Abstract
A central question for ontology is the question of whether numbers really exist. But it seems easy to answer this question in the affirmative. The truth of a sentence like (1) ‘Seven students came to the party’ can be established simply by looking around at the party and counting students. A trivial paraphrase of (1) is (2) ‘The number of students who came to the party is seven’. But (2) appears to entail the existence of a number, and so it seems that we must conclude that numbers exist. This is sometimes called the puzzle of how we can get something from nothing. Most extant attempts to solve the puzzle take it for granted that (1) is ontologically innocent, and focus their attention either on (2) or on the transition from (1) to (2). We argue that both attempts go wrong at the first step: the assumption that (1) is ontologically innocent is undermined by a highly attractive and independently well-motivated degree-based account of number word constructions. Thus the degree-based account provides a straightforward linguistic resolution of the puzzle of how we can get something from nothing. But the paper also has a second aim. The semantics we present treats ‘seven’ as a referring expression that refers to a degree of a certain sort. But what are degrees? We consider various anti-platonist proposals that seek to account for degrees in terms of relations between concrete entities, and argue that they are incompatible with the Universal Density of Measurement hypothesis (UDM) of Fox and Hackl (Linguist Philos 29:537–586, 2006). While the UDM cannot yet claim to be the consensus view among degree-based semanticists, our aim is to use it to illustrate how views about the nature of degrees can be evaluated by considering the properties degrees must have if they are to play the explanatory roles they are called upon to play in linguistics. In the present state of development of degree-based semantics there are difficult open questions about what these properties are. These questions need to be addressed if we are to develop a clear picture of what natural language semantics has to contribute to ontology and metaphysics.
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References
Anderson, C., & Morzycki, M. (2015). Degrees as kinds. Natural Language & Linguistic Theory, 33(3), 791–828.
Balcerak Jackson, B. (2013). Defusing easy arguments for numbers. Linguistics and Philosophy, 36(6), 447–461.
Bale, A. C. (2011). Scales and comparison classes. Natural Language Semantics, 19(2), 169–190.
Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4, 159–219.
Beck, S. (2011). Comparison constructions. In K. von Heusinger, C. Maienborn, & P. Portner (Eds.), Semantics (HSK 33.2) (pp. 1341–1390). Berlin: de Gruyter.
Benacerraf, P. (1965). What numbers could not be. Philosophical Review, 74(1), 47–73.
Brogaard, B. (2007). Number words and ontological commitment. Philosophical Quarterly, 57, 1–20.
Cecchetto, C. (2000). Connectivity and anti-connectivity in pseudoclefts. In M. Hirotani et al. (Eds.), Proceedings of the North Eastern Linguistic Society (= NELS) 30 (pp. 137–151). Amherst, MA: GLSA.
Chierchia, G. (1998). Reference to kinds across languages. Natural Language Semantics, 6(4), 339–405.
Cresswell, M. J. (1976). The semantics of degree. In B. Partee (Ed.), Montague grammar (pp. 261–292). New York: Academic Press.
den Dikken, M., Meinunger, A., & Wilder, C. (2000). Pseudoclefts and ellipsis. Studia Linguistica, 54, 41–89.
Eklund, M. (2005). Fiction, indifference, and ontology. Philosophy and Phenomenological Research, 71(3), 557–579.
Eklund, M. (2006). Metaontology. Philosophy Compass, 1(3), 317–334.
Felka, K. (2014). Number words and reference to numbers. Philosophical Studies, 168, 261–282.
Fine, K. (2009). The question of ontology. In D. Chalmers, D. Manley, & R. Wasserman (Eds.) Metametaphysics: New essays on the foundation of ontology (pp. 157–177). Oxford: Oxford University Press.
Fox, D., & Hackl, M. (2006). The universal density of measurement. Linguistics and Philosophy, 29, 537–586.
Frege, G. (1884). Die Grundlagen der Arithmetik: eine logische-mathematische Untersuchung über den Begriff der Zahl. Breslau: W. Koebner.
Groenendijk, J., & Stokhof, M. (1990). Partitioning logical space. In Annotated handout, Second European Summer school in Logic, Language and Information, Leuven, August 1990.
Gross, S. (2006). Can empirical theories of semantic competence really help limn the structure of reality? Noûs, 40, 43–81.
Hackl, M. (2000). Comparative quantifiers. Ph.D. Dissertation. MIT, Cambridge, MA.
Hackl, M. (2009). On the grammar and processing of proportional quantifiers: Most versus more than a half. Natural Language Semantics, 17, 63–98.
Hale, B. (1987). Abstract objects. Oxford: Blackwell Publishing.
Heim, I. (2000). Degree operators and scope. In B. Jackson & T. Matthews (Eds.), Proceedings of semantics and linguistic theory (SALT) 10 (pp. 40–64). Ithaca, NY: CLC Publications.
Heller, D. (2002). On the relation of connectivity and specificational pseudoclefts. Natural Language Semantics, 10, 243–284.
Higgins, R. F. (1979). The Pseudo-Cleft Construction in English. New York: Garland.
Hoeksema, J. (1983). Negative polarity and the comparative. Natural Language & Linguistic Theory, 1(3), 403–434.
Hofweber, T. (2007). Innocent statements and their metaphysically loaded counterparts. Philosopher’s Imprint, 7(1), 1–33.
