Vague predicates are expressions such as “red”, “tall”, “heap” or “many”, whose meaning does not allow us to draw a fixed and determinate boundary between cases to which these expressions apply and cases to which they do not apply.

The aim of this course is to give a systematic introduction to logics for vagueness and to recent advances on the semantic treatment of vague predicates. The focus of the lectures will be on non-classical logics for first-order languages and on the comparison between three main frameworks: partial two-valued logics (super- and sub-valuationism), three-valued logics (LP and K3), and similarity-based logics (tolerant and strict semantics, Cobreros, Egré, Ripley, van Rooij 2010).

The main originality of the course will be the emphasis put on the duality between the main logics definable in each of these frameworks. Our ambition is to show systematic correspondences and differences between them, in particular concerning the ways in which they either preserve classical logic or depart from it. The last lecture will confront experimental evidence on vagueness (Ripley 2009, Alxatib and Pelletier 2010, Serchuk et al. 2010, Egré, Gardelle, Ripley, in progress) with each of the frameworks examined in the course.

Main Readings

  • S. Alxatib, J.Pelletier (2010). The psychology of vagueness: Borderline cases and contradictions. Mind and Language. (forthcoming).
  • P. Cobreros, P. Egré, D. Ripley, R. van Rooij (2011), Tolerant, Classical, Strict, Journal of Philosophical Logic.
  • P. Cobreros, P. Egré, D. Ripley, R. van Rooij (2011), Tolerance and Mixed Consequence in a super/sub-valuationist setting, Proceedings of LOGKA2010.
  • P. Cobreros (2011), Supervaluationism and Classical Logic, In Nouwen, van Rooij, Sauerland and Schmitz (eds), Vagueness in Communication, LNAI.
  • P. Cobreros (2011), Paraconsistent Vagueness: A Positive Argument (Cobreros). Forthcoming in Synthese.
  • P. Egré (2011), Perceptual Ambiguity and the Sorites in R. Nouwen, R. van Rooij and H-C. Schmitz (eds), Vagueness in Communication, LNAI, Springer.
  • D. Ripley (2011), Contradictions at the Borders, in R. Nouwen, R. van Rooij and H-C. Schmitz (eds), Vagueness in Communication, LNAI, Springer.
  • D. Ripley (2011), Sorting out the Sorites, in F. Berto and E. Mares and K. Tanaka, Paraconsistency: Logic and applications, Springer (Logic, Epistemology, and Unity of Science series).
  • Serchuk, P., Hargreaves, I., & Zach, R. (2010). Vagueness, logic and use: Four experimental studies on vagueness. Mind and Language. (forthcoming).
  • Smith, N. J. J. (2008). Vagueness and degrees of truth. Oxford: Oxford University Press.
  • R. van Rooij (2011). Vagueness, tolerance and non-transitive entailment. in P. Cintula et al. (eds.), Reasoning Under Vagueness: Logical, Philosophical, and  Linguistic Perspectives, College Publications, to appear.
  • E. Zardini (2008). A model of tolerance. Studia Logica, 90, 337–368.


  • Project "Borderlineness and Tolerance" (Ministerio de Ciencia e Innovación, Government of Spain, FFI2010-16984)
  • ANR program "Cognitive Origins of Vagueness" (ANR-07-JCJC-0070), funded by the Agence Nationale de la Recherche.
  • Program VAAG (funded by the European Science Foundation, ESF)
  • Program 'Vagueness, and when to be precise' (funded by the Dutch Science Foundation, NWO)