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Sketch for a Systematic Metaphysics$
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D. M. Armstrong

Print publication date: 2010

Print ISBN-13: 9780199590612

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199590612.001.0001

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(p.97) Chapter 14 Classes
Sketch for a Systematic Metaphysics

David M. Armstrong

Oxford University Press

David Lewis' major contribution to the ontology of classes is to perceive that many‐membered classes are mereological sums of the singletons (unit‐classes of their members: {a, b, c, d, . . .} is identical with {a + {b} + }c} + {d} . . . This raises the question of what singletons are ontologically. My proposal that they are all states of affairs was refuted by Gideon Rosen. But a more limited claim is tenable. Only some singletons are states of affairs. Because set theory is a mathematical system it will produce structures that may not be instantiated, and therefore are no more than possibilities. Nelson Goodman's protest at using set theory to do metaphysics is endorsed. The null class is rejected as an existent.

Keywords:   classes, David Lewis, singletons, mereology, Gideon Rosen, Nelson Goodman, null class

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