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The logic of probabilistic knowledge

  • Patricia RichEmail author
Article
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Abstract

Sarah Moss’ thesis that we have probabilistic knowledge is from some perspectives unsurprising and from other perspectives hard to make sense of. The thesis is potentially transformative, but not yet elaborated in sufficient detail for epistemologists. This paper interprets Mossean probabilistic knowledge in a suitably-modified Kripke framework, thus filling in key details. It argues that probabilistic knowledge looks natural and plausible when so interpreted, and shows how the most pressing challenges to the thesis can be overcome. Most importantly, probabilistic knowledge can satisfy factivity in the framework, though we are not forced to accept a specific account of probabilistic “facts”. The framework also reflects Moss’ claim that old-fashioned propositional knowledge is just a limiting case of probabilistic knowledge, and all knowledge is fundamentally probabilistic. Finally, Moss endorses a failure of contraposition: for example, p implies probably p, but not probably p does not imply not p. The framework makes clear the sense in which the valid inferences regarding probably p are as Moss claims.

Keywords

Knowledge Probability Modal logic Kripke semantics Factivity Knowledge-first 

Notes

Acknowledgements

This work was carried out as part of the project “Knowledge and Decision,” funded by the Deutsche Forschungsgemeinschaft (Project Number 315078566). Discussions during the project’s symposium on Sarah Moss’ book were instrumental in showing the need for such a paper. The author thanks especially Roman Heil, Jakob Koscholke, Thomas Krödel, Moritz Schulz, Sergiu Spatan and Jacques Vollet for helpful discussions of the manuscript, and audiences at the Charles University in Prague and the Mind, World and Action summer school in Dubrovnik for feedback on presentations of the material. She also thanks an anonymous referee of this journal for helpful suggestions.

References

  1. Artemov, S. (2008). The logic of justification. The Review of Symbolic Logic, 1(4), 477–513.CrossRefGoogle Scholar
  2. Bílková, M., Majer, O., & Peliš, M. (2015). Epistemic logics for sceptical agents. Journal of Logic and Computation, 26(6), 1815–1841.CrossRefGoogle Scholar
  3. Easwaran, K. (2018). Sarah Moss: Probabilistic knowledge. Notre Dame Philosophical Reviews. https://ndpr.nd.edu/news/probabilistic-knowledge/.
  4. Fagin, R., & Halpern, J. Y. (1994). Reasoning about knowledge and probability. Journal of the Association for Computing Machinery, 41(2), 340–367.CrossRefGoogle Scholar
  5. Hájek, A. (2012). Is strict coherence coherent? Dialectica, 66(3), 411–424.CrossRefGoogle Scholar
  6. Hawthorne, J., & Stanley, J. (2008). Knowledge and action. The Journal of Philosophy, 105(10), 571–590.CrossRefGoogle Scholar
  7. Joyce, J. M. (2010). A defense of imprecise credences in inference and decision making. Philosophical Perspectives, 24, 281–323.CrossRefGoogle Scholar
  8. Kooi, B. P. (2003). Probabilistic dynamic epistemic logic. Journal of Logic, Language and Information, 12(4), 381–408.CrossRefGoogle Scholar
  9. McGlynn, A. (2014). Knowledge first?. London: Palgrave Macmillan.CrossRefGoogle Scholar
  10. Moss, S. (2013). Epistemology formalized. Philosophical Review, 122(1), 1–43.CrossRefGoogle Scholar
  11. Moss, S. (2017). Probabilistic knowledge. Oxford: Oxford University Press.Google Scholar
  12. Mueller, A., & Ross, J. (2017). Knowledge dethroned. Analytic Philosophy, 58(4), 283–296.CrossRefGoogle Scholar
  13. Sack, J. (2009). Extending probabilistic dynamic epistemic logic. Synthese, 169(2), 241–257.CrossRefGoogle Scholar
  14. Savage, L. J. (1954). The foundations of statistics. New York: Dover Publications Inc.Google Scholar
  15. Smithies, D. (2012). The normative role of knowledge. Noûs, 46(2), 265–288.CrossRefGoogle Scholar
  16. Stalnaker, R. (2006). On logics of knowledge and belief. Philosophical Studies, 128(1), 169–199.CrossRefGoogle Scholar
  17. van Benthem, J., & Pacuit, E. (2011). Dynamic logics of evidence-based beliefs. Studia Logica, 99(1/3), 61–92.CrossRefGoogle Scholar
  18. van Ditmarsch, H., Halpern, J. Y., van der Hoek, W., & Kooi, B. P. (Eds.). (2015). Handbook of epistemic logic. London: College Publications.Google Scholar
  19. Williamson, J. (2010). In defence of objective Bayesianism. Oxford: Oxford University Press.CrossRefGoogle Scholar
  20. Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.Google Scholar
  21. Yalcin, S. (2011). Nonfactualism about epistemic modality. In A. Egan & B. Weatherson (Eds.), Epistemic modality (pp. 295–332). Oxford: Oxford University Press.CrossRefGoogle Scholar
  22. Yalcin, S. (2012). A counterexample to modus tollens. Journal of Philosophical Logic, 41(6), 1001–1024.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Philosophy DepartmentUniversity of HamburgHamburgGermany

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