of semantic games pertain to actions performed on first-order objects, combinatorial properties of sets of plays can only be formulated in second-order terms. As soon as game rules are defined for a language fragment, also the corresponding combinatorial properties are fully determined, among them the properties labeled as truth and falsity.