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Readings in Formal Epistemology pp 649–693Cite as

The Logic of Justification

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Part of the book series: Springer Graduate Texts in Philosophy ((SGTP,volume 1))

Abstract

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidence-based foundation for epistemic logic.

As a case study, we offer a resolution of the Goldman-Kripke ‘Red Barn’ paradox and analyze Russell’s ‘prime minister example’ in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning.

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Notes

  1. 1.

    This work has been supported by NSF grant 0830450, CUNY Collaborative Incentive Research Grant CIRG1424, and PSC CUNY Research Grant PSCREG-39-721.

  2. 2.

    More elaborate models considered below in this paper also use additional operations on justifications, e.g., verifier ‘! ’ and negative verifier ‘?’.

  3. 3.

    Dretske (2005).

  4. 4.

    This proof for LP was offered by Fitting in Fitting (2005).

  5. 5.

    Which was common knowledge back in 1912.

  6. 6.

    In our notation, LP can be assigned the name JT4. However, in virtue of a fundamental role played by LP for Justification Logic, we suggest keeping the name LP for this system.

  7. 7.

    A proof-compliant way to represent negative introspection in Justification Logic was suggested in Artemov et al. (1999), but we will not consider it here.

  8. 8.

    Brezhnev (2000) also considered variants of Justification Logic systems which, in our notations, would be called “JD” and “JD4.”

  9. 9.

    To be precise, we have to substitute c for x everywhere in s and t.

  10. 10.

    Equality is interpreted as identity in the model.

  11. 11.

    Assuming that there are people seeking the job other than Jones and Smith does not change the analysis.

  12. 12.

    Strictly speaking, Case I explicitly states only that Smith has a strong evidence that C(Jones), which is not sufficient to conclude that C(Jones), since Smith’s justifications are not necessarily factive. However, since the actual truth value of C(Jones) does not matter in Case I, we assume that in this instance, Smith’s belief that C(Jones) was true.

  13. 13.

    We assume that everybody is aware that Smith ≠ Jones.

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Acknowledgements

The author is very grateful to Walter Dean, Mel Fitting, Vladimir Krupski, Roman Kuznets, Elena Nogina, Tudor Protopopescu, and Ruili Ye, whose advice helped with this paper. Many thanks to Karen Kletter for editing this text. Thanks to audiences at the CUNY Graduate Center, Bern University, the Collegium Logicum in Vienna, and the 2nd International Workshop on Analytic Proof Systems for comments on earlier versions of this paper. This work has been supported by NSF grant 0830450, CUNY Collaborative Incentive Research Grant CIRG1424, and PSC CUNY Research Grant PSCREG-39-721.

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    Sergei Artemov

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Correspondence to Sergei Artemov .

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  1. (deceased), Dordrecht, The Netherlands

    Horacio Arló-Costa

  2. Center for Information and Bubble Studies, University of Copenhagen, Copenhagen, Denmark

    Vincent F. Hendricks

  3. University of Amsterdam, Amsterdam, The Netherlands

    Johan van Benthem

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Artemov, S. (2016). The Logic of Justification. In: Arló-Costa, H., Hendricks, V., van Benthem, J. (eds) Readings in Formal Epistemology. Springer Graduate Texts in Philosophy, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-20451-2_32

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