David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Philosophical Logic 41 (5):853-875 (2012)
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
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
Thomas J. McKay (2006). Plural Predication. Oxford University Press.
Timothy Williamson (2003). Everything. Philosophical Perspectives 17 (1):415–465.
Geoffrey Hellman (1989). Mathematics Without Numbers: Towards a Modal-Structural Interpretation. Oxford University Press.
Citations of this work BETA
Øystein Linnebo (forthcoming). Plurals and Modals. Canadian Journal of Philosophy:1-23.
Øystein Linnebo (2013). The Potential Hierarchy of Sets. Review of Symbolic Logic 6 (2):205-228.
Simon Hewitt (2015). When Do Some Things Form a Set? Philosophia Mathematica 23 (3):311-337.
Keith Hossack (2014). Sets and Plural Comprehension. Journal of Philosophical Logic 43 (2-3):517-539.
Fredrik Haraldsen (2015). On What Actually Is. Erkenntnis 80 (3):643-656.
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