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Plural Predication (Hardcover, New)
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Plural Predication (Hardcover, New)
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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.
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