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.Author's Profile
DOI
10.1093/philmat/11.1.67
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Citations of this work
The Many and the One: A Philosophical Study of Plural Logic.Salvatore Florio & Øystein Linnebo - 2021 - Oxford, England: Oxford University Press.
Varieties of Indefinite Extensibility.Gabriel Uzquiano - 2015 - Notre Dame Journal of Formal Logic 56 (1):147-166.
A neglected resolution of Russell’s paradox of propositions.Gabriel Uzquiano - 2015 - Review of Symbolic Logic 8 (2):328-344.
E pluribus unum: Plural logic and set theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
References found in this work
To be is to be a value of a variable (or to be some values of some variables).George Boolos - 1984 - Journal of Philosophy 81 (8):430-449.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.