Probabilistic Representations of Belief

by

Darren Bradley

• LAST REVIEWED: 09 May 2023
• LAST MODIFIED: 27 March 2019
• DOI: 10.1093/obo/9780195396577-0393

Introduction

Formal epistemology is epistemology that uses mathematical tools. Foremost among them is probability theory. We can represent the strength of a belief by assigning it a number between zero and one, with one representing belief with maximal strength, and zero with minimal strength. Using these, and other, formal tools, we can investigate a range of epistemological questions, such as: What justifies beliefs? How should evidence inform belief? How should we update our beliefs over time?

General Overviews

There are lots of excellent overviews, and are the best place to start. All have a slightly different focus. Strevens 2017 is very introductory and user-friendly. Huber 2007 and Vickers 2022 connect probabilistic methods with the problem of induction. Genin and Huber 2020 discusses probabilistic methods and connects them with other formal tools for modeling beliefs. Talbott 2022 and Weisberg 2011 offer detailed discussions of various forms of Bayesianism and their costs and benefits. Weisberg 2021 connects probabilistic theories with other issues in epistemology. Hájek 2019 focuses on the interpretation of probability.

• Hájek, Alan. “Interpretations of Probability.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University, 2019.

  Explains the various interpretations of probability, including the subjective interpretation of probabilities as degrees of belief.

• Huber, Franz. “Confirmation and Induction.” In The Internet Encyclopedia of Philosophy. Edited by J. Fieser and B. Dowden, 2007.

  Discusses the problem of induction and attempts to solve the problem which use probabilities, drawing largely on Carnap’s work.

• Genin, Konstantin, and Franz Huber. “Formal Representations of Belief.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University, 2020.

  Explains how beliefs can be modeled with probabilities, gives some arguments for and against, and also explain nonprobabilistic approaches such as AGM and ranking theory.

• Strevens, Michael. Notes on Bayesian Confirmation Theory. 2017.

  An introductory discussion and defense of Bayesianism.

• Talbott, William. “Bayesian Epistemology.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University, 2022.

  A brief discussion of the basics of Bayesianism, explaining the arguments for and problems it faces.

• Vickers, John. “The Problem of Induction.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta Stanford, CA: Stanford University, 2022.

  Explains the problem of induction and attempts to solve it which use probabilities. Similar to, but less technical than, Huber’s “Confirmation and Induction.”

• Weisberg. “Varieties of Bayesianism.” In Inductive Logic. Handbook of the History of Logic: Vol. 10. Edited by D. M. Gabbay, S. Hartmann, and J. Woods, 477–551. New York: Elsevier, 2011.

  DOI: 10.1016/B978-0-444-52936-7.50013-6

  A detailed textbook style discussion of Bayesianism.

• Weisberg, Jonathan. “Formal Epistemology.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University, 2021.

  Explains many of the applications of formal epistemology to wider epistemological problems, including not only the problem of induction but also the regress problem and the knowability paradox.