Introduction
This paper brings together several approaches to vagueness, and ends by suggesting a new approach. The common thread in these approaches is the crucial role played by context. In Section 2, we treat game-theoretic rationales for vagueness, and for the related concepts of ambiguity and generality. Common about these rationales is that they are based on the assumption of a conflict of interest between speaker and listener. We review this literature using a single example. We argue that the most plausible application to vagueness in natural language of these models is one where the listener only imperfectly observes the context in which the speaker makes her utterances. Yet, it is clear that not all vagueness can be accounted for by conflicts of interest. This is why the rest of the paper looks at the case of common interest. Section 3 argues that being vague by saying that someone is bald makes sense in a context where precision is of less importance; in a context where precision is of more importance, one can then refer to someone as completely bald. This make sense because the longer and therefore more costly to utter expression ‘completely bald’ is then used less often. Vagueness is thus seen as an application of Horn’s pragmatic rule that (un)marked states get an (un)marked expression. Section 4 tackles the Sorites paradox, which apparently leads to the violation of standard axioms of rational behaviour, and shows that this paradox arises from the use of vague predicates in an inappropriate context. If, as suggested by the Sorites paradox, fine-grainedness is important, then a vague language should not be used. Once vague language is used in an appropriate context, standard axioms of rational behaviour are no longer violated. Section 5 finally takes a different approach from the previous sections, and following prospect theory assumes that context directly enter agents’ utility functions in the form of reference points, with respect to which agents think in gains and losses. The rationale for vagueness here is that vague predicates allow players to express their valuations, without necessarily uttering the context, so that the advantage of vague predicates is that they can be expressed across contexts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arrow, K.: Rational choice functions and orderings. Economica 26, 121–127 (1959)
Aumann, R.: Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics 1, 67–96 (1974)
van Benthem, J.: Later than late: on the logical origin of the temporal order. Pacific Philosophical Quarterly 63, 193–203 (1982)
Blume, A., Board, O.J., Kawamura, K.: Noisy talk. Theoretical Economics 2, 395–440 (2007)
Blume, A., Board, O.: Intentional vagueness working paper. University of Pittsburgh (2008)
Crawford, V.P., Sobel, J.: Strategic information transmission. Econometrica 50, 1431–1451 (1982)
De Jaegher, K.: Error-proneness as a handicap signal. Journal of Theoretical Biology 224, 139–152 (2003a)
De Jaegher, K.: A game-theoretic rationale for vagueness. Linguistics and Philosophy 26, 637–659 (2003b)
De Jaegher, K.: The evolution of Horn’s rule. Journal of Economic Methodology 15, 275–284 (2008)
De Jaegher, K., Rosenkranz, S., Weitzel, U.: Economic laboratory experiment on Horn’s rule. Utrecht University (2008) (working paper)
Dummett, M.: Wang’s paradox. Synthese 30, 301–324 (1975)
Farrell, J.: Meaning and credibility in cheap-talk games. Games and Economic Behavior 5, 514–531 (1993)
Forges, F.M.: An approach to communication equilibria. Econometrica 54, 1375–1385 (1986)
Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge (1991)
Gaifman, H.: Vagueness, tolerance and contextual logic. Columbia University (1997) (manuscript)
Graff, D.: Shifting sands: An interest relative theory of vagueness. Philosophical Topics 28, 45–81 (2000)
Harsanyi, J.C.: Games with randomly disturbed payoffs: a new rationale for mixed-strategy equilibrium points. International Journal of Game Theory 2, 1–23 (1973)
Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291 (1979)
Kamp, H.: Two theories of adjectives. In: Keenan, E. (ed.) Formal Semantics of Natural Language, pp. 123–155. Cambridge University Press, Cambridge (1975)
Kamp, H.: The paradox of the heap. In: Mönnich, U. (ed.) Aspects of Philosophical Logic, pp. 225–277. D. Reidel, Dordrecht (1981)
Keefe, R.: Vagueness without context change. Mind 116, 462 (2007)
Klein, E.: The semantics of positive and comparative adjectives. Linguistics and Philosophy 4, 1–45 (1980)
Krantz, D., Duncan Luce, R., Suppes, P., Tversky, T.: Foundations of Measurement, vol. 1. Academic Press, New York (1971)
Lipman, B.L.: Why is language vague? Boston University (2006) (working paper)
Luce, R.D.: Semiorders and a theory of utility discrimination. Econometrica 24, 178–191 (1956)
Myerson, R.B.: Game Theory – Analysis of Conflict. Harvard University Press, Cambridge (1991)
Pinkal, M.: Consistency and context change: The Sorites paradox. In: Landman, F., Veltman, F. (eds.) Varieties of Formal Semantics, Proceedings of the fourth Amsterdam Colloquium. Groningen-Amsterdam Studies in Semantics, Foris Publications, Dordrecht (1984)
Raffman, D.: Vagueness without paradox. The Philosophical Review 103, 41–74 (1994)
Raffman, D.: Vagueness and Context-Relativity. Philosophical Studies 81, 175–192 (1996)
van Rooij, R.: Revealed preference and satisficing behavior. In: Bonano, G., et al. (eds.) Proceedings of LOFT 2008, Amsterdam University Press (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
De Jaegher, K., van Rooij, R. (2011). Strategic Vagueness, and Appropriate Contexts. In: Benz, A., Ebert, C., Jäger, G., van Rooij, R. (eds) Language, Games, and Evolution. Lecture Notes in Computer Science(), vol 6207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18006-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-18006-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18005-7
Online ISBN: 978-3-642-18006-4
eBook Packages: Computer ScienceComputer Science (R0)