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.
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 University Press.
The Proper Theory of Quantification.Richard Montague - 1973 - In Jaakko Hintikka (ed.), Approaches to Natural Language. D. Reidel Publishing.
Semantics and Property Theory.Gennaro Chierchia & Raymond Turner - 1988 - Linguistics and Philosophy 11 (3):261 - 302.

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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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