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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References found in this work BETA
K. Hossack (2000). Plurals and Complexes. British Journal for the Philosophy of Science 51 (3):411-443.
Øystein Linnebo, Plural Quantification. Stanford Encyclopedia of Philosophy.

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Citations of this work BETA
Keith Hossack (2014). Sets and Plural Comprehension. Journal of Philosophical Logic 43 (2-3):517-539.
Similar books and articles
Byeong-uk Yi (2006). The Logic and Meaning of Plurals. Part II. Journal of Philosophical Logic 35 (3):239-288.
K. Hossack (2000). Plurals and Complexes. British Journal for the Philosophy of Science 51 (3):411-443.
Barry Schein (2006). Plurals. In Ernest Lepore & Barry Smith (eds.), The Oxford Handbook of Philosophy of Language. Oxford University Press. 716--767.
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