The truth predicates in natural languages do not come with any ouvert type restriction. Therefore typed theories of truth (axiomatic as well as semantic theories) have been thought to be inadequate for analysing the truth predicate of natural language, although recently hierarchical theories have been advocated by Glanzberg (2015) and others. This is one motive for investigating type-free theories of truth, that is, systems of truth that allow one to prove the truth of sentences involving the truth predicate. Some type-free theories of truth have much higher expressive power than the typed theories that have been surveyed in the previous section (at least as long as indexed truth predicates are avoided). Therefore type-free theories of truth are much more powerful tools in the reduction of other theories (for instance, second-order ones). 