Skip to main content
SpringerLink
Log in

Unrestricted quantification and extraordinary context dependence?

  • Published:
Philosophical Studies Aims and scope Submit manuscript

Abstract

This paper revisits a challenge for contextualist approaches to paradoxes such as the Liar paradox and Russell’s paradox. Contextualists argue that these paradoxes are to be resolved by appeal to context dependence. This can offer some nice and effective ways to avoid paradox. But there is a problem. Context dependence is, at least to begin with, a phenomenon in natural language. Is there really such context dependence as the solutions to paradoxes require, and is it really just a familiar linguistic phenomenon at work? Not so clearly. In earlier work, I argued that the required form of context dependence does not look like our most familiar instances of context dependence in natural language. I called this extraordinary context dependence. In this paper, I shall explore, somewhat tentatively, a way that we can see the context dependence needed to address paradoxes as not so extraordinary. Doing so will also allow us to connect thinking about the context dependence of quantifier domains with some interesting ideas about the distinctive semantic properties of certain quantifiers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Though of course, Williamson is arguing against the kind of position I am offering here. Another classic response is from Boolos (1999).

  2. In addition to the papers already mentioned, other good sources on this debate include the papers in the volume edited by Rayo and Uzquiano (2006), McGee (2000), and extended works by Ferrier (2018) and Studd (2019). Among many other more recent papers, see Florio and Shapiro (2014), Linnebo (2013), Linnebo and Rayo (2012), and Uzquiano (2015).

  3. For non-classical responses to the Liar, see the many references in Beall et al. (2018). For a non-classical view of Russell’s paradox, see Restall (1993).

  4. A thorough critique of the contextualist approach is offered by Gauker (2006).

  5. See Peters and Westerståhl (2006) for an extensive overview. The classic papers in semantics are a trio of Barwise and Cooper (1981), Higginbotham and May (1981), and Keenan and Stavi (1986), and work of van Benthem (1986). The logical underpinnings of this theory were explored by Lindström (1966) and Mostowski (1957).

  6. The generalized quantifier literature distinguishes type \(\langle 1\rangle\), quantifiers, which are sets of sets, from type \(\langle 1, 1 \rangle\) quantifiers, which are relations between sets. I shall for the most part suppress this.

  7. For local results see van Benthem (1986) and Keenan and Stavi (1986). For overviews on the many global results about generalized quantifiers see the surveys of Peters and Westerståhl (2006) and Westerståhl (1989). A few noteworthy papers include Hella et al. (1996), Hella et al. (1997), and Westerståhl (1985b).

  8. Much interesting discussion ensued from their work. See, among many references, Breheny (2003), Collins (2018), Giannakidou (2004), and Martí (2002).

  9. There was a lively debate over whether domain restrictors are represented in the syntax of sentences. I have sided with the view that they are, but it is not really important here. King and Stanley (2004), Stanley (2000) and Stanley and Gendler Szabó (2000) are among those that said they are. Bach (2000), Carston (2002), and Recanati (2004) said they are not.

  10. A little more precisely, we have already observed from Westerståhl’s arguments that M is not the source of ordinary context dependence for quantifier domains.

  11. Actually, I think that speakers’ intention works with other contextual factors (Glanzberg, 2007, 2020). A thoroughly intentionalist account is given by King (2014). Gauker (1997) holds that external factors rather than intentions are involved.

  12. Principal filters have sometimes been seen as linked to definiteness (e.g. Barwise and Cooper, 1981; Heim, 1991). The Montagovian treatment of names as quantifiers also generates a principal filter (Montague, 1973).

  13. See Beghelli and Stowell (1997) and Szabolcsi (1997) for more extensive discussion. As they note, there are some important differences between each and every, and the claim that every is always distributive is more delicate than I am making it appear here.

  14. Especially for Landman and Link, there are some background issues of whether we should be talking about sets, mereological pluralities, or groups. I am ignoring these subtle issues for now.

  15. There are a number of substantial issues about how to implement these ideas fully. As I mentioned with both, presuppositions can be a substantial part of determiner meaning. We also want to explain the various potentials for scope that different determiners show. To capture such data, Szabolcsi (1997) uses a DRT-style framework, while Beghelli and Stowell (1997) use a highly articulated syntax, where there is a DistP functional head that contributes the universal force of distribution. As Szabolcsi mentions, we can also make use of choice functions.

