Two Diamonds Are More Than One

Transitivity and the Factivity of Feasible Knowability
  • Elia Zardini
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 23)


After introducing semantic anti-realism and the paradox of knowability, the paper considers a new threat posed to a restricted version of semantic anti-realism by a group of recent arguments. These arguments purport to achieve with respect to a restricted version of anti-realism what the paradox of knowability achieves with respect to an unrestricted version. Building on features of the informal notion of feasible knowability which occurs in the formulation of the anti-realist’s thesis—in particular, on its factivity—the paper shows how the accessibility relation for the relevant modality must be relativized to particular facts, and how this relativization can lead to peculiar failures of transitivity. The paper also argues that the relevant modality cannot be identified with (non-transitive) epistemic possibility. Together, these results suffice to show the unsoundness of the arguments considered, and contribute to an appreciation of the distinctive semantics and logic underlying the anti-realist’s notion of feasible knowability.


Accessibility Relation Restriction Strategy Restricted Version Epistemic Possibility Factivity Constraint 
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Earlier versions of the material in this paper were given in 2005 at the Arché Modality Seminar (University of St Andrews); in 2006, at the International Colloquium on (Anti-)Realisms, Logic and Metaphysics (University of Nancy 2); in 2007, at the Arché Epistemology Seminar (University of St Andrews). I would like to thank all these audiences for very stimulating comments and discussions. Special thanks go to Ross Cameron, Roy Cook, Bob Hale, Jonathan Lowe, Agustín Rayo, Sven Rosenkranz, Crispin Wright and an anonymous referee. In writing this paper, I have benefitted, at different stages, from an AHRC Doctoral Award and from a RIP Jacobsen Fellowship.


  1. 1.
    Božić, M., and K. Došen. 1984. “Models for Normal Intuitionistic Modal Logics.” Studia Logica 43:217–45.CrossRefGoogle Scholar
  2. 2.
    Brogaard, B., and J. Salerno. 2002. “Clues to the Paradoxes of Knowability: Reply to Dummett and Tennant.” Analysis 62:143–50.CrossRefGoogle Scholar
  3. 3.
    Brogaard, B., and J. Salerno. 2009. “Fitch’s Paradox of Knowability.” Stanford Encyclopedia of Philosophy. Accessed March 4, 2010.
  4. 4.
    Došen, K. 1985. “Models for Stronger Normal Intuitionistic Modal Logics.” Studia Logica 44:39–70.CrossRefGoogle Scholar
  5. 5.
    Dummett, M. 1975. Truth and Other Enigmas. London: Duckworth.Google Scholar
  6. 6.
    Dummett, M. 2001. “Victor’s Error.” Analysis 61:1–2.CrossRefGoogle Scholar
  7. 7.
    Fitch, F. 1963. “A Logical Analysis of Some Value Concepts.” The Journal of Symbolic Logic 28:135–42.CrossRefGoogle Scholar
  8. 8.
    Hacking, I. 1967. “Possibility.” The Philosophical Review 76:143–68.CrossRefGoogle Scholar
  9. 9.
    Mackie, J. 1980. “Truth and Knowability.” Analysis 40:90–92.CrossRefGoogle Scholar
  10. 10.
    Rosenkranz, S. 2004. “Fitch Back in Action Again?” Analysis 64:67–71.CrossRefGoogle Scholar
  11. 11.
    Salerno, J. 2009. “Knowability Noir: 1945–1963.” In New Essays on the Knowability Paradox, edited by J. Salerno, 29–48. Oxford: Oxford University Press.Google Scholar
  12. 12.
    Tennant, N. 1997. The Taming of the True. Oxford: Clarendon Press.Google Scholar
  13. 13.
    Tennant, N. 2001. “Is Every Truth Knowable? Reply to Williamson.” Ratio 14:263–80.CrossRefGoogle Scholar
  14. 14.
    Tennant, N. 2002. “Victor Vanquished.” Analysis 62:135–42.CrossRefGoogle Scholar
  15. 15.
    Tennant, N. 2009. “Revamping the Restriction Strategy.” In New Essays on the Knowability Paradox, edited by J. Salerno, 223–38. Oxford: Oxford University Press.Google Scholar
  16. 16.
    Tennant, N. 2010. “Williamson’s Woes.” Synthese 173:9–23.CrossRefGoogle Scholar
  17. 17.
    Williamson, T. 1992. “On Intuitionistic Modal Epistemic Logic.” Journal of Philosophical Logic 21:63–89.Google Scholar
  18. 18.
    Williamson, T. 2000. Knowledge and Its Limits. Oxford: Oxford University Press.Google Scholar
  19. 19.
    Williamson, T. 2000. “Tennant on Knowable Truth.” Ratio 13:99–114.CrossRefGoogle Scholar
  20. 20.
    Williamson, T. 2009. “Tennant’s Troubles.” In New Essays on the Knowability Paradox, edited by J. Salerno, 183–204. Oxford: Oxford University Press.Google Scholar
  21. 21.
    Zardini, E. 2008. “Truth and What Is Said.” Philosophical Perspectives 22:545–74.CrossRefGoogle Scholar
  22. 22.
    Zardini, E. 2011. “Truth without Contra(di)ction.” Forthcoming in The Philosophical Review.Google Scholar
  23. 23.
    Zardini, E. 2011. “Truth, Demonstration and Knowledge. A Solution to the Paradox of Knowability.” ms.Google Scholar
  24. 24.
    Zardini, E. 2011. “Black Boxes. The Semantics and Logic of Obliterative Modalities”. ms.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of PhilosophyNorthern Institute of Philosophy, University of AberdeenAberdeenUK

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