(Horwich's view differs in some specific respects from what is presented here, such as predicating truth of propositions, but we believe it is close enough to what is sketched here to justify the name).
The range of each predicate is restricted to that subpart of the language whose sentences contain either no truth predicate at all or truth predicates of a level less than n.
The formulation of the base theory does not involve the truth predicate or any specific truth-theoretic assumptions.
In this respect the hierarchical approach does not fit the framework outlined in Section 2, because the language does not feature a single unary truth predicate applying to sentences but rather many unary truth predicates or a single binary truth predicate (or even a single unary truth predicate applying to pairs of ordinal notations and sentences).
In formal settings satisfying certain natural conditions, Tarski's theorem on the undefinability of the truth predicate shows that a definition of a truth predicate requires resources that go beyond those of the formal language for which truth is going to be defined and thus definitional approaches to truth have to fail.
For instance, it is fair to ask why we think the truth predicate really has a contextual parameter, especially if we mean a truth predicate like the one we use in natural language.
In pursuing that aim, Austin also made a number of distinctive proposals about the descriptive function of the truth predicate.[5] Let's turn, then, to the core of Austin's account of truth.
This shows that Lγ is actually a language containing its own truth predicate: Any sentence φ is true (false) if and only if the sentence expressing its truth, T<φ>, is true (false).
Fast track quasi-realism begins by earning the right for the truth predicate to be applied to moral sentences, and then observes that once the legitimacy of the truth predicate is established much (all?) other realist talk comes along for free.
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.
