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Plurals and modals

Published online by Cambridge University Press:  01 January 2020

Øystein Linnebo*
Affiliation:
Department of Philosophy IFIKK, University of Oslo, Oslo, Norway.

Abstract

Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question.

Type
Articles
Copyright
Copyright © Canadian Journal of Philosophy 2016

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References

Bernays, P. 1935. " On Platonism in Mathematics”. ’, 34, pp. 5269. Reprinted in (Benacerraf and Putnam, 1983).Google Scholar
Benacerraf, P., and Putnam, H.. editors 1983. Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press. Second editionGoogle Scholar
Boolos, G. 1971. "The Iterative Conception of Set”. Journal of Philosophy 68: 215232. Reprinted in (Benacerraf and Putnam, 1983).CrossRefGoogle Scholar
Boolos, G. 1985. “Reading the Begriffsschrift.” Mind 94(375): 331344.CrossRefGoogle Scholar
Boolos, G. 1998. Logic, Logic, and Logic. Cambridge, MA: Harvard University Press.Google Scholar
Feferman, S. 2005. “Predicativity.” In Oxford Handbook of the Philosophy of Mathematics and Logic, edited by Shapiro, S., 590624. Oxford: Oxford University Press.CrossRefGoogle Scholar
Fine, K. 2005. Modality and Tense. Oxford: Oxford University Press.CrossRefGoogle Scholar
Hellman, G. 1989. Mathematics without Numbers. Oxford: Clarendon.Google Scholar
Hewitt, S. T. 2012. “Modalising Plurals.” Journal of Philosophical Logic 41(5): 853875.CrossRefGoogle Scholar
Hossack, K. 2000. “Plurals and Complexes.” British Journal for the Philosophy of Science 51(3): 411443.CrossRefGoogle Scholar
Landman, F. 1989. “Groups, I.” Linguistics and Philosophy 12(5): 559605.CrossRefGoogle Scholar
Linnebo, Ø. 2010. “Pluralities and Sets.” Journal of Philosophy 107(3): 144164.CrossRefGoogle Scholar
Linnebo, Ø. 2013. “The Potential Hierarchy of Sets.” Review of Symbolic Logic 6(2): 205228.CrossRefGoogle Scholar
Parsons, C. 1983. “Sets and Modality”. In Mathematics in Philosophy, edited by Parsons, C., 298341. Cornell, NY: Cornell University Press.Google Scholar
Parsons, C. 2012. “Some Remarks on Frege's Conception of Extension.” In From Kant to Husserl: Selected Essays, edited by Parsons, C., Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Putnam, H. 1967. “Mathematics without Foundations.” Journal of Philosophy LXIV(1): 522. Reprinted in (Benacerraf and Putnam, 1983).CrossRefGoogle Scholar
Quine, W. V. 1960. Word and Object. Cambridge, MA: The MIT Press.Google Scholar
Rumfitt, I. 2005. “Plural Terms: Another Variety of Reference.” In Thought, Reference and Experience, edited by Bermudez, J. L., 84123. Oxford: Clarendon.CrossRefGoogle Scholar
Stalnaker, R. 1997. “Reference and Necessity.” In Blackwell Companion to the Philosophy of Language, edited by Hale, B. and Wright, C., 534554. Oxford: Blackwell.Google Scholar
Uzquiano, G. 2004. “The Supreme Court and the Supreme Court Justices: A Metaphysical Puzzle.” Noûs 38(1): 135153.CrossRefGoogle Scholar
Uzquiano, G. 2011. “Plural Quantification and Modality.” Proceedings of the Aristotelian Society 111(2pt2): 219250.CrossRefGoogle Scholar
Uzquiano, G. 2014. “Mereology and Modality”. In Mereology and Location, edited by Kleinschmidt, S., 3356. Oxford University Press.CrossRefGoogle Scholar
Williamson, T. 1996. “The Necessity and Determinacy of Distinctness.” In Essays for David Wiggins: Identity, Truth and Value, edited by Lovibond, S. and Williams, S., 117. Oxford: Blackwell.Google Scholar
Williamson, T. 2003. “Everything.” In Philosophical Perspectives 17: Language and Philosophical Linguistics, edited by Hawthorne, J. and Zimmerman, D.. Boston: Blackwell.Google Scholar
Williamson, T. 2010. “Necessitism, Contingentism, and Plural Quantification.” Mind 119(475): 657748.CrossRefGoogle Scholar
Williamson, T. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.CrossRefGoogle Scholar