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.
Keywords typed lambda calculus  Russell's paradox  property theory  polymorphism  natural  language semantics
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DOI 10.1007/BF01050787
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References found in this work BETA

Quality and Concept.George Bealer - 1982 - Oxford, England: Oxford University Press.
The Proper Treatment of Quantification in Ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.
The Proper Treatment of Quantification in Ordinary English.Richard Montague - 1974 - In Richmond H. Thomason (ed.), Formal Philosophy. Yale University Press.
Quality and Concept.George Bealer - 1983 - Revue Philosophique de la France Et de l'Etranger 173 (3):347-348.

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A Type Free Theory and Collective/Distributive Predication.Fairouz Kamareddine - 1995 - Journal of Logic, Language and Information 4 (2):85-109.

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