  16. The literature on these issues is large. For an overview, see Szabolcsi (2010), in addition to the already mentioned Beghelli and Stowell (1997) and Szabolcsi (1997). Other important work includes Kratzer (1998), Landman (2004), Reinhart (1997), and Winter (1997).

  17. See the references in note 16 above.

  18. Thanks to Julien Murzi and an anoymous referee for pressing these issues. I discuss some further issues about what makes something a quantifier in Glanzberg (2008). Again see also Landman (2004) and Szabolcsi (2010).

  19. See Moltmann (2003, 2004) on other aspects of thing.

  20. As mentioned above, Beghelli and Stowell (1997) discuss a great deal of the subtle behavior of every.

  21. Again, see Landman (2004) and Szabolcsi (2010) for extended discussion.

  22. As explored by many authors, including Kratzer (1998), Reinhart (1997), Schwarzschild (2002), and Winter (1997).

References

  • Adger, D. (2003). Core syntax. Oxford: Oxford University Press.

    Google Scholar 

  • Bach, K. (2000). Quantification, qualification, and context: A reply to Stanley and Szabó. Mind and Language, 15, 262–283.

    Article  Google Scholar 

  • Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4, 159–219.

    Article  Google Scholar 

  • Beall, J., Glanzberg, M., & Ripley, D. (2018). Formal theories of truth. Oxford: Oxford University Press.

    Google Scholar 

  • Beghelli, F., & Stowell, T. (1997). Distributivity and negation: The syntax of each and every. In A. Szabolcsi (Ed.), Ways of scope taking (pp. 71–107). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Boolos, G. (1999). Reply to Charles Parsons’ “Sets and classes”. In R. C. Jeffrey (Ed.), Logic, logic, and logic (pp. 30–36). Cambridge: Harvard University Press. Orignally written in 1974.

  • Breheny, R. (2003). A lexicalist account of implicit (bound) context dependence. SALT, 13, 55–73.

    Article  Google Scholar 

  • Burge, T. (1979). Semantical paradox. Journal of Philosophy, 76, 169–198.

    Article  Google Scholar 

  • Carston, R. (2002). Thoughts and utterances. Oxford: Blackwell.

    Book  Google Scholar 

  • Collins, C. (2018). Quantifer domain restriction as ellipsis. Glossa, 3, 1–7.

    Article  Google Scholar 

  • Ferrier, E. (2018). Quantification and paradox. Ph.D. dissertation, University of Massachusetts at Amherst.

  • Florio, S., & Shapiro, S. (2014). Set theory, type theory, and absolute generality. Mind, 123, 157–174.

    Article  Google Scholar 

  • Gauker, C. (1997). Domain of discourse. Mind, 106, 1–32.

    Article  Google Scholar 

  • Gauker, C. (2006). Against stepping back: A critique of contextualist approaches to the semantic paradoxes. Journal of Philosophical Logic, 35, 393–422.

    Article  Google Scholar 

  • Giannakidou, A. (2004). Domain restriction and the arguments of quantificational determiners. SALT, 14, 110–128.

    Article  Google Scholar 

  • Glanzberg, M. (2001). The Liar in context. Philosophical Studies, 103, 217–251.

    Article  Google Scholar 

  • Glanzberg, M. (2004a). A contextual-hierarchical approach to truth and the Liar paradox. Journal of Philosophical Logic, 33, 27–88.

    Article  Google Scholar 

  • Glanzberg, M. (2004b). Quantification and realism. Philosophy and Phenomenological Research, 69, 541–572.

    Article  Google Scholar 

  • Glanzberg, M. (2006). Context and unrestricted quantification. In A. Rayo & G. Uzquiano (Eds.), Absolute generality (pp. 45–74). Oxford: Oxford University Press.

    Google Scholar 

  • Glanzberg, M. (2007). Context, content, and relativism. Philosophical Studies, 136, 1–29.

    Article  Google Scholar 

  • Glanzberg, M. (2008). Quantification and contributing objects to thoughts. Philosophical Perspectives, 22, 207–231.

    Article  Google Scholar 

  • Glanzberg, M. (2015). Complexity and hierarchy in truth predicates. In T. Achourioti, H. Galinon, J. Martínez Fernández, & K. Fujimoto (Eds.), Unifying the philosophy of truth (pp. 211–243). Berlin: Springer.

    Chapter  Google Scholar 

  • Glanzberg, M. (2020). Indirectness and intentions in metasemantics. In T. Ciecierski & P. Grabarczyk (Eds.), The architecture of context and context-sensitivity (pp. 29–53). Berlin: Springer.

