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On the presuppositions of number sentences

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Abstract

This paper is concerned with an intuitive contrast that arises when we consider sentences containing empty definite descriptions. A sentence like ‘The king of France is bald’ appears neither true nor false, while a sentence like ‘My friend was visited by the king of France’ appears false. Recently, Stephen Yablo has suggested an account of this intuitive contrast. Yablo’s account is particularly interesting, since it has important consequences for the ontological commitments of number sentences like ‘The number of planets is even’. However, the paper argues that Yablo’s account is not convincing and that it can thus not establish these consequences. Further, it develops a Strawsonian account of the intuitive contrast. The developed account allows us to draw important conclusions regarding the correct analysis of definite descriptions and of existence sentences containing definite descriptions.

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Notes

  1. I use \(e\) and \(t\) for the two basic types of semantic values: entity and truth-value (Heim and Kratzer 1998, p. 28). A semantic value of type \(<\!\!e,t\!\!>\) is a first-order function that maps entities to truth-values (in set-theoretic terms: a set of entities). A semantic value of type \(<\!<\!\!e,t\!\!>,t\!\!>\) (for short:\(<\!\!et,t\!\!>\)) is a second-order function that maps first-order functions to truth-values (in set-theoretic terms: a set of sets of entities).

  2. Apart from (4), the examples (or at least variations of them) can be found in Lasersohn (1993, p. 113), Strawson (1950, p. 230) and Strawson (1964, p. 114).

  3. Note that one can also formulate the quantificational analysis such that definite descriptions have semantic values only if there is a unique individual that corresponds to the relevant description (cp. Gamut 1991, p. 230f.).

  4. We obtain the same result when e.g. the king of Sweden is sitting in the chair. In this case the relevant falsity-maker for (7) is ‘The king of Sweden (and nobody else) is sitting in that chair’. This falsity-maker obtains in worlds where (3)’s presupposition is true and, thus, (3) has a false \(\pi \)-free entailment in this situation as well.

  5. Note that this commits Yablo to the controversial view that there are worlds at which numbers exist.

  6. This expression is due to von Fintel (2004, p. 340).

  7. Actually, one can be king of France without being France’s head of state, as one retains the title ‘king’ after retiring. To avoid this difficulty, take ‘The present king of France is bald’ instead of (15).

  8. Actually, in some contexts the fact that nobody is bald might influence our intuitions. Suppose, for instance, it is all over the news that there are no bald people left and someone watching the news utters (2). In this context the sentence might appear false. In section 5 an explanation for this observation is provided.

  9. The observation that the sentence ‘The king of France is bald’ appears false as an answer to questions like (19) is due to Strawson (1964, p. 114).

  10. The same kind of worry is raised in (Schoubye 2009, p. 592). However, he does not spell it out in detail.

  11. Cp., e.g., Elbourne (2013, p. 79f.), Jandrić (2014, p. 176), Lasersohn (1993, p. 114), Schoubye (2009, p. 529) and von Fintel (2004, p. 322ff.). An exception is Atlas (cp., e.g., Atlas (1988)). He adopts a similar thesis but neither presents an explanation for it nor defends it against significant objections. This is achieved in the following.

  12. Kadmon (2001, p. 406ff.) thinks that Strawson has in mind questions under discussion rather than the notion of topic. Cp. Schoubye (2009) for an elaboration of this interpretation.

  13. The first sentence is misleadingly formulated, as Ryle does not want to say that \(S\) is about an expression contained in \(S\) but about its denotation.

  14. In the following I mostly rely on the explication given by Reinhart (1981). Cp. for further discussions of the notion of topic e.g. Gundel (1974), Krifka (2007), and Lambrecht (1996). Note that Strawson (1964, p. 114) also uses the notion of topic. But since most of the linguistic research on this notion was done after 1964, he could not rely on a more precise understanding.

  15. In some specific cases one can use (23) as an answer to (26), namely if one points out a contrast, e.g.: ‘PAUL called the plumber and MARY called the landlord.’ (cp., e.g., Krifka (2007, Sect. 5.2) for further details).

  16. But, still, we cannot appropriately substitute this utterance of (2) with ‘As for who is bald, the king of France is bald’, since the question is about baldness and the sentence proposes baldness as a new topic.

  17. Actually, it would be more precise to say that a sentence purports to be about the king of France.

  18. As an anonymous referee pointed out to me, this thesis is rendered false by atypical uses of definite descriptions such as in the sentence ‘The whale is a mammal’, in which ‘the whale’ does not seem to have a semantic value of type \(e\), but is rather used generically (cp. Strawson (1950, p. 320) for related discussion). Thesis (M) should be understood to be restricted to typical uses of definite descriptions, although I do not have a neat explication of typical at hand and have to rely on the reader’s ability to recognize such uses.

  19. Note that every semantic presupposition induces a pragmatic presupposition (but not vice versa). For if a sentence is only true or false if \(\phi \) is true, then speakers who assert or deny \(S\) take \(\phi \) for granted (Stalnaker 1970, p. 279).

References

  • Atlas, D. J. (1988). What are negative existence statements about? Linguistics and Philosophy, 11, 373–394.

