  It is clear that most Englishmen do not possess all the properties that most Englishmen possess. Therefore, a typical Englishman, according to this definition, should be untypical. The problem, according to Russell, is that the word “typical” has been defined by a reference to all properties and has been treated as itself a property. (It is remarkable that similar problems arise when defining the notion of random numbers, cf. Martin-Löf “Notes on constructive mathematics” (1970).) Russell introduced the ramified hierarchy in order to deal with the apparent circularity of such impredicative definitions. One should make a distinction between the first-order properties, like being Corsican, that do not refer to the totality of properties, and consider that the second-order properties refer only to the totality of first-order properties. One can then introduce third-order properties, that can refer to the totality of second-order property, and so on. This clearly eliminates all circularities connected to impredicative definitions.