Philosophical Studies

, Volume 165, Issue 3, pp 765–786 | Cite as

Luminosity and determinacy

  • Elia Zardini


The paper discusses some ways in which the phenomenon of borderline cases may be thought to bear on the traditional philosophical idea that certain domains of facts are fully open to our view. The discussion focusses on a very influential argument (due to Tim Williamson) to the effect that, roughly, no such domains of luminous facts exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts that are best candidates for being luminous plays an illicit role in the argument. The paper investigates this issue by centring around the idea that vagueness brings with itself borderline cases, and that these in turn generate absence of a fact of the matter and hence epistemically benign lack of knowledge. It is argued that, given the possibility of absence of a fact of the matter, the idea of luminosity should be reformulated using the notion of determinacy, and that the resulting reformulation is not immediately subject to the original anti-luminosity argument. However, it is shown that the specific understanding of determinacy required by this strategy validates a new argument against the reformulated version of luminosity. Moreover, reflection on the connection between mistake and absence of a fact of the matter offers another argument against such version, with the surprising upshot that, granting the soundness of the original anti-luminosity argument, not even the determinacy of a certain fact would guarantee its knowability.


Borderline cases Determinacy Ignorance Luminosity Sorites Vagueness 



Earlier versions of the material in this paper have been presented in 2008 at the Arché Audit and at the Arché Basic Knowledge Seminar (University of St Andrews); in 2009, at the Formal Epistemology Project Research Seminar (University of Leuven), at a research seminar at the University of Aarhus, at the 5th SOPHA Congress (University of Geneva), at the COGITO Epistemology Seminar (University of Bologna) and at the NIP Formal Epistemology Seminar (University of Aberdeen); in 2010, at the 2nd Workshop on Vagueness and Physics, Metaphysics, and Metametaphysics (University of Barcelona). I’d like to thank all these audiences for very stimulating comments and discussions. Special thanks go to Derek Ball, Annalisa Coliva, Laura Delgado, Dylan Dodd, Julien Dutant, Paul Égré, Gabriel Gomez, Chris Kelp, Hannes Leitgeb, Dan López de Sa, Aidan McGlynn, Sebastiano Moruzzi, Sven Rosenkranz, Ian Rumfitt, Johanna Seibt, Jason Stanley, Brian Weatherson, Robbie Williams and Crispin Wright. I’m particularly grateful to Stew Cohen for his support, feed-back and advice on my luminosity-related work throughout the years. But my greatest intellectual debt here is obviously to Tim Williamson, whose seminal articles on the topic provide much of the foundation for the present investigations. In writing this paper, I have benefitted, at different stages, from an AHRC Postdoctoral Research Fellowship and a UNAM Postdoctoral Research Fellowship, as well as from partial funds from the project FFI2008-06153 of the Spanish Ministry of Science and Innovation on Vagueness and Physics, Metaphysics, and Metametaphysics, from the project CONSOLIDER-INGENIO 2010 CSD2009-00056 of the Spanish Ministry of Science and Innovation on Philosophy of Perspectival Thoughts and Facts (PERSP) and from the European Commission’s 7th Framework Programme FP7/2007–2013 under Grant FP7-238128 for the European Philosophy Network on Perspectival Thoughts and Facts (PETAF).


