5.252 Only thus is the advance from term to term possible in a formal series (from type to type in the hierarchy of Russell and Whitehead). (Russell and Whitehead did not admit the possibility of this advancing, but they made use of it again and again.)

Black (p. 260): “W.’s criticism can properly be leveled against the use of ‘typical ambiguity’ in Principia (for which see vol. 1, p. 65, and the ‘prefatory statement’ to vol. 2). It has often been pointed out that Russell needs, for example, not a single axiom of reducibility, but an indefinite number of such axioms, applicable to entities of different types. For a specific criticism of this sort, see Anscombe, Introduction, p. 130.”