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The Property Paradox in (Not So Plain) English

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Chapter Summary

Reference to properties is widely used in semantic analyses of natural language. The naïve theory of properties has many virtues, but it seems to have been shattered by (the property version of) Russell's paradox. The Russell paradox involves the Russell property R corresponding to the predicate 'does not instantiate itself'. Field's enterprise is to find a logic that is strong enough to capture part of the naïve theory of properties, yet not so strong that it generates paradoxes. This is certainly a worthy logical task; but if one is interested in the semantics of natural language, one should first ask whether paradoxes can or cannot be constructed from fragments of English that only include 'property talk'. This chapter presents brief remarks about individual-denoting quantifiers and pronouns. It shows that property-denoting pronouns and quantifiers make it possible to express the property paradox with the grammatical resources of ordinary English.

Keywords: individual-denoting pronouns; individual-denoting quantifiers; naïve theory of properties; property paradox; Russell's paradox; semantic analyses

10.1163/9789004279377_010
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