\(Bew_{S} (x)\) expresses here provability of sentences in the system S (we omit discussion here of the problems of defining \(Bew_{S} (x))\). The truth predicate has to satisfy certain principles; otherwise the global reflection principle would be vacuous. Thus not only the global reflection principle has to be added, but also axioms for truth. If a natural theory of truth like T(PA) below is added, however, it is no longer necessary to postulate the global reflection principle explicitly, as theories like T(PA) prove already the global reflection principle for PA. One may therefore view truth theories as reflection principles as they prove soundness statements and add the resources to express these statements.