Leonard Goddard

Abstract

Abstract Leonard Goddard (b. 1925) was a senior lecturer in philosophy at the University of New England in New South Wales, Australia when he wrote to Gödel in 1965. Later he taught at St. Andrews University in Scotland, and from 1977 until his retirement in 1989 he was professor and chair of the philosophy department at the University of Melbourne. His letter inquires about the connection between Bertrand Russell’s vicious circle principle and the theory of types, and in particular Russell’s apparent claim in Whitehead and Russell 1910, p. 48, that the simple theory of types is a consequence of the vicious circle principle. In his draft reply, which was never sent, Gödel asserts that, contrary to Russell’s claim, there is no route from the vicious circle principle to the theory of types, because the vicious circle principle at best supports a cumulative hierarchy. Gödel thus sharply distinguishes the theory of types from any theory that allows a cumulative hierarchy, taking it to be central to type theory that a propositional function can have arguments of only one type.