Plural quantification and classes

Philosophia Mathematica 11 (1):67-81 (2003)
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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From States of Affairs to a Necessary Being.Joshua Rasmussen - 2010 - Philosophical Studies 148 (2):183 - 200.
The Price of Universality.Gabriel Uzquiano - 2006 - Philosophical Studies 129 (1):137-169.
Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.
The Groundedness Approach to Class Theory.Jönne Kriener - 2014 - Inquiry : An Interdisciplinary Journal of Philosophy 57 (2):244-273.

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