Skip to main content
Log in

Ignorance of ignorance

Synthese Aims and scope Submit manuscript

Cite this article

Not ignorance, but ignorance of ignorance, is the death of knowledge.

Alfred North Whitehead

But there are also unknown unknowns. These are things we don’t know we don’t know.

Donald Rumsfeld


I discuss the question of when knowledge of higher order ignorance is possible and show in particular that, under quite plausible assumptions, knowledge of second order ignorance is impossible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others


  1. I am grateful to Eli Alshanetsky, Tom Donaldson, Tim Williamson, the participants in an Academia discussion session and two referees for helpful comments.

  2. The critical observation that second order ignorance implies first order ignorance (Remark (1) below and Lemma 3 of the appendix) goes back to Montgomery and Routley (1966). The earlier literature also deals with some related issues. Montgomery and Routley (1968), Humberstone (1995) and Kuhn (1995) investigate the question of axiomatizing a modal logic with a contingency (or non-contingency) operator as primitive; Cresswell (1988) and Humberstone (1995) consider the question of when necessity can be defined in terms of contingency; and Montgomery and Routley (1966, 1969) and Mortensen (1976) study logics obtained by adding various special non-contingency axioms to a base logic of non-contingency. Hoek and Lomuscio (2004) is a more recent treatment of some of these questions, though apparently written in ignorance of the earlier literature.

  3. I have talked in this section on ‘orders’ in an informal way. See Williamson (1999) for a more formal discussion of the notion.

  4. See Brogaard and Salerno (2013) for a survey of recent work on the topic.

  5. The system S4M, in which all continency is contingent, features prominently in Suzanne Bobzien’s work on vagueness, as in Bobzien (2010) for example.

  6. Thanks to Martin Pleitz for pointing me in the direction of this observation.


  • Bobzien, S. (2010). Higher-order vagueness, radical unclarity and absolute agnosticism. Philosophers’ Imprint, 10(10), 1–30.

    Google Scholar 

  • Brogaard, B., & Salerno, J. (2013) Fitch’s paradox of unknowability. In Stanford encyclopedia of philosophy.

  • Cresswell, M. J. (1988). Necessity and contingency. Studia Logica, 47, 145–149.

    Article  Google Scholar 

  • Fine, K. (2008). The impossibility of vagueness. Philosophical Perspectives, 22(1), 111–136.

    Article  Google Scholar 

  • Fitch, F. (1963). A logical analysis of some value concepts. The Journal of Symbolic Logic, 28, 135–142.

    Article  Google Scholar 

  • Humberstone, I. L. (1995). The logic of non-contingency. Notre Dame Journal of Formal Logic, 36(2), 214–229.

    Article  Google Scholar 

  • Kuhn, T. S. (1995). Minimal non-contingency logics. Notre Dame Journal of Formal Logic, 36, 230–234.

    Article  Google Scholar 

  • Montgomery, H., & Routley, R. (1966). Contingency and non-contingency bases for normal modal logics. Logique et Analyse, 9, 318–328.

    Google Scholar 

  • Montgomery, H., & Routley, R. (1968). Non-contingency axioms for S4 and S5. Logique et Analyse, 11, 422–424.

    Google Scholar 

  • Montgomery, H., & Routley, R. (1969). Modalities in a sequence of normal non-contingency modal systems. Logique et Analyse, 12, 225–227.

    Google Scholar 

  • Mortensen, C. (1976). A sequence of normal modal systems with non-contingency bases. Logique et Analyse, 19, 341–344.

    Google Scholar 

  • Van der Hoek, W., & Lomuscio, A. (2004). A logic for ignorance. Electronic Notes in Computer Science, 85(2), 1–17.

    Google Scholar 

  • Williamson, Timothy. (1999). On the structure of higher-order vagueness. Mind, 108, 127–142.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Kit Fine.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fine, K. Ignorance of ignorance. Synthese 195, 4031–4045 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: