 The point of introducing the additional machinery was not just to rediscover the language \(L_{\gamma}\). The point is rather to have provided a much more general and abstract framework which may lead to new theories of truth and give further insights into the semantic paradoxes. It turns out that the truth revision operator \(\tau\) defined above has many interesting fixed-points in addition to \(L_{\gamma}\). It is also possible to obtain new theories of truth by considering alternative ways of making the set of interpreted languages into a ccpo. One may for instance add an additional truth value and consider the situation in a four-valued logic, as considered by Fitting (1997); or one may remove the third truth value undefined and construct a ccpo in a completely classical setting. In the classical setting, attention is restricted to the totally interpreted languages (languages in which every sentence is either true or false), and an ordering on them is defined by: \(L_1 \le L_2\) holds iff the extension of the truth predicate in \(L_1\) is included in the extension of the truth predicate in \(L_2\), that is, iff \(L_2\) points out at least as many sentences as true as \(L_1\). This gives a ccpo. By using the fixed point theorem in this setting on a suitably defined revision operator, it is fairly easy to prove the existence of a totally interpreted language containing a positive definition of truth. By this is meant that the interpreted language has a predicate \(T\) satisfying the following restricted version of the \(T\)-schema: