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

Authors
Gabriel Uzquiano
University of Southern California
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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DOI 10.1093/philmat/11.1.67
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References found in this work BETA

Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
The Roots of Reference.W. V. Quine - 1974 - Lasalle, Ill., Open Court.
Parts of Classes.Michael Potter - 1993 - Philosophical Quarterly 43 (172):362-366.

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Citations of this work BETA

Varieties of Indefinite Extensibility.Gabriel Uzquiano - 2015 - Notre Dame Journal of Formal Logic 56 (1):147-166.
Plural Quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
E Pluribus Unum: Plural Logic and Set Theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
The Price of Universality.Gabriel Uzquiano - 2006 - Philosophical Studies 129 (1):137-169.

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