    Article  Google Scholar 

  • Chiercha, G., & McConnell-Ginet, S. (2000). Meaning and grammar: An introduction to semantics. Cambridge MA: MIT Press.

  • Donnellan, K. S. (1966). Reference and definite descriptions. Philosophical Review, 75, 281–304.

    Article  Google Scholar 

  • Duranti, A., & Ochs, E. (1979). Left dislocation in Italian conversation. In T. Givon (Ed.), Discourse and syntax: Syntax and semantics (Vol. 12). New York: Academic Press.

    Google Scholar 

  • Elbourne, P. (2013). Definite descriptions. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Fara, D. G. (2001). Descriptions as predicates. Philosophical Studies, 102, 1–42.

    Article  Google Scholar 

  • Gamut, L. T. F. (1991). Logic, language, and meaning, volume 2: Intensional logic and logical grammar. Chicago: Chicago University Press.

    Google Scholar 

  • Gundel, J. (1974). The role of topic and comment in linguistic theory. Ph.D. thesis, Austin: University of Texas.

  • Gundel, J. (1977). Where do cleft sentences come from? Language, 53, 543–559.

    Article  Google Scholar 

  • Hale, B. (1988). Abstract objects. Oxford: Blackwell Publishers.

    Google Scholar 

  • Heim, I., & Kratzer, A. (1998). Semantics in generative grammar. Oxford: Blackwell Publishers.

    Google Scholar 

  • Jandrić, A. (2014). ‘The King of France is bald’ reconsidered: A case against Yablo. Philosophical Studies, 169, 173–181.

    Article  Google Scholar 

  • Kadmon, N. (2001). Formal pragmatics. Oxford: Blackwell Publishers.

    Google Scholar 

  • Keenan-Ochs, E., & Schieffelin, B. (1976). Foregrounding referents: A reconsideration of left-dislocation in discourse. In Proceedings of the 2nd annual meeting of the Berkeley Linguistics Society, Berkeley: University of California, Berkeley.

  • Krifka, M. (2007). Basic notions of information structure. In C. Féry, G. Fanselow, & M. Krifka (Eds.), Interdisciplinary studies of information structure 06 (pp. 13–56). Potsdam: Universitätsverlag.

    Google Scholar 

  • Lambrecht, K. (1996). Information structure and sentence form. Cambridge: Cambridge University Press.

  • Lasersohn, P. (1993). Existence presuppositions and background knowledge. Journal of Semantics, 10, 113–122.

    Article  Google Scholar 

  • McCawley, J. (1981). Everything that linguists have always wanted to know about logic (but were ashamed to ask). Chicago: Chicago University Press.

    Google Scholar 

  • Partee, B. (1986). Noun phrase interpretation and type-shifting principles. In J. Groenendijk, D. de Jongh, & M. Stokhof (Eds.), Studies in discourse representation theory and the theory of generalized quantifiers (pp. 115–144). Dordrecht: Foris.

    Google Scholar 

  • Reinhart, T. (1981). Pragmatics and linguistics: An analysis of sentence topics. Philosophica, 27, 53–94.

    Google Scholar 

  • Ross, J. R. (1967). Constraints on variables in syntax. Ph.D. thesis, Cambridge MA: Massachusetts Institute of Technology.

  • Ryle, G. (1933). About. Analysis, 1, 10–12.

    Article  Google Scholar 

  • Schnieder, B., & Correia, F. (Eds.). (2012). Metaphysical grounding: Understanding the structure of reality. Cambridge: Cambridge University Press.

  • Schoubye, A. J. (2009). Descriptions, truth value intuitions, and questions. Linguistics and Philosophy, 32, 583–617.

    Article  Google Scholar 

  • Stalnaker, R. (1970). Pragmatics. Synthese, 22, 272–289.

    Article  Google Scholar 

  • Strawson, P. F. (1950). On referring. Mind, 59, 320–344.

    Article  Google Scholar 

  • Strawson, P. F. (1964). Identifying reference and truth values. Theoria, 30, 96–118.

    Article  Google Scholar 

  • von Fintel, K. (2004). Would you believe it? The King of France is back! In A. Bezuidenhout & M. Reimer (Eds.), Descriptions and beyond (pp. 315–341). Oxford: Oxford University Press.

  • Yablo, S. (2006). Non-catastrophic presupposition failure. In A. Byrne & J. J. Thomson (Eds.), Content and modality: Themes from the philosophy of Robert Stalnaker (pp. 164–190). Oxford: Oxford University Press.

  • Yablo, S. (2009). Must existence-questions have answers? In D. J. Chalmers, D. Manley, & R. Wassermann (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 507–525). Oxford: Oxford University Press.

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Acknowledgments

Many thanks to Daniel Dohrn, Peter Fritz, Stephen Yablo, two anonymous referees of this journal, as well as my fellow Phloxers Stephan Krämer, Benjamin Schnieder, and Alexander Steinberg for very helpful comments and discussion of the paper’s material at various stages of completion. I would also like to thank the participants of conferences and colloquia in Berlin, Cambridge (MA), Hamburg, Mainz, Paris, and Salzburg.

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    Katharina Felka

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Felka, K. On the presuppositions of number sentences. Synthese 192, 1393–1412 (2015). https://doi.org/10.1007/s11229-014-0629-5

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