  1. Barnett, D. (2011). Does vagueness exclude knowledge? Philosophy and Phenomenological Research, 82, 22–45.CrossRefGoogle Scholar
  2. Dorr, C. (2003). Vagueness without ignorance. Philosophical Perspectives, 17, 83–113.CrossRefGoogle Scholar
  3. Dummett, M. (1991). The logical basis of metaphysics. Cambridge: Harvard University Press.Google Scholar
  4. Fara, D. (2003). Gap principles, penumbral consequence, and infinitely higher-order vagueness. In J. C. Beall (Ed.), Liars and heaps (pp. 195–221). Oxford: Oxford University Press.Google Scholar
  5. Field, H. (1973). Theory change and the indeterminacy of reference. The Journal of Philosophy, 70, 462–481.CrossRefGoogle Scholar
  6. Field, H. (1994). Disquotational truth and factually defective discourse. The Philosophical Review, 103, 405–452.CrossRefGoogle Scholar
  7. Field, H. (2003). No fact of the matter. Australasian Journal of Philosophy, 81, 457–480.CrossRefGoogle Scholar
  8. Fine, K. (1975). Vagueness, truth and logic. Synthese, 30, 265–300.CrossRefGoogle Scholar
  9. Goldman, A. (1976). Discrimination and perceptual knowledge. The Journal of Philosophy, 73, 771–791.CrossRefGoogle Scholar
  10. Gómez-Torrente, M. (1997). Two problems for an epistemicist view of vagueness. Philosophical Issues, 8, 237–245.CrossRefGoogle Scholar
  11. Hawthorne, J. (2005a). Vagueness and the mind of God. Philosophical Studies, 122, 1–25.CrossRefGoogle Scholar
  12. Hawthorne, J. (2005b). Knowledge and evidence. Philosophy and Phenomenological Research, 70, 452–458.CrossRefGoogle Scholar
  13. Heck, R. (1993). A note on the logic of (higher-order) vagueness. Analysis, 53, 201–208.Google Scholar
  14. McGee, V., & McLaughlin, B. (2004). Logical commitment and semantic indeterminacy: A reply to Williamson. Linguistics and Philosophy, 27, 123–136.CrossRefGoogle Scholar
  15. Richard, M. (1981). Temporalism and eternalism. Philosophical Studies, 39, 1–13.CrossRefGoogle Scholar
  16. Schiffer, S. (2003). The things we mean. Oxford: Oxford University Press.CrossRefGoogle Scholar
  17. Sorensen, R. (1988). Blindspots. Oxford: Clarendon Press.Google Scholar
  18. Stalnaker, R. (1981). Indexical belief. Synthese, 49, 129–151.Google Scholar
  19. Tennant, N. (2000). Anti-realist aporias. Mind, 109, 831–860.CrossRefGoogle Scholar
  20. Williamson, T. (1992). Inexact knowledge. Mind, 101, 217–242.CrossRefGoogle Scholar
  21. Williamson, T. (1994). Vagueness. London: Routledge.Google Scholar
  22. Williamson, T. (1995). Does assertibility satisfy the S4 axiom? Crítica, 27, 3–22.Google Scholar
  23. Williamson, T. (1996). Cognitive homelessness. The Journal of Philosophy, 93, 554–573.CrossRefGoogle Scholar
  24. Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.Google Scholar
  25. Wright, C. (2001). On being in a quandary: Relativism, vagueness, logical revisionism. Mind, 60, 45–98.CrossRefGoogle Scholar
  26. Zardini, E. (2006). Higher-order vagueness and paradox: The glory and misery of S4 definiteness. In J. Šķilters, M. Eklund, Ó. Jónsson & O. Wiegand (Eds.), Paradox: Logical, cognitive and communicative aspects, vol. I of The Baltic international yearbook of cognition, logic and communication (pp. 203–220). Riga: University of Latvia Press.Google Scholar
  27. Zardini, E. (2008a). A model of tolerance. Studia Logica, 90, 337–368.CrossRefGoogle Scholar
  28. Zardini, E. (2008b). Living on the slippery slope. The nature, sources and logic of vagueness. PhD thesis, Department of Logic and Metaphysics, University of St Andrews.Google Scholar
  29. Zardini, E. (2012a). Higher-order sorites paradox. Journal of Philosophical Logic, Forthcoming.Google Scholar
  30. Zardini, E. (2012b). First-order tolerant logics. The Review of Symbolic Logic, Forthcoming.Google Scholar
  31. Zardini, E. (2012c). Luminosity and vagueness. Dialectica, Forthcoming.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Northern Institute of Philosophy, Department of Philosophy, School of Divinity, History and PhilosophyUniversity of AberdeenAberdeenUK

Personalised recommendations