    Chapter  Google Scholar 

  • Heim, I. (1991). Artikel und definitheit. In A. von Stechow & D. Wunderlich (Eds.), Semantics: An international handbook of contemporary research (pp. 487–535). Berlin: de Gruyter.

    Google Scholar 

  • Hella, L., Luosto, K., & Väänänen, J. (1996). The hierarchy theorem for generalized quantifiers. Journal of Symbolic Logic, 61, 802–817.

    Article  Google Scholar 

  • Hella, L., Väänänen, J., & Westerståhl, D. (1997). Definability of polyadic lifts of generalized quantifiers. Journal of Logic, Language, and Information, 6, 305–335.

    Article  Google Scholar 

  • Higginbotham, J., & May, R. (1981). Questions, quantifiers and crossing. Linguistic Review, 1, 41–79.

    Article  Google Scholar 

  • Keenan, E. L., & Stavi, J. (1986). A semantic characterization of natural language determiners. Linguistics and Philosophy, 9, 253–326. Versions of this paper were circulated in the early 1980s.

    Article  Google Scholar 

  • King, J. C. (2014). The metasemantics of contextual sensitivity. In A. Burgess & B. Sherman (Eds.), Metasemantics: New essays on the foundations of meaning (pp. 97–118). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  • King, J. C., & Stanley, J. (2004). Semantics, pragmatics, and the role of semantic content. In Z. G. Szabó (Ed.), Semantics versus pragmatics (pp. 111–164). Oxford University Press.

    Google Scholar 

  • Kratzer, A. (1998). Scope or pseudoscope: Are there wide-scope indefinites? In S. Rothstein (Ed.), Events and grammar (pp. 163–196). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Landman, F. (1989). Groups, I. Linguistics and Philosophy, 12, 569–605.

    Article  Google Scholar 

  • Landman, F. (2004). Indefinites and the Type of Sets. Oxford: Blackwell.

    Book  Google Scholar 

  • Lasersohn, P. (1990). A semantics for groups and events. New York: Garland.

    Google Scholar 

  • Lindström, P. (1966). First order predicate logic with generalized quantifiers. Theoria, 32, 186–195.

    Google Scholar 

  • Link, G. (1998). Algebraic semantics in language and philosophy. Stanford: CSLI Publications.

    Google Scholar 

  • Linnebo, Ø. (2013). The potential hierarchy of sets. Review of Symbolic Logic, 6, 205–228.

    Article  Google Scholar 

  • Linnebo, Ø., & Rayo, A. (2012). Hierarchies ontological and ideological. Mind, 121, 269–308.

    Article  Google Scholar 

  • Martí, M. L. (2002). Contextual variables. Ph.D. dissertation, University of Connecticut.

  • McGee, V. (2000). Everything. In R. Tieszen & G. Sher (Eds.), Between logic and intuition: Essays in honor of Charles Parsons (pp. 54–78). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Moltmann, F. (2003). Nominalizing quantifiers. Journal of Philosophical Logic, 32, 445–481.

    Article  Google Scholar 

  • Moltmann, F. (2004). Nonreferential complements, derived objects, and nominalizations. Journal of Semantics, 13, 1–43.

    Article  Google Scholar 

  • Montague, R. (1973). The proper treatment of quantification in ordinary English. In J. Hintikka, J. Moravcsik, & P. Suppes (Eds.), Approaches to natural language (pp. 221–242). Dordrecht: Reidel.

    Chapter  Google Scholar 

  • Mostowski, A. (1957). On a generalization of quantifiers. Fundamenta Mathematicae, 44, 12–36.

    Article  Google Scholar 

  • Murzi, J., & Rossi, L. (2018). Reflection principles and the Liar in context. Philosophers Imprint, 18, 1–18.

    Google Scholar 

  • Parsons, C. (1974a). The Liar paradox. Journal of Philosophical Logic, 3, 381–412.

    Article  Google Scholar 

  • Parsons, C. (1974b). Sets and classes. Nous, 8, 1–12.

    Article  Google Scholar 

  • Peters, S., & Westerståhl, D. (2006). Quantifiers in language and logic. Oxford: Clarendon.

    Google Scholar 

  • Rayo, A. (2003). When does everything mean everything. Analysis, 63, 100–106.

    Article  Google Scholar 

  • Rayo, A., & Uzquiano, G. (Eds.). (2006). Absolute generality. Oxford: Oxford University Press.