Hofweber, T. (2014). Extraction, displacement, and focus: a reply to Balcerak Jackson. Linguistics and Philosophy, 37, 263–267.
Horn, L. (1972). On the semantic properties of logical operators in English. Los Angeles, CA: University of California, Los Angeles Ph.D. thesis.
Keenan, E. L., & Stavi, J. (1986). A semantic characterization of natural language determiners. Linguistics and Philosophy, 9, 253–326.
Kennedy, C. (2015). A “de-Fregean” semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics, 8(10), 1–44.
Klein, E. (1991). Comparatives. In A. von Stechow & D. Wunderlich (Eds.), Semantik/semantics: An international handbook of contemporary research (pp. 673–691). Berlin: Walter de Gruyter.
Liebesman, D. (2015). We do not count by identity. Australasian Journal of Philosophy, 93(1), 21–42.
Link, G. (1982). The logical analysis of plurals and mass terms: A lattice-theoretical approach. In R. Bäuerle, C. Schwarze, & A. von Stechow (Eds.), Meaning, use and interpretation of language (pp. 303–323). Berlin: Walter de Gruyter.
Mikkelsen, L. (2011). Copular clauses. In K. von Heusinger, C. Maienborn, & P. Portner (Eds.), Semantics (HSK 33.2) (pp. 1829–1848). Berlin: de Gruyter.
Moltmann, F. (2004). Properties and kinds of tropes: New linguistic facts and old philosophical insights. Mind, 113(449), 1–41.
Moltmann, F. (2007). Events, tropes, and truthmaking. Philosophical Studies, 134(3), 363–403.
Moltmann, F. (2009). Degree structure as trope structure: A trope-based analysis of positive and comparative adjectives. Linguistics and Philosophy, 32, 51–94.
Moltmann, F. (2013). Reference to numbers in natural language. Philosophical Studies, 162(3), 499–536.
Partee, B. (1986). Ambiguous pseudoclefts with unambiguous be. In S. Berman, J. Choe, & J. McDonough (Eds.), Proceedings of the North Eastern Linguistic Society (= NELS) 16 (pp. 354–366). GLSA: Amherst, MA.
Rayo, A. (2013). The construction of logical space. Oxford: Oxford University Press.
Romero, M. (2005). Concealed questions and specificational subjects. Linguistics and Philosophy, 28, 687–737.
Rosen, G. (1993). The refutation of nominalism(?). Philosophical Topics, 21, 149–186.
Ross, J. R. (1972). Act. In D. Davidson & G. Harman (Eds.), Semantics of natural language (pp. 70–126). Dordrecht: Reidel.
Rullmann, H. (1995). Maximality in the semantics of Wh-constructions. Doctoral dissertation, University of Massachusetts Amherst.
Schaffer, J. (2009). On what grounds what. In D. Chalmers, D. Manley, & R. Wasserman (Eds.), Metametaphysics: New essays on the foundation of ontology (pp. 347–383). Oxford: Oxford University Press.
Schiffer, S. (1994). A paradox of meaning. Noûs, 28, 279–324.
Schlenker, P. (2003). Clausal equations (a note on the connectivity problem). Natural Language & Linguistic Theory, 21, 157–214.
Schwarzschild, R. (2005). Measure phrases as modifiers of adjectives. Recherches Linguistiques de Vincennes, 34, 207–228.
Schwarzschild, R. (2013). Degrees and segments. Proceedings of SALT, 23, 212–238.
Sharvit, Y. (1999). Connectivity in specificational sentences. Natural Language Semantics, 7, 299–339.
Solt, S. (2009). The semantics of adjectives of quantity. Ph.D. Dissertation. City University of New York.
Szabó, Z. G. (2003). Believing in things. Philosophy and Phenomenological Research, 66, 584–611.
Thomasson, A. (2015). Ontology made easy. New York: Oxford University Press.
von Stechow, A. (1984). Comparing semantic theories of comparison. Journal of Semantics, 3, 1–77.
Williams, E. (1983). Semantic vs. syntactic categories. Linguistics and Philosophy, 6, 423–446.
Wright, C. (1983). Frege’s conception of numbers as objects. Aberdeen: Aberdeen University Press.
Yablo, S. (2001). Go figure: A path through fictionalism. Midwest Studies in Philosophy, 25(1), 72–102.
Yablo, S. (2005). The myth of the seven. In M. Kalderon (Ed.), Fictionalist approaches to metaphysics (pp. 88–115). Oxford: Oxford University Press.
Acknowledgements
The research for this essay was carried out at the Zukunftskolleg at the University of Konstanz; we are grateful to the Zukunftskolleg for providing such a supportive environment for interdisciplinary collaboration. We want to thank two anonymous referees as well as the editors Craige Roberts and Stewart Shapiro for their valuable comments. We would also like to express our gratitude to Magdalena Balcerak Jackson, David Liebesman and Maribel Romero, as well as to the members of the Konstanz Working Group on the Foundations of Semantics, for their feedback and encouragement. Funding was provided by Deutsche Forschungsgemeinschaft.
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Balcerak Jackson, B., Penka, D. Number word constructions, degree semantics and the metaphysics of degrees. Linguist and Philos 40, 347–372 (2017). https://doi.org/10.1007/s10988-017-9213-z
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DOI: https://doi.org/10.1007/s10988-017-9213-z