Abstract
There are different views of the logic of plurals that are now in circulation, two of which we will compare in this paper. One of these is based on a two-place relation of being among, as in ‘Peter is among the juveniles arrested’. This approach seems to be the one that is discussed the most in philosophical journals today. The other is based on Bertrand Russell’s early notion of a class as many, by which is meant not a class as one, i.e., as a single entity, but merely a plurality of things. It was this notion that Russell used to explain plurals in his 1903 Principles of Mathematics; and it was this notion that I was able to develop as a consistent system that contains not only a logic of plurals but also a logic of mass nouns as well. We compare these two logics here and then show that the logic of the Among relation is reducible to the logic of classes as many.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bell J.: Sets and classes as many. Journal of Philosphical Logic 29, 585–601 (2000)
Boolos, G., To be is to be a value of a variable (or to be some values of some variables), Journal of Philosophy 81:430–450, 1984.
Cocchiarella N. B.: A conceptualist interpretation of Leśniewski’s ontology. History and Philosophy of Logic 22, 29–43 (2001)
Cocchiarella N. B.: On the logic of classes as many. Studia Logica 70, 303–338 (2002)
Cocchiarella, N. B., Denoting concepts, reference, and the logic of names, classes as many, groups, and plurals, Linguistics and Philosophy 28:135–179, 2005.
Cocchiarella, N. B., Formal Ontology and Conceptual Realism, Synthese Library vol. 339, Springer, Dordrecht, 2007.
Cocchiarella, N. B., Mass nouns in a logic of classes as many, Journal of Philosophical Logic 38(3):343–361, 2009.
Evans G.: The Varieties of Reference. Clarendon Press, Oxford (1982)
Goodman, N., A world of individuals, in The Problem of Universals, University of Notre Dame Press, Notre Dame, 1956, reprinted in Goodman’s Problems and Projects, The Bobbs-Merrill Co., Inc., Indianapolis and New York, 1972.
Eberle, R. A., Nominalistic Systems, Synthese Library, D. Reidel Publishing Company, Dordrecht, 1970.
Kalish, D., and R. M. Montague, On Tarski’s formalization of predicate logic with identity, Archiv für mathematische Logik und Grundlagenforschung 7:81–101, 1965.
Leonard, H. S., and N. Goodman, The calculus of individuals, The Journal of Symbolic Logic 5:45–55, 1940.
Linnebo, Ø., Plural quantification, 2004, Stanford Encyclopedia of Philosophy, revised 2012.
McKay T.: Plural Predication. Oxford University Press, Oxford (2006)
Oliver, A., and T. Smiley, Journal of Philosophical Logic 35:317–348, 2006.
Oliver A., Smiley T.: Plural Logic. Oxford University Press, Oxford (2013)
Russell, B., 1903, The Principles of Mathematics, second edition, Norton & Co., New York, 1938.
Schein, B., Plurals and Events, MIT Press, Cambridge, MA, 1993.
Tarski, A., A simplified formulation of predicate logic with identity, Archiv für mathematische Logik und Grundlagenforschung 7:61–79, 1965.
Yi, B.-U., The logic and meaning of plurals, Part I, Journal of Philosophical Logic 34:459–506, 2005.
Yi B.-U.: The logic and meaning of plurals, Part II. Journal of Philosophical Logic 35, 239–288 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cocchiarella, N.B. Two Views of the Logic of Plurals and a Reduction of One to the Other. Stud Logica 103, 757–780 (2015). https://doi.org/10.1007/s11225-014-9591-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-014-9591-y