  • Recanati, F. (2004). Literal meaning. Cambridge: Cambridge University Press.

    Google Scholar 

  • Reinhart, T. (1997). Quantifier scope: How labor is divided between QR and choice functions. Linguistics and Philosophy, 20, 335–397.

    Article  Google Scholar 

  • Restall, G. (1993). How to be really contraction free. Studia Logica, 52, 381–391.

    Article  Google Scholar 

  • Roberts, C. (1987). Modal subordination, anaphora, and distributivity. Ph.D. dissertation, University of Massachusetts at Amherst. Published in revised form by Garland, New York, 1990.

  • Schwarzschild, R. (1996). Pluralities. Dordrecht: Kluwer.

    Book  Google Scholar 

  • Schwarzschild, R. (2002). Singleton indefinites. Journal of Semantics, 19, 289–314.

    Article  Google Scholar 

  • Simmons, K. (1993). Universality and the Liar. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Stanley, J. (2000). Context and logical form. Linguistics and Philosophy, 23, 391–434.

    Article  Google Scholar 

  • Stanley, J. (2002). Making it articulated. Mind and Language, 17, 149–168.

    Article  Google Scholar 

  • Stanley, J., & Gendler Szabó, Z. (2000). On quantifier domain restriction. Mind and Language, 15, 219–261.

    Article  Google Scholar 

  • Stanley, J., & Williamson, T. (1995). Quantifiers and context dependence. Analysis, 55, 291–295.

    Article  Google Scholar 

  • Studd, J. P. (2019). Everything, more or less: A defense of generality relativism. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Szabolcsi, A. (1997). Strategies for scope taking. In A. Szabolcsi (Ed.), Ways of scope taking (pp. 109–154). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Szabolcsi, A. (2010). Quantification. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Uzquiano, G. (2015). Varieties of indefinite extensibility. Notre Dame Journal of Formal Logic, 56, 147–166.

    Article  Google Scholar 

  • van Benthem, J. (1986). Essays in logical semantics. Dordrecht: Reidel.

    Book  Google Scholar 

  • von Fintel, K. (1994). Restrictions on quantifier domains. Ph.D. dissertation, University of Massachusetts at Amherst.

  • Westerståhl, D. (1985a). Determiners and context sets. In J. van Benthem & A. ter Meulen (Eds.), Generalized quantifiers in natural language (pp. 45–71). Dordrecht: Foris.

    Google Scholar 

  • Westerståhl, D. (1985b). Logical constants in quantifier languages. Linguistics and Philosophy, 8, 387–413.

    Article  Google Scholar 

  • Westerståhl, D. (1987). Branching generalized quantifiers and natural language. In P. Gärdenfors (Ed.), Generalized quantifiers: Linguistic and logical approaches (pp. 269–298). Dordrecht: Reidel.

    Chapter  Google Scholar 

  • Westerståhl, D. (1989). Quantifiers in formal and natural languages. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic (Vol. IV, pp. 1–131). Dordrecht: Kluwer.

  • Williamson, T. (2003). Everything. Philosophical Perspectives, 17, 415–465.

    Article  Google Scholar 

  • Winter, Y. (1997). Choice functions and the scopal semantics of indefinites. Linguistics and Philosophy, 20, 399–467.

    Article  Google Scholar 

Download references

Acknowledgements

This paper grew over many years. A first attempt was presented a workshop on absolute generality at the Institut Jean Nicod in September 2009. I tried again some years later, at a workshop on truth, contextualism, and paradox at The Ohio State University in March 2017. Finally, the paper reached its more or less current form at a workshop on semantic paradox, context, and generality at the University of Salzburg in June 2019. I got a great deal of valuable feedback from all those attempts. Special thanks are due to Jc Beall, Paul Egré, Salvatore Florio, Chris Gauker, Eric Guindon, Øystein Linnebo, Julien Murzi, David Nicholas, Agustín Rayo, Lorenzo Rossi, Stewart Shapiro, James Studd, Gabriel Uzquiano, and an anonymous referee.

Author information

Authors and Affiliations

  1. Department of Philosophy, Rutgers University, 106 Somerset Street, 5th Floor, New Brunswick, NJ, 08901, USA

    Michael Glanzberg

Authors
  1. Michael Glanzberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Glanzberg.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Glanzberg, M. Unrestricted quantification and extraordinary context dependence?. Philos Stud 180, 1491–1512 (2023). https://doi.org/10.1007/s11098-021-01746-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11098-021-01746-6

Keywords

Search

Navigation