Godel claimed that Zermelo-Fraenkel set theory is `what becomes of the theory of
types if certain superfluous restrictions are removed'. The aim of this paper is to develop
a clearer understanding of Godel's remark, and of the surrounding philosophical terrain. In
connection with this, we discuss some technical issues concerning in finitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages
