 Although first introduced in 1903, the theory of types was further developed by Russell in his 1908 article “Mathematical Logic as Based on the Theory of Types” and in the three-volume work he co-authored with  Alfred North Whitehead,  Principia Mathematica (1910, 1912, 1913). The theory thus admits of two versions, the “simple theory” of 1903 and the “ramified theory” of 1908. Both versions of the theory came under attack: the simple theory for being too weak, the ramified theory for being too strong. For some, it was important that any proposed solution be comprehensive enough to resolve all known paradoxes at once. For others, it was important that any proposed solution not disallow those parts of classical mathematics that remained consistent, even though they appeared to violate the vicious circle principle. (For discussion of related paradoxes, see Chapter 2 of the Introduction to Whitehead and Russell (1910), as well as the entry on  paradoxes and contemporary logic  in this encyclopedia.)