Two methods to find truth-value gaps and their application to the projection problem of homogeneity
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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.
KeywordsPlurals Homogeneity Presupposition projection Scalar implicatures Truth-value gaps Experimental pragmatics
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- Abrusán, M., and K. Szendrői. 2013. Experimenting with the king of France. Semantics & Pragmatics 6(10): 1–43. doi: 10.3765/sp.6.10.
- 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.Google Scholar
- 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.
- Breheny, R. 2005. Exhaustivity, homogeneity, and definiteness. In Proceedings of the fifth Amsterdam Colloquium, ed. P. Dekker and M. Franke, 59–65.Google Scholar
- Brisson, C. 1998. Distributivity, maximality, and floating quantifiers. Unpublished doctoral dissertation, Rutgers University.Google Scholar
- 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.Google Scholar
- Burnett, H. 2013. Vague predication, definiteness, and distributivity. Talk at the Substructural Approaches to Paradox workshop, University of Barcelona, Nov. 2013.Google Scholar
- 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.
- Chemla, E., and B. George. Forthcoming. Can we agree about ‘agree’? The Review of Philosophy and Psychology (Accepted with minor revisions).Google Scholar
- 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.Google Scholar
- Fodor, J.D. 1970. The linguistic description of opaque contexts. Unpublished doctoral dissertation, MIT.Google Scholar
- 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 BlackwellGoogle Scholar
- Gajewski, J. 2005. Neg-raising: Polarity and presupposition. Unpublished doctoral dissertation, MIT.Google Scholar
- 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.Google Scholar
- George, B. 2008b. Prediction presupposition projection: Some alternatives in the strong Kleene tradition. Manuscript, UCLA.Google Scholar
- George,B. 2008c. Presupposition repairs: A static, trivalent approach to predicting projection.Unpublished master’s thesis, UCLA.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Križ, M., and Spector, B. 2015. A theory of homogeneous plural predication. Manuscript, University of Vienna and Institut Jean Nicod.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Marty, P., E. Chemla, and B. Spector. 2014. Phantom readings: The case of modified numerals. Manuscript, IJN, LSCP, MIT.Google Scholar
- 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/.
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Schwarz, F. 2013b. False but slow: Rejecting statements with non-referring definites. Manuscript, University of Pennsylvania.Google Scholar
- 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.Google Scholar
- Spector, B. 2015. Multivalent semantics for vagueness and presupposition. Topoi. doi: 10.1007/s11245-014-9292-1.
- Steedman M. (2012) Taking scope. MA: MIT Press, CambridgeGoogle Scholar
- Tarski A. (1935) Zur Grundlegung der Boole’schen Algebra I. Fundamenta Mathematicae 24(1): 177–198Google Scholar
- Tarski A. (1956) The concept of truth in formalized languages. Logic, Semantics, Metamathematics 2: 152–278Google Scholar
- 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/.
- Wickham, H. 2009. ggplot2: Elegant graphics for data analysis. New York: Springer. Retrieved from http://had.co.nz/ggplot2/book.
- 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/.
- Zehr, J. 2014a. Truth-judgments for vagueness and presupposition. Presented at the Experimental Philosophy Group at Institut Jean Nicod, Paris.Google Scholar
- Zehr, J. 2014b. Vagueness, presupposition and truth-value judgments. Unpublished doctoral dissertation, École Normale Supérieure de Paris.Google Scholar