Nominalization,predication and type containment

In an attempt to accommodate natural language phenomena involving nominalization and self-application, various researchers in formal semantics have proposed abandoning the hierarchical type system which Montague inherited from Russell, in favour of more flexible type regimes. We briefly review the main extant proposals, and then develop a new approach, based semantically on Aczel's notion of Frege structure, which implements a version ofsubsumption polymorphism. Nominalization is achieved by virtue of the fact that the types of predicative and propositional complements are contained in the type of individuals. Russell's paradox is avoided by placing a type-constraint on lambda-abstraction, rather than by restricting comprehension.Kamareddine is grateful to the Department of Mathematics and Computing Science, Technical University of Eindhoven, for their financial support and hospitality during the academic year 1991–92.Klein's work has been carried out as part of the research programmes of the dyana project (BR 3175 and BR 6852), funded by CEC esprit Basic Research Division, and of the Human Communication Research Centre, supported by the UK Economic and Social Research Council.