Two methods to find truth-value gaps and their application to the projection problem of homogeneity

Abstract

Presupposition, vagueness, and oddness can lead to some sentences failing to have a clear truth value. The homogeneity property of plural predication with definite descriptions may also create truth-value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them are, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying methods of general interest to identify truth-value gaps. Method A consists in collecting both truth judgments (completely true vs. not completely true) and, independently, falsity judgments (completely false vs. not completely false). The second method, employed in experiment series B and C, is based on one-shot ternary judgments: completely true vs. completely false vs. neither. After a calibration of these methods, we use them to demonstrate that homogeneity projects out of negation, the scope of universal sentences and the scope of non-monotonic quantifiers such as exactly two, to some extent (i.e., in two out of three conceivable kinds of gap situations). We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions, scalar implicatures, and something like supervaluations, respectively. We identify free parameters in these theories and assess various variants of them based on our results. Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value.

This is a preview of subscription content, access via your institution.

References

  1. Abrusán, M., and K. Szendrői. 2013. Experimenting with the king of France. Semantics & Pragmatics 6(10): 1–43. doi:10.3765/sp.6.10.

  2. Alxatib, S., and J. Pelletier. 2011. On the psychology of truth-gaps. In Vagueness and communication, ed. R. Nouwen, R. van Rooij, and H.-C. Schmitz, vol. 6517, 13–36. Heidelberg: Springer.

  3. Barr D.J., Levy R., Scheepers C., Tily H.J. (2013) Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language 68: 255–278

    Article  Google Scholar 

  4. Bates, D., M. Maechler, B. Bolker, and S. Walker. 2014. lme4: Linear mixed-effects models using Eigen and S4. ArXiV e-pring. Retrieved from http://arxiv.org/abs/1406.5823.

  5. Bott L., Noveck I.A. (2004) Some utterances are underinformative: The onset and time course of scalar inferences. Journal of Memory and Language 51(3): 437–457

    Article  Google Scholar 

  6. Breheny, R. 2005. Exhaustivity, homogeneity, and definiteness. In Proceedings of the fifth Amsterdam Colloquium, ed. P. Dekker and M. Franke, 59–65.

  7. Brisson, C. 1998. Distributivity, maximality, and floating quantifiers. Unpublished doctoral dissertation, Rutgers University.

  8. Büring, D., and M. Križ. 2013. It’s that and that’s it! Exhaustivity and homogeneity presuppositions in clefts (and definites). Semantics & Pragmatics 6: 1–29.

  9. Burnett, H. 2013. Vague predication, definiteness, and distributivity. Talk at the Substructural Approaches to Paradox workshop, University of Barcelona, Nov. 2013.

  10. Chemla E. (2009) Presuppositions of quantified sentences: Experimental data. Natural Language Semantics 17(4): 299–340

    Article  Google Scholar 

  11. Chemla, E., and L. Bott. 2014. Processing inferences at the semantics/pragmatics frontier: Disjunctions and free choice. Cognition 130(3): 380–396. doi:10.1016/j.cognition.2013.11.013.

  12. Chemla, E., and B. George. Forthcoming. Can we agree about ‘agree’? The Review of Philosophy and Psychology (Accepted with minor revisions).

  13. Chierchia, G., D. Fox, and B. Spector. 2012. Scalar implicatures as a grammatical phenomenon. In Semantics: An international handbook of natural language meaning, ed. C. Maienborn, K. von Heusinger, and P. Portner, vol. 3, 2297–2331. Berlin: Mouton de Gruyter.

  14. Egré P., de Gardelle V., Ripley D. (2013) Vagueness and order effects in color categorization. Journal of Logic, Language and Information 22(4): 391–420

    Article  Google Scholar 

  15. Fodor, J.D. 1970. The linguistic description of opaque contexts. Unpublished doctoral dissertation, MIT.

  16. Frege, G. 1892. On sense and reference. Translated by M. Black, in P. Geach and M. Black (eds.) (1970) Translations from the Philosophical Writings of Gottlob Frege. Oxford: Basil Blackwell

  17. Gajewski, J. 2005. Neg-raising: Polarity and presupposition. Unpublished doctoral dissertation, MIT.

  18. George, B. 2008a. A new predictive theory of presupposition projection. In Proceedings of SALT 18, ed. T. Friedman and S. Ito, 358–375. Ithaca, NY: CLC Publications.

  19. George, B. 2008b. Prediction presupposition projection: Some alternatives in the strong Kleene tradition. Manuscript, UCLA.

  20. George,B. 2008c. Presupposition repairs: A static, trivalent approach to predicting projection.Unpublished master’s thesis, UCLA.

  21. Heim, I. 1983. On the projection problem for presuppositions. In Proceedings of WCCFL 2, ed. Michael Barlow, Daniel Flickinger, and Michael Wescoat, 114–125. Stanford: Stanford University.

  22. Karttunen, L., and S. Peters. 1979. Conventional implicature. In Syntax and semantics 11: Presupposition, ed. C.-K. Oh and D. Dinneen. New York: Academic Press.

