Modalising Plurals Authors
First Online: 17 May 2011 Received: 29 May 2010 Accepted: 13 April 2011 DOI:
Cite this article as: Hewitt, S.T. J Philos Logic (2012) 41: 853. doi:10.1007/s10992-011-9194-2
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.
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