Modalising Plurals

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)
DOI 10.1007/s10992-011-9194-2
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,479
External links
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
Timothy Williamson (2003). Everything. Philosophical Perspectives 17 (1):415–465.

View all 17 references / Add more references

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

Add more citations

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. pp. 716--767.

Monthly downloads

Added to index


Total downloads

33 ( #145,868 of 1,925,795 )

Recent downloads (6 months)

11 ( #81,914 of 1,925,795 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.