Factive knowability and the problem of possible omniscience

  • Jan HeylenEmail author


Famously, the Church–Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can be avoided. In this article we will look closer at two proposals along these lines (Edgington in Mind 94(376):557–568, 1985; Fuhrmann in Synthese 191(7):1627–1648, 2014a), because there are formal models available for each. It will be argued that, even though the problem of omniscience can be averted, the problem of possible or potential omniscience cannot: there is an accessible state at which all (actual) truths are known. Furthermore, it will be argued that possible or potential omniscience is a price that is too high to pay. Others who have proposed to solve the paradox with the help of a factive concept of knowability should take note (Fara in Synthese 173(1):53–73, 2010; Spencer in Mind 126(502):466–497, 2017).


Factive knowability Actuality Potential knowledge Knowability thesis Church–Fitch paradox of knowability Possible omniscience Potential omniscience 


  1. Boolos, G. S., Burgess, J. P., & Jeffrey, R. C. (2003). Computability and logic (4th ed.). New York: Cambridge University Press.Google Scholar
  2. Carnap, R. (1931). Die Physikalische Sprache als Universalsprache der Wissenschaft. Erkenntnis, 2(1), 432–465.CrossRefGoogle Scholar
  3. De Clercq, R., & Horsten, L. (2004). Perceptual indiscriminability: In defence of Wright’s proof. Philosophical Quarterly, 54(216), 439–444.CrossRefGoogle Scholar
  4. Dummett, M. (1977). Elements of intuitionism. Oxford: Oxford University Press.Google Scholar
  5. Edgington, D. (1985). The paradox of knowability. Mind, 94(376), 557–568.CrossRefGoogle Scholar
  6. Edgington, D. (2010). Possible knowledge of unknown truth. Synthese, 173(1), 41–52.CrossRefGoogle Scholar
  7. Fara, M. (2010). Knowability and the capacity to know. Synthese, 173(1), 53–73.CrossRefGoogle Scholar
  8. Fischer, M. (2013). Some remarks on restricting the knowability principle. Synthese, 190(1), 63–88.CrossRefGoogle Scholar
  9. Fitch, F. B. (1963). A logical analysis of some value concepts. Journal of Symbolic Logic, 28(2), 135–142.CrossRefGoogle Scholar
  10. Fuhrmann, A. (2014a). Knowability as potential knowledge. Synthese, 191(7), 1627–1648.CrossRefGoogle Scholar
  11. Fuhrmann, A. (2014b). Erratum to: Knowability as potential knowledge. Synthese, 191(7), 1649.CrossRefGoogle Scholar
  12. Hart, W. D. (1979). The epistemology of abstract objects: Access and inference. Aristotelian Society Supplementary, 53(1), 153–166.Google Scholar
  13. Hart, W. D., & McGinn, C. (1976). Knowledge and necessity. Journal of Philosophical Logic, 5(2), 205–208.CrossRefGoogle Scholar
  14. Heylen, J. (2016). Counterfactual theories of knowledge and the notion of actuality. Philosophical Studies, 173(6), 1647–1673.CrossRefGoogle Scholar
  15. Hughes, G. E., & Cresswell, M. J. (1996). A new introduction to modal logic. London: Routledge.CrossRefGoogle Scholar
  16. Kaplan, D. (1977). Demonstratives. In J. Almog, J. Perry, & H. Wettstein (Eds.), Themes from Kaplan (pp. 481–563). Oxford: Oxford University Press.Google Scholar
  17. Kripke, S. A. (1963). Semantical analysis of modal logic I. Normal propositional calculi. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik, 9(56), 67–96.CrossRefGoogle Scholar
  18. Maffezioli, P., Naibo, A., & Negri, S. (2013). The Church–Fitch knowability paradox in the light of structural proof theory. Synthese, 190(14), 2677–2716.CrossRefGoogle Scholar
  19. Moore, G. E. (1942). A reply to my critics. In P. A. Schilpp (Ed.), The philosophy of G. E. Moore. Chicago, IL: Open Court.Google Scholar
  20. Percival, P. (1990). Fitch and intuitionistic knowability. Analysis, 50(3), 182–187.CrossRefGoogle Scholar
  21. Rabinowicz, W., & Segerberg, K. (1994). Actual truth, possible knowledge. Topoi, 13(2), 101–115.CrossRefGoogle Scholar
  22. Spencer, J. (2017). Able to do the impossible. Mind, 126(502), 466–497.CrossRefGoogle Scholar
  23. Williamson, T. (1982). Intuitionism disproved? Analysis, 42(4), 203–207.CrossRefGoogle Scholar
  24. Williamson, T. (1987). On the paradox of knowability. Mind, 96(382), 256–261.CrossRefGoogle Scholar
  25. Williamson, T. (1988). Knowability and constructivism. Philosophical Quarterly, 38(153), 422–432.CrossRefGoogle Scholar
  26. Williamson, T. (1992). On intuitionistic modal epistemic logic. Journal of Philosophical Logic, 21(1), 63–89.Google Scholar
  27. Williamson, T. (1994). Never say never. Topoi, 13(2), 135–145.CrossRefGoogle Scholar
  28. Williamson, T. (2000). Knowledge and its limits. New York: Oxford University Press.Google Scholar
  29. Williamson, T. (2016). Absolute provability and safe knowledge of axioms. In L. Horsten & P. Welch (Eds.), Gödel’s Disjunction: The scope and limits of mathematical knowledge (pp. 243–252). Oxford: Oxford University Press.CrossRefGoogle Scholar
  30. Yap, A. (2014). Idealization, epistemic logic, and epistemology. Synthese, 191(14), 3351–3366.CrossRefGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of Science, Institute of PhilosophyKU LeuvenLeuvenBelgium

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