Whitehead and Russell (1927) devised a hierarchy of ``types'' in order to eliminate self-referential statements from *Principia Mathematica*, which purported to derive all of mathematics from logic. A set of the lowest type contained only
objects (not sets), a set of the next higher type could contain only objects or sets of the lower type, and so on.
Unfortunately, Gödel's Incompleteness Theorem showed that both *Principia
Mathematica* and all consistent formal systems must be incomplete.

**References**

Hofstadter, D. R. *Gödel, Escher, Bach: An Eternal Golden Braid.*
New York: Vintage Books, pp. 21-22, 1989.

Whitehead, A. N. and Russell, B. *Principia Mathematica.* New York: Cambridge University
Press, 1927.

© 1996-9

1999-05-26