Bayesian Epistemology

by

Jürgen Landes

• LAST REVIEWED: 12 January 2021
• LAST MODIFIED: 12 January 2021
• DOI: 10.1093/obo/9780195396577-0417

Introduction

Everyone agrees that it is good to know. We however believe many more things than we know, which has made the notion of belief a target of recent work in epistemology. Not only do we believe propositions, we also believe them to different degrees. That beliefs come in degrees is often taken as a psychological fact and as a normative principle of rationality. The most prominent normative approach to beliefs which come in degrees is Bayesian epistemology. Bayesian degrees of belief are postulated to be represented by numbers in the unit interval [0, 1] obeying the axioms of probability. The convention is that a greater number expresses a stronger belief. The second postulate of Bayesian epistemology governs the change of beliefs whenever new evidence becomes available via updating procedures, Bayesian updating for categorical evidence and the more general Jeffrey updating for uncertain evidence.

General Overviews

A number of traditional philosophical topics of interest have been addressed from a Bayesian point of view. Recent Oxford Bibliographies in Philosophy articles now document the impact of Bayesian epistemology: “Inductive Reasoning” (how previous observations provide inductive support for universal generalizations and/or how they inform our beliefs about the next as yet unobserved instance), “Confirmation” (if and by how much evidence, observations and/or data speak in favor of hypotheses and/or theories), and then there is “Bayesianism” over-viewing Bayesianism (a broad term referring to, among others, the theses that the principles of Bayesian epistemology are true/applicable/useful as well as applications of Bayesian inference, e.g., Sprenger and Hartmann 2019). Weisberg 2015 is an entry in the Stanford Encyclopedia of Philosophy on formal epistemology putting Bayesian epistemology into a wider context. Pettigrew and Weisberg 2019 is another welcome free electronic resource on this topic. See also the separate Oxford Bibliographies in Philosophy article “Formal Epistemology.” Since “Bayesianism” went to press, the Stanford Encyclopedia of Philosophy entry “Formal Representations of Belief” (Huber 2016) has received a substantial update, and a basic introduction to Bayesian epistemology has been published in the form of Landes 2020a. Finally, Joyce 2011 and Briggs 2015 are overviews not mentioned in “Bayesianism.” Since these overviews already mention the main classical monographs, the rest of this bibliography focuses on more recent work. Furthermore, topics which have not already been covered are given priority.

• Briggs, Rachael. “Foundations of Probability.” Journal of Philosophical Logic 44.6 (2015): 625–640.

  DOI: 10.1007/s10992-015-9377-3

  Thorough review of the subjective interpretation of probability boasting 112 references.

• Huber, Franz. “Formal Representations of Belief.” In Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University, 2016.

  Provides discussion and references also of non-Bayesian approaches to beliefs that come in degrees: Imprecise Probabilities, Qualitative Belief, Dempster-Shafer Theory, Possibility Theory, Ranking Theory, Belief Revision Theory, and Nonmonotonic Reasoning. This shows that the Bayesian point of view is not without competitors.

• Joyce, James M. “The Development of Subjective Bayesianism.” In Handbook of the History of Logic. Vol. 10, Inductive Logic. Edited by Dov Gabbay, Stefan Hartmann, and John Woods, 415–475. Oxford: North Holland, 2011.

  Is mainly concerned with the development of the subjective Bayesian point of view according to which the choice of an initial, a prior, probability function is a matter of subjective choice. This view is contrasted with objective Bayesianism by comparing how they deal with the problem of the prior.

• Landes, Jürgen. “Bayesian Epistemology.” In Encyclopaedia of Educational Theory and Philosophy. Edited by Michael A. Peters. Singapore: Springer, 2020a.

  DOI: 10.1007/978-981-287-532-7_693-1

  Short introduction written for an audience with a basic understanding of philosophical issues referencing only a few major (overview) works.

• Pettigrew, Richard, and Jonathan Weisberg. The Open Handbook of Formal Epistemology. PhilPapers Foundation, 2019.

  Contains eleven chapters devoted to different topics. The chapters are aimed at nonspecialists and proceed at a moderate pace.

• Sprenger, Jan, and Stephan Hartmann. Bayesian Philosophy of Science. Oxford: Oxford University Press, 2019.

  Gives a number of applications of Bayesian epistemology in the philosophy of science such as old evidence, the no alternatives argument, the no miracles argument, and explanatory power.

• Weisberg, Jonathan. “Formal Epistemology”. In Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University, 2015.

  Discusses the standard topics of confirmation and induction but also looks at the regress problem (with insights suggested by coherentism—cf. the separate Oxford Bibliographies in Philosophy article “Coherentism”—and foundationalism) and the limits of knowledge from a modal logic perspective.