Philosophical Studies

, Volume 161, Issue 3, pp 453–470

Modelling vagueness: what can we ignore?



A theory of vagueness gives a model of vague language and of reasoning within the language. Among the models that have been offered are Degree Theorists’ numerical models that assign values between 0 and 1 to sentences, rather than simply modelling sentences as true or false. In this paper, I ask whether we can benefit from employing a rich, well-understood numerical framework, while ignoring those aspects of it that impute a level of mathematical precision that is not present in the modelled phenomenon of vagueness. Can we ignore apparent implications for the phenomena by pointing out that it is “just a model” and that the unwanted features are mere artefacts? I explore the distinction between representors and artefacts and criticise the strategy of appealing to features as mere artefacts in defence of a theory. I focus largely on theories using numerical resources, but also consider other, related theories and strategies, including theories appealing to non-linear structures.


Vagueness Modelling Sorites paradox Degree theories Artefacts 


  1. Cook, R. (2002). Vagueness and mathematical precision. Mind, 111, 226–247.CrossRefGoogle Scholar
  2. Edgington, D. (1996). Vagueness by degrees. In R. Keefe & P. Smith (Eds.), Vagueness: A reader (pp. 294–316). Cambridge: MIT Press.Google Scholar
  3. Edgington, D. (unpublished manuscript). Vagueness: Filling the gaps.Google Scholar
  4. Keefe, R. (1998). Vagueness by numbers. Mind, 107, 565–579.Google Scholar
  5. Keefe, R. (2000). Theories of vagueness. Cambridge: Cambridge University Press.Google Scholar
  6. MacFarlane, J. (2010). Fuzzy epistemicism. In R. Dietz & S. Moruzzi (Eds.), Cuts and clouds (pp. 438–463). Oxford: Oxford University Press.CrossRefGoogle Scholar
  7. Machina, K. (1976). Truth, belief and vagueness. Journal of Philosophical Logic, 5, 47–78. Reprinted in R. Keefe & P. Smith (Eds), Vagueness: A reader. MIT Press, 1996.Google Scholar
  8. Sanford, D. (1993). The problem of the many, many composition questions and naive mereology. Nous, 27, 219–228.CrossRefGoogle Scholar
  9. Shapiro, S. (1998). Logical consequence: Models and modality. In M. Schirn (Ed.), Philosophy of mathematics today: Proceedings of an international congress in Munich (pp. 131–156). Oxford: Oxford University Press.Google Scholar
  10. Shapiro, S. (2006). Vagueness in context. Oxford: Oxford University Press.CrossRefGoogle Scholar
  11. Smith, N. J. J. (2008). Vagueness and degrees of truth. Oxford: Oxford University Press.CrossRefGoogle Scholar
  12. Tye, M. (1994). Sorites paradoxes and the semantics of vagueness. Philosophical Perspectives 8: Logic and Language, 189–206.Google Scholar
  13. van Fraassen, B. (1984). Belief and the will. Journal of Philosophy, 81, 235–256.CrossRefGoogle Scholar
  14. Weatherson, B. (2005). True, truer, truest. Philosophical Studies, 123, 47–70.CrossRefGoogle Scholar
  15. Williamson, T. (1994). Vagueness. London: Routledge.Google Scholar
  16. Zardini, E. (2008). A model of tolerance. Studia Logica, 90, 337–368.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of SheffieldSheffieldUK

Personalised recommendations