 Another challenge Tarski’s hierarchy faces is explaining why we cannot just define truth for the whole hierarchy, by quantifying over levels. We would thus have a predicate like ‘true at some level’. If such predicates are allowed, we are back in paradox, so defenders of the Tarskian hierarchy must say they are not possible. Explaining why is a problem for all hierarchical views. (See Glanzberg (2015) for further discussion.)