Studia Logica

, Volume 70, Issue 3, pp 303–338 | Cite as

On the Logic of Classes as Many

  • Nino B. Cocchiarella

Abstract

The notion of a "class as many" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases.

class(es) as many atom(s) common names plural reference plural objects nominalization extensionality 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Nino B. Cocchiarella
    • 1
  1. 1.Department of PhilosophyIndiana UniversityUSA

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