 Not only is \(\neg \phi\) not itself a formula of \(\mathbf{IFL}\), but it cannot in general even be expressed in \(\mathbf{IFL}\) (see Subsect. 4.2). The law of excluded middle holds for the contradictory negation: for all sentences \(\phi\) and all models \(M\), indeed \(M \vDash(\phi \vee \neg \phi)\). In Section 5 it will be seen how Hintikka has proposed to make use of \(\mathbf{EIFL}\) when discussing issues in the philosophy of mathematics. 