  23. Krifka, M. 1996. Pragmatic strengthening in donkey sentences and plural predications. In Proceedings of SALT 6, ed. T. Galloway and J. Spence, 136–153. Ithaca, NY: CLC Publications.

  24. Križ, M., and Spector, B. 2015. A theory of homogeneous plural predication. Manuscript, University of Vienna and Institut Jean Nicod.

  25. Lasersohn P. (1999) Pragmatic halos. Language 3(75): 522–551

    Article  Google Scholar 

  26. Löbner, S. 1987. The conceptual nature of natural language quantification. In Proceedings of the ’87 Debrecen symposion on logic and language, ed. I. Rusza and A. Szabolcsi, 81–94. Budapest: Akadémiai Kiadó.

  27. Löbner S. (2000) Polarity in natural language: Predication, quantification and negation in particular and characterizing sentences. Linguistics and Philosophy 23: 213–308

    Article  Google Scholar 

  28. Magri G. (2009) A theory of individual-level predicates based on blind mandatory scalar implicatures. Natural Language Semantics 17(3): 245–297

    Article  Google Scholar 

  29. Magri, G. 2014. An account for the homogeneity effects triggered by plural definites and conjunction based on double strengthening. In Semantics, pragmatics and the case of scalar implicatures, ed. S. Pistoia Reda, 99–145. Basingstoke: Palgrave Macmillan.

  30. Malamud S. (2012) The meaning of plural definites: A decision-theoretic approach. Semantics & Pragmatics 5: 1–58

    Article  Google Scholar 

  31. Marty, P., E. Chemla, and B. Spector. 2014. Phantom readings: The case of modified numerals. Manuscript, IJN, LSCP, MIT.

  32. R Core Team. 2014. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. Retrieved from http://www.R-project.org/.

  33. Ripley, D. 2011. Contradictions at the borders. In Vagueness and communication, ed. R. Nouwen, R. van Rooij, and H.-C. Schmitz, vol. 6517, 169–188. Heidelberg: Springer.

  34. Sauerland, U. 2011. Vagueness in language: The case against fuzzy logic revisited. In Understanding vagueness—Logical, philosophical and linguistic perspectives, ed. P. Cintula, C. Fermüuller, L. Godo, and P. Hájek, 185–198. London: College Publications.

  35. Schwarz, F. 2013a. Maximality and definite plurals: Experimental evidence. In Proceedings of Sinn und Bedeutung 17, ed. E. Chemla, V. Homer, and G. Winterstein, 509–526.

  36. Schwarz, F. 2013b. False but slow: Rejecting statements with non-referring definites. Manuscript, University of Pennsylvania.

  37. Schwarzschild R. (1994) Plurals, presuppositions and the sources of distributivity. Natural Language Semantics 2(3): 201–248

    Article  Google Scholar 

  38. Serchuk P., Hargreaves I., Zach R. (2011) Vagueness, logic and use: Four experimental studies on vagueness. Mind & Language 26(5): 540–573

    Article  Google Scholar 

  39. Spector, B. 2013, Homogeneity and plurals: From the strongest meaning hypothesis to supervaluations. Presented at Sinn und Bedeutung 18, University of the Basque Country, Sept. 2013.

  40. Spector, B. 2015. Multivalent semantics for vagueness and presupposition. Topoi. doi:10.1007/s11245-014-9292-1.

  41. Steedman M. (2012) Taking scope. MA: MIT Press, Cambridge

    Google Scholar 

  42. Tarski A. (1935) Zur Grundlegung der Boole’schen Algebra I. Fundamenta Mathematicae 24(1): 177–198

    Google Scholar 

  43. Tarski A. (1956) The concept of truth in formalized languages. Logic, Semantics, Metamathematics 2: 152–278

    Google Scholar 

  44. Wickham, H. 2007. Reshaping data with the reshape package. Journal of Statistical Software 21(12): 1–20. Retrieved from http://www.jstatsoft.org/v21/i12/.

  45. Wickham, H. 2009. ggplot2: Elegant graphics for data analysis. New York: Springer. Retrieved from http://had.co.nz/ggplot2/book.

  46. Wickham, H. 2011. The split-apply-combine strategy for data analysis. Journal of Statistical Software 40(1): 1–29. Retrieved from http://www.jstatsoft.org/v40/i01/.

  47. Zehr, J. 2014a. Truth-judgments for vagueness and presupposition. Presented at the Experimental Philosophy Group at Institut Jean Nicod, Paris.

  48. Zehr, J. 2014b. Vagueness, presupposition and truth-value judgments. Unpublished doctoral dissertation, École Normale Supérieure de Paris.

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Manuel Križ.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Križ, M., Chemla, E. Two methods to find truth-value gaps and their application to the projection problem of homogeneity. Nat Lang Semantics 23, 205–248 (2015). https://doi.org/10.1007/s11050-015-9114-z

Download citation

Keywords

  • Plurals
  • Homogeneity
  • Presupposition projection
  • Scalar implicatures
  • Truth-value gaps
  • Experimental pragmatics