Bayesianism

by

Kenny Easwaran

• LAST REVIEWED: 28 May 2013
• LAST MODIFIED: 28 May 2013
• DOI: 10.1093/obo/9780195396577-0204

Introduction

Bayesianism is a set of related views in epistemology, statistics, philosophy of science, psychology, and any other subject that deals with notions of belief or confidence. The basic idea is that rather than being an all-or-nothing phenomenon, belief comes in degrees, and these degrees obey some formal constraints related to the axioms of probability theory. In epistemology, these views temper some traditional thoughts about belief and knowledge, and they may give rise to alternative views of justification and evidence. In philosophy of science, these views help structure views about the general practice of science. Many philosophical questions arise not only about these applications of Bayesianism, but also about the formalism used to structure it.

General Overviews

For those who are interested in learning more about a range of issues in Bayesianism, a variety of other resources are available. In particular, The Stanford Encyclopedia of Philosophy is a freely available online resource, with many relevant articles, including Hájek 2011, Hawthorne 2011, Huber 2012, Joyce 2003, and Talbott 2008. The Internet Encyclopedia of Philosophy is also quite helpful, though apart from Huber 2007, it appears to have fewer articles on these topics. Easwaran 2011a and Easwaran 2011b are also overviews that give an outline of many relevant issues, though they are not as easily available.

• Easwaran, Kenny. “Bayesianism I: Introduction and Arguments in Favor.” Philosophy Compass 6.5 (2011a): 312–320.

  DOI: 10.1111/j.1747-9991.2011.00399.x

  Describes the views that make up Bayesianism and discusses some of the arguments that are generally used to support it. Focuses on the Dutch book and representation theorem arguments. Available online for purchase or by subscription.

• Easwaran, Kenny. “Bayesianism II: Applications and Criticisms.” Philosophy Compass 6.5 (2011b): 321–332.

  DOI: 10.1111/j.1747-9991.2011.00398.x

  Shows some applications of Bayesianism in the philosophy of science and discusses several problems that apply there. Also gives a brief overview of some applications of Bayesianism in epistemology and in statistics. Available online for purchase or by subscription.

• Hájek, Alan. “Interpretations of Probability.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2011.

  A discussion of various interpretations of probability. The logical and subjective interpretations are the most relevant for Bayesianism, but many issues that arise in the others are relevant too.

• Hawthorne, James. “Inductive Logic.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2011.

  A very good discussion of some issues in inductive logic, which includes much of Bayesian confirmation theory. Has useful discussion of theorems showing that different priors will converge, given sufficiently similar evidence.

• Huber, Franz. “Confirmation and Induction.” Internet Encyclopedia of Philosophy. 2007.

  Discusses several approaches to the theory of confirmation across the 20th century. Section 4 (on inductive logic) and section 6 (on Bayesian confirmation theory) are the most relevant to the topic of this bibliography.

• Huber, Franz. “Formal Representations of Belