Modalising Plurals

Journal of Philosophical Logic 41 (5):853-875 (2012)
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-f which does not validate (Necinc). An Appendix discusses (Necinc) in relation to counterpart theory. Of course, it would be a mistake to think that the rules for "multiple pointing" follow automatically from the rules for pointing proper. Max Black—The Elusiveness of Sets In some influential articles during the 1980s George Boolos proposed an interpretation of monadic second-order logic in terms of plural quantification [4, 5]. One objection to this proposal, pressed by Williamson [22, 456-7], focuses on the modal behaviour of plural variables, arguing that the proposed interpretation yields the wrong results in respect of the modal status of atomic predications. In the present paper I will present this objection and argue against it. In the course of developing the argument, I will have cause to consider the under-investigated question of how a logic for plurals should be extended to incorporate modal operators
Keywords Second-order logic  Plural quantification  Modal logic
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DOI 10.1007/s10992-011-9194-2
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References found in this work BETA
Philosophy of Logic.W. V. Quine - 1970 - Harvard University Press.
Logic, Logic, and Logic.George Boolos - 1998 - Harvard University Press.
Plural Predication.Thomas J. McKay - 2006 - Oxford University Press.
Everything.Timothy Williamson - 2003 - Philosophical Perspectives 17 (1):415–465.

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Citations of this work BETA
The Potential Hierarchy of Sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
Plurals and Modals.Øystein Linnebo - 2016 - Canadian Journal of Philosophy 46 (4-5):654-676.
Sets and Plural Comprehension.Keith Hossack - 2014 - Journal of Philosophical Logic 43 (2-3):517-539.
On What Actually Is.Fredrik Haraldsen - 2015 - Erkenntnis 80 (3):643-656.
When Do Some Things Form a Set?Simon Hewitt - 2015 - Philosophia Mathematica 23 (3):311-337.

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