David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
Geoffrey Hellman (1989). Mathematics Without Numbers: Towards a Modal-Structural Interpretation. Oxford University Press.
Timothy Williamson (2003). Everything. Philosophical Perspectives 17 (1):415–465.
Citations of this work BETA
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.
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.
Friederike Moltmann (forthcoming). Plural Reference and Reference to a Plurality. Linguistic Facts and Semantic Analyses. In Massimiliano Carrara, Alexandra Arapinis & Friederike Moltmann (eds.), Unity and Plurality. Logic, Philosophy, and Semantics. Oxford University Press
Eytan Zweig (2009). Number-Neutral Bare Plurals and the Multiplicity Implicature. Linguistics and Philosophy 32 (4):353-407.
Gabriel Uzquiano (2004). Plurals and Simples. The Monist 87 (3):429-451.
C. Brisson (2003). Plurals, All, and the Nonuniformity of Collective Predication. Linguistics and Philosophy 26 (2):129-184.
AlexOliver & TimothySmiley (2001). Strategies for a Logic of Plurals. Philosophical Quarterly 51 (204):289–306.
Barry Schein (2006). Plurals. In Ernest Lepore & Barry Smith (eds.), The Oxford Handbook of Philosophy of Language. Oxford University Press 716--767.
Alex Oliver & Timothy Smiley (2001). Strategies for a Logic of Plurals. Philosophical Quarterly 51 (204):289-306.
Added to index2012-09-16
Total downloads20 ( #176,896 of 1,789,933 )
Recent downloads (6 months)9 ( #93,420 of 1,789,933 )
How can I increase my downloads?