General information

Course description

If you have a heap of sand, and take away one grain, it is still a heap. This seems like an intuitively correct property of heaps: if you take away one element, it remains a heap. But keep taking away grains, one at a time, and eventually you will only have one grain left, and one grain of sand is not a heap—a contradiction. This paradox is known as the sorites paradox, or the paradox of the heap, and is one example of the more general problem of vagueness. Vague predicates—tall, fast, old, red—are everywhere in our language, so the fact that such basic forms of reasoning lead us astray when we apply them to vague predicates is deeply problematic. In this course we will explore the paradoxes of vagueness, and assess the different philosophical accounts that have emerged in response to them, such as supervaluationism, degree theories, contextualism, and epistemicism.

Content and readings

For details, see the schedule below.


The course will be assessed by means of a final essay of 10–12 pages. Further details will be provided prior to the end of the course.


Date Topic Readings
26 April

Introduction and overview. The sorites paradox and why it matters. Ways of resolving the paradox.

Session 1 lecture notes.

Supplementary: chapter 3 of [Sainsbury 2009], chapter 1 of [Keefe 2000], [Hyde & Raffman 2018], [Sorenson 2018].

3 May

Russell on vagueness. The ideal language view.

Session 2 lecture notes.

Required: [Russell 1923], chapter 2 of [Williamson 1994].

Supplementary: [Hyde 1992].

10 May

Vague predicates and degrees of truth.

Session 3 lecture notes.

Required: [Tye 1994], chapter 4 of [Williamson 1994].

Supplementary: chapter 4 of [Keefe 2000], [Smith 2008].

17 May


Session 4 lecture notes.

Required: [Fine 1975], [Keefe 2008].

Supplementary: chapter 5 of [Williamson 1994], [Keefe 2000].

24 May No class.
31 May No class.
7 June


Session 5 lecture notes.

Required: [Williamson & Simons 1992] (up to page 173).

14 June

Ontic vagueness.

Session 6 lecture notes.

Required: [Tye 1990], [Williams 2008].

Supplementary: [Barnes 2010].

21 June


Session 7 lecture notes.

Required: [Fara 2000].

Supplementary: [Åkerman 2012].

28 June


Session 8 lecture notes.

Required: [Unger 1979].

Supplementary: chapter 6 of [Williamson 1994].

5 July

Higher-order vagueness.

Session 9 lecture notes.

Required: [Fara 2004].

12 July

Continuous sorites paradoxes.

Session 10 lecture notes.

Required: [Weber & Colyvan 2010].

19 July

The sorites paradox and ultrafinitism.

Required: [Dummett 1975].

Supplementary: [Dean 2018].

26 July

Supervaluationism and higher-order vagueness.

Session 12 lecture notes.

Required: [Cobreros 1975].

23 September Assessment submission deadline.


  • Åkerman, J. (2012). Contextualist Theories of Vagueness. Philosophy Compass 7(7):470–480. [link]
  • Barnes, E. (2010). Arguments Against Metaphysical Indeterminacy and Vagueness. Philosophy Compass 5(11):953–964. [link]
  • Cobreros, P. (2011). Supervaluationism and Fara’s Argument Concerning Higher-Order Vagueness. In Vagueness and Language Use (P. Egré and N. Klinedinst, eds.), Palgrave Macmillan, pages 207–221. [link]
  • Dean, W. (2018). Strict finitism, feasibility, and the sorites. The Review of Symbolic Logic 11(2):295–346. [link]
  • Dummett, M. (1975). Wang’s paradox. Synthese 30(3–4):301–324. [link]
  • Egré, P. and N. Klinedinst (2011). Vagueness and Language Use. Palgrave Studies in Pragmatics, Language and Cognition, Palgrave Macmillan.
  • Fara, D. G. (2000). Shifting Sands: An Interest-Relative Theory of Vagueness. Philosophical Topics 28(1):45–81. Originally published under the name Delia Graff. [link]
  • Fara, D. G. (2004). Gap Principles, Penumbral Consequence, and Infinitely Higher-Order Vagueness. In Liars and Heaps (JC Beall, ed.), Oxford University Press, pages 195–221. Originally published under the name Delia Graff.
  • Fine, K. (1975). Vagueness, truth and logic. Synthese 30(3–4):265–300. [link]
  • Hyde, D. (1992). Rehabilitating Russell. Logique et Analyse 35(137–138):139–173. [link]
  • Hyde, D. and D. Raffman (2018). Sorites Paradox. In E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Summer 2018 Edition). [link]
  • Keefe, R. (2000). Theories of Vagueness. Cambridge University Press.
  • Keefe, R. (2008). Vagueness: Supervaluationism. Philosophy Compass 3(2):315–324. [link]
  • Keefe, R. and P. Smith (1997). Vagueness: A Reader. MIT Press.
  • Russell, B. (1923). Vagueness. The Australasian Journal of Psychology and Philosophy 1:84–92. [link]
  • Sainsbury, M. (2009). Paradoxes (third edition). Cambridge University Press.
  • Smith, N. J. (2008). Vagueness and Degrees of Truth. Oxford University Press.
  • Sorenson, R. (2018). Vagueness. In E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Summer 2018 Edition). [link]
  • Tye, M. (1990). Vague objects. Mind 99(396):535–557. [link]
  • Tye, M. (1994). Sorites paradoxes and the semantics of vagueness. Philosophical Perspectives 8:189–206. [link]
  • Unger, P. (1979). There are no ordinary things. Synthese 41(2):177–154. [link]
  • Weber, Z. and M. Colyvan (2010). A topological sorites. The Journal of Philosophy 107(6):311–325. [link]
  • Williams, J. R. G. (2008). Ontic Vagueness and Metaphysical Indeterminacy. Philosophy Compass 3(4):763–788. [link]
  • Williamson, T. (1994). Vagueness. Routledge.
  • Williamson, T. and P. Simons (1992). Vagueness and ignorance. Proceedings of the Aristotelian Society, Supplementary Volume 66(1):145–178. [link]