Abstract
This paper contributes to the debate over the so-called “easy argument for numbers”, an argument that uses evidence from natural language to support the metaphysically significant claim that numbers exist. It presents novel data showing that critical examples in the literature are ambiguous between two readings, contrary to previous assumptions. It then accounts for these data using independently motivated linguistic theory. The account developed rescues the easy argument from the primary challenges leveled against it in the literature and sets the agenda for future work to determine whether or not the argument is valid.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bach, E. (1986). Natural language metaphysics. In R. Barcan Marcus, G. J. W. Dorn, & P. Weingartner (Eds.), Logic, methodology and philosophy of science VII, Studies in logic and the foundations of mathematics (Vol. 114, pp. 573–595). Amsterdam: North Holland.
Balcerak Jackson, B. (2013). Defusing easy arguments for numbers. Linguistics and Philosophy, 36(6), 447–461.
Balcerak Jackson, B. (2014). What does displacement explain, and what do congruence effects show? A response to Hofweber (2014). Linguistics and Philosophy, 37(3), 269–274.
Bar-Hillel, Y. (1967). Review of Fodor and Katz 1964. Language, 43(2), 526–550.
Beaver, D., & Clark, B. (2003). Always and only: Why not all focus-sensitive operators are alike. Natural Language Semantics, 11(4), 323–362.
Brogaard, B. (2007). Number words and ontological committment. The Philosophical Quarterly, 57(226), 1–20.
Büring, D. (2007). Semantics, intonation and information structure. In G. Ramchand & C. Reiss (Eds.), The Oxford handbook of linguistic interfaces (pp. 445–474). Oxford: Oxford University Press.
Declerk, R. (1988). Studies on copular sentences, clefts, and pseudo-clefts. Louvain: Leuven University Press.
Dummett, M. (1981). Frege: Philosophy of language. Cambridge, MA: Harvard University Press.
Felka, K. (2014). Number words and reference to numbers. Philosophical Study, 168(1), 261–282.
Féry, C., & Samek-Lodovici, V. (2006). Focus projection and prosodic prominence in nested foci. Language, 82(1), 131–150.
Frege, G. (1884). The foundations of arithmetic: A logical-mathematical investigation into the concept of number. New York: Pearson Longman. Dale Jacquette, trans.
Geist, L. (2007). Predication and equation in copular sentences: Russian vs. English. In I. Comorovski & K. von Heusinger (Eds.), Existence: Semantics and syntax, studies in linguistics and philosophy (pp. 79–105). Berlin: Springer.
Hale, B., & Wright, C. (2001). The Reason’s proper study: Essays toward a Neo-Fregean philosophy of mathematics. Oxford: Clarendon Press.
Heycock, C., & Kroch, A. (2002). Topic, focus, and syntactic representations. In L. Mikkelsen & C. Potts (Eds.), WCCFL 21 Proceedings (pp. 141–165). Somerville, MA: Cascadilla Press.
Higgins, R. F. (1979). The Pseudo-cleft construction in English. New York: Garland.
Hofweber, T. (2005). Number determiners, numbers, and arithmetic. Philosophical Review, 114(2), 179–225.
Hofweber, T. (2007). Innocent statements and their metaphysically loaded counterparts. Philosophers Imprint, 7(1), 1–33.
Hofweber, T. (2014). Extraction, displacement, and focus a reply to Balcerak Jackson (2013). Linguistics and Philosophy, 37(3), 263–267.
Hofweber, T. (2016). Ontology and the ambitions of metaphysics. Oxford: Oxford University Press.
Krifka, M. (2006). Can focus accenting be eliminated in favor of deaccenting Given constituents? In B. Gyuris, L. Kálmán, C. Piñón, & K. Varasdi (Eds.), Ninth symposium on logic and language (pp. 107–119). Budapest: Hungarian Academy of Sciences & Eötvös Loránd University.
Krifka, M. (2007). Basic notions of information structure. In C. Féry, G. Fanselow, & M. Krifka (Eds.), Interdisciplinary studies on information structure (Vol. 6, pp. 13–55). Potsdam: Universitätsverlag Potsdam.
Ladd, D. R. (2008). Intonational phonology (2nd ed.). Cambridge: Cambridge Univesity Press.
Matushansky, O. (2000). The instrument of inversion: Instrumental case in the Russian copula. In R. Billerey & B. D. Lillehaugen (Eds.), Proceedings of the 19th West Coast conference on formal linguistics (pp. 288–301). Somerville, MA: Cascadilla Press.
