  Predicativism has its origins in the writings of Poincaré and Russell, who responded to the paradoxes that were discovered in Cantor’s and Frege’s set theories in the early 20th century. Subsequently Weyl made fundamental contributions to the study of predicative mathematics (Weyl 1918, see also Feferman 1988). According to one notion, a definition is impredicative if it defines an object by reference to a totality which includes the object to be defined. With his Vicious Circle Principle (VCP), Russell intended to eliminate the circularity in mathematics that arises from such impredicative definitions. Russell gave various formulations of the VCP, one of which is: