On the Logic of Classes as Many
- Nino B. Cocchiarella
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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.
- Aczel, P. (1988) Non-Well-Founded Sets. CSLI, Stanford
- Bell, J. L. (2000) Sets and Classes as Many. Journal of Philosophical Logic 29: pp. 585-601
- Boolos, (1984) To Be Is To Be a Value of a Variable (or to Be Some Values of Some Variables). The Journal of Philosophy LXXXI: pp. 430-449
- Cocchiarella, N. B. (1977) Sortals, Natural Kinds and Re-identification. Logique et Analyse 80: pp. 439-474
- Cocchiarella, N. B. (1987) Logical Studies in Early Analytic Philosophy. Ohio State University Press, Columbus
- Cocchiarella, N. B. (1989) Conceptualism, Realism, and Intensional Logic. Topoi 7: pp. 15-34
- Cocchiarella, N. B. Conceptual Realism as a Formal Ontology. In: Poli, R., Simons, P. M. eds. (1996) Formal Ontology. Kluwer Academic Press, Dordrecht, pp. 27-60
- Cocchiarella, N. B. (1998) Reference in Conceptual Realism. Synthese 114: pp. 169-202
- Cocchiarella, Nino B., 2001, “A conceptualist Interpretation of Leśniewski's Ontology,” History and Philosophy of Logic, vol. 22.
- Freund, M. (2001) A Temporal Logic for Sortals. Studia Logica 69: pp. 351-380
- Geach, P. T. (1980) Reference and Generality. Cornell University Press, Ithaca and London
- Goodman, N. (1956) A World of Individuals. The Problem of Universals. University of Notre Dame Press, Notre Dame
- Holmes, M. R. (1998) Elementary Set Theory with a Universal Set. Cahiers Du Centre De Logique, Bruylant-Academia, Louvain-la-Neuve, Belgium
- Quine, W. V. O. (1974) The Roots of Reference. Open Court, La Salle, Ill.
- Russell, B. (1903) The Principles of Mathematics. Norton & Co., N. Y.
- Russell, B. (1919) Introduction to Mathematical Philosophy. George Allen & Unwin, LTD., London
- Schein, B. (1993) Plurals and Events. MIT Press, Cambridge
- Sellars, Wilfrid F., 1963, “Grammar and Existence: A Preface to Ontology,” reprinted in Science, Perception and Reality, Routledge & Kegan Paul, London.
- Simons, P. M. Plural Reference and Set Theory. In: Smith, B. eds. (1982) Parts and Moments, Studies in Logic and Formal Ontology. Philosophia Verlag, Munich and Vienna, pp. 199-260
- On the Logic of Classes as Many
Volume 70, Issue 3 , pp 303-338
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- Kluwer Academic Publishers
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- class(es) as many
- common names
- plural reference
- plural objects
- Author Affiliations
- 1. Department of Philosophy, Indiana University, USA