Mikkelsen, L. (2005). Copular clauses: Specification, predication, and equation. Amsterdam: John Benjamins.
Mikkelsen, L. (2011). Copular clauses. In K. von Heusinger, C. Maienborn, & P. Portner (Eds.), Semantics (pp. 1805–1829). Berlin: De Gruyter Mouton.
Moltmann, F. (2013). Reference to numbers in natural language. Philosophical Study, 162(3), 499–536.
Moro, A. (1997). The raising of predicates: Predicative noun phrases and the theory of clause structure. Cambridge: Cambridge University Press.
Partee, B. H. (1986). Ambiguous pseudoclefts with unambiguous be. In S. Berman, J.-W. Choe, & J. McDonough (Eds.), Proceedings of the North East Linguistic Society (NELS) XVI (pp. 354–366).
Partee, B. H. (1987). Noun phrase interpretation and type-shifting principles. In J. A. G. Groenendijk, D. de Jongh, & M. J. B. Stokhof (Eds.), Studies in discourse representation theory and the theory of generalized quantifiers (Vol. 8, pp. 115–143). Berlin: Walter de Gruyter.
Pelletier, F. J. (2011). Descriptive metaphysics, natural language metaphysics, Sapier-Whorf, and all that stuff: Evidence from the mass-count distinction. In B. H. Partee, M. Glanzberg, & J. Skilters (Eds.), Formal semantics and pragmatics: Discourse, context, and models, volume 6 of The Baltic International Yearbook of Cognition, Logic, and Communication (pp. 1–46).
Pierrehumbert, J. B. (1980). The phonology and phonetics of English intonation, Ph.D. thesis. Cambridge: MIT.
Roberts, C. (1996/2012). Information structure in discourse: Towards an integrated formal theory of pragmatics. In J. H. Yoon, & A. Kathol (Eds.), Ohio State University Working Papers in linguistics (Vol. 49). Reprinted in the 1998 version with a new Afterword in Semantics and Pragmatics, 5(6), 1–69 (2012).
Roberts, C. (2008). Resolving focus. Columbus, OH: Ms., The Ohio State University.
Romero, M. (2005). Concealed questions and specificational subjects. Linguistics and Philosophy, 28(6), 687–737.
Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics, 1(1), 75–116.
Schlenker, P. (2003). Clausal equations (a note on the connectivity problem). Natural Language and Linguistic Theory, 21(1), 157–214.
Schwarzschild, R. (1999). Givenness, AvoidF, and other constraints on the placement of accent. Natural Language Semantics, 7(2), 141–177.
Selkirk, E. O. (1984). Phonology and syntax: The relation between sound and structure. Current Studies in Linguistics. Cambridge, MA: MIT Press.
Snyder, E. (2017). Numbers and cardinalities: What’s really wrong with the easy argument for numbers? Linguistics and Philosophy, 40(4). doi:10.1007/s10988-017-9215-x.
Terken, J., & Hirschberg, J. (1994). Deaccentuation and persistence of grammatical function and surface position. Language and Speech, 37(2), 125–145.
Velleman, D., Beaver, D., Destruel, E., Bumford, D., Onea, E., & Coppock, L. (2012). It-clefts are it (inquiry terminating) constructions. In A. Chereches (Ed.), Proceedings of semantics and linguistic theory (SALT) (Vol. 22, pp. 441–460). Ithaka, NY: Cornell University Press.
Yablo, S. (2005). The myth of the seven. In M. Kalderon (Ed.), Fictionalism in metaphysics (pp. 88–115). New York: Oxford University Press.
Acknowledgements
I would like to thank Craige Roberts and Stewart Shapiro for inviting me to comment on Thomas Hofweber’s paper at the OSU Workshop on the Semantics of Cardinals in the spring of 2014. Commenting on that paper sparked my interest in this topic. I am also grateful to the other participants at that workshop, especially Thomas Hofweber and Stewart Shapiro, for discussion, and to Thomas Hofweber, Craige Roberts, Eric Snyder, and Judith Tonhauser for comments on an earlier draft. Finally, special thanks to Eric Snyder for extensive discussion of these and related issues. Funding was provided by National Science Foundation (Grant No. BCS-0952571).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barlew, J. Focus on numbers. Linguist and Philos 40, 401–426 (2017). https://doi.org/10.1007/s10988-017-9217-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10988-017-9217-8