David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 2 (3):171-215 (1993)
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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References found in this work BETA
P. Aczel (1980). Frege Structures and the Notions of Truth and Proposition. In J. Barwise, H. J. Keisler & K. Kunen (eds.), The Kleene Symposium. North-Holland
George Bealer (1989). On the Identification of Properties and Propositional Functions. Linguistics and Philosophy 12 (1):1 - 14.
George Bealer (1982). Quality and Concept. Oxford University Press.
Gennaro Chierchia & Raymond Turner (1988). Semantics and Property Theory. Linguistics and Philosophy 11 (3):261 - 302.
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