The logic of probabilistic knowledge
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.
KeywordsKnowledge Probability Modal logic Kripke semantics Factivity Knowledge-first
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.
- Easwaran, K. (2018). Sarah Moss: Probabilistic knowledge. Notre Dame Philosophical Reviews. https://ndpr.nd.edu/news/probabilistic-knowledge/.
- Moss, S. (2017). Probabilistic knowledge. Oxford: Oxford University Press.Google Scholar
- Savage, L. J. (1954). The foundations of statistics. New York: Dover Publications Inc.Google Scholar
- van Ditmarsch, H., Halpern, J. Y., van der Hoek, W., & Kooi, B. P. (Eds.). (2015). Handbook of epistemic logic. London: College Publications.Google Scholar
- Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.Google Scholar