Plural Predication
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Plural Predication
Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. Yet the apparatus of predication and quantification in standard modern logic does not allow a place for such non-distributive predicates. Thomas McKay's book explores the enrichment of modern logic with plural predication and quantification. We can have genuinely non-distributive predication without relying on singularizing procedures from set theory and mereology. The fundamental 'among' relation can be understood in a way that does not generate any hierarchy of plurals analogous to a hierarchy of types or a hierarchy of higher-order logics. Singular quantification can be understood as a special case, with the general type being quantifiers that allow both singular and plural quantification. The 'among' relation is formally similar to a 'part of' relation, but the relations are distinct, so that mass quantification and plural quantification cannot be united in the same way that plural and singular are united. Analysis of singular and plural definite descriptions follows, with a defense of a fundamentally Russellian analysis, but coupled with some new ideas about how to be sensitive to the role of context. This facilitates an analysis of some central features of the use of pronouns, both singular and plural.
Plural Logic
Author: Alex Oliver
language: en
Publisher: Oxford University Press, USA
Release Date: 2016
Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.
Plurals and Events
Barry Schein proposes combining a second-order treatment of plurals with Donald Davidson's suggestion that there are positions for reference to events in ordinary predicates in order to account for several of the more puzzling features of plurals without invoking plural objects, with its attendant metaphysics, and also provide an absolute truth-theoretic characterization of the semantics of sentences with plurals in them. How do we make sense of sentences with plural noun phrases in them? In Plurals and Events, Barry Schein proposes combining a second-order treatment of plurals with Donald Davidson's suggestion that there are positions for reference to events in ordinary predicates in order to account for several of the more puzzling features of plurals without invoking plural objects, with its attendant metaphysics, and also provide an absolute truth-theoretic characterization of the semantics of sentences with plurals in them. Schein's highly original argument should have significant impact on how natural-language semantics is done, with repercussions for philosophy and logic. The book opens with foundational arguments that the logical language should have four major features: reduction to singular predication via a Davidsonian logical form, amereology of events, a logical syntax that allows the constituents of a Davidsonian analysis to be predicated of distinct events and separated from one another by other logical elements, and descriptive anaphors that cross-refer to the events described by antecedent clauses. A semantics for plurality and quantification is developed in the remaining chapters, which address some of the empirical and formal questions raised by the variety of interpretations in which plurals and quantifiers participate.