 For further discussion of the Vicious-Circle Principle, see Russell 1908, Whitehead and Russell 1925, Gödel 1944, and Chihara 1973. For a formal presentation of Ramified Type Theory, see Church 1976; for a more informal presentation, see Hazen 1983. See also the entries on  type theory  and  Principia Mathematica,  which contain further references.