Plural quantification and classes

Philosophia Mathematica 11 (1):67-81 (2003)
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Abstract

When viewed as the most comprehensive theory of collections, set theory leaves no room for classes. But the vocabulary of classes, it is argued, provides us with compact and, sometimes, irreplaceable formulations of largecardinal hypotheses that are prominent in much very important and very interesting work in set theory. Fortunately, George Boolos has persuasively argued that plural quantification over the universe of all sets need not commit us to classes. This paper suggests that we retain the vocabulary of classes, but explain that what appears to be singular reference to classes is, in fact, covert plural reference to sets.

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Gabriel Uzquiano
University of Southern California

Citations of this work

Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Varieties of Indefinite Extensibility.Gabriel Uzquiano - 2015 - Notre Dame Journal of Formal Logic 56 (1):147-166.
E pluribus unum: Plural logic and set theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.

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References found in this work

Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
The roots of reference.W. V. Quine - 1974 - LaSalle, Ill.,: Open Court.

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