Journal of Philosophical Logic

, Volume 41, Issue 5, pp 853–875

Modalising Plurals

Article

Abstract

There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (NecInc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (NecInc), noting that it isn’t a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and showing that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language plurals, motivating a case against (NecInc) by developing a case that natural language plural terms are not de jure rigid designators. The paper concludes by developing a model theory for modal PFO+ which does not validate (NecInc). An Appendix discusses (NecInc) in relation to counterpart theory.

Keywords

Second-order logic Plural quantification Modal logic 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyBirkbeck College, University of LondonLondonUK

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