 A uniform solution of both problems is obtained by introducing the notion of a truth value. Namely, by applying the criterion of “saturatedness” Frege provides a negative answer to the first of the above problems. Since sentences are a kind of complete entities, they should be treated as a sort of proper names, but names destined to denote some specific objects, namely the truth values: the True and the False. In this way one also obtains a solution of the second problem. Predicates are to be interpreted as some kind of functional expressions, which being applied to these or those names generate sentences referring to one of the two truth values. For example, if the predicate ‘is a city’ is applied to the name ‘Kyiv’, one gets the sentence ‘Kyiv is a city’, which designates the True (i.e., ‘Kyiv is a city’ is true). On the other hand, by using the name ‘Mount Everest’, one obtains the sentence ‘Mount Everest is a city’ which clearly designates the False, since ‘Mount Everest is a city’ is false.