 Kripke begins with a fully classical language \(\mathcal{L}_0\) containing no truth predicate (or more generally, no semantic terms). (Recall, we are assuming a language comes equipped with a valuation scheme. For \(\mathcal{L}_0\) it is classical.) He then considers extending it to a language \(\mathcal{L}^{+}_0\) which contains a truth predicate \(\Tr\). The predicate \(\Tr\) is taken to apply to every sentence of the expanded language \(\mathcal{L}^{+}_0\), including those of the original \(\mathcal{L}_0\). Thus, it is a self-applicative truth predicate (as the deflationist-inspired picture we mentioned must require), even though we begin with a language without a truth predicate.