 The same reasoning can be applied to \(\mathbf{ESO}\) itself, and thereby to \(\mathbf{IFL}\) (Hintikka 1991, 1996; Hyttinen &amp; Sandu 2000; Sandu 1996, 1998). Namely, an \(\mathbf{ESO}\) formula \(\chi(x)\) of vocabulary \(\tau \cup \{\TRUE\}\) can be formulated which is an implicit truth-definition of \(\mathbf{ESO}[\tau]\) for \(N\). Therefore the \(\mathbf{ESO}[\tau]\) formula \(\exists \TRUE\, \chi(x)\) is an explicit truth-definition of \(\mathbf{ESO}[\tau]\) for \(N\). Here the truth-predicate is formulated in the very same language whose notion of truth is being defined: \(\mathbf{ESO}\). Hence \(\mathbf{ESO}\), and thereby \(\mathbf{IFL}\), is capable of explicitly defining its own truth-predicate relative to  \(N\).[58]  This result does not contradict Tarski’s undefinability result, because here non-determined sentences are possible; the negation used is not contradictory  negation.[59]