 Russell himself had recognized several of these same concerns as early as 1903, noting that it was unlikely that any single solution would resolve all the known paradoxes. Together with Whitehead, he was also able to introduce a new axiom, the axiom of reducibility, which lessened the vicious circle principle’s scope of application and so resolved many of the most worrisome aspects of type theory. Even so, critics claimed that the axiom was simply too ad hoc to be justified philosophically. (For additional discussion see Linsky (1990), Linsky (2002) and Wahl (2011).)