 The definability of truth can only be discussed in connection with languages capable of speaking of themselves. Let us consider an arithmetical vocabulary \(\tau\) and restrict attention to the standard model \(N\) of Peano’s axioms. Each sentence \(\phi\) of vocabulary \(\tau\) can then be represented by a natural number \(\ulcorner \phi \urcorner\), its Gödel number. It is assumed that \(\tau\) contains a numeral \(\boldsymbol{{}^\ulcorner \phi {}^\urcorner}\) for each number \(\ulcorner \phi \urcorner\). If \(L\) and \(L'\) are abstract logics of vocabulary \(\tau\), such as \(\mathbf{FO}\) or \(\mathbf{IFL}\), and \(\TRUE(x)\) is a formula of \(L'\) such that every sentence \(\phi\) of \(L\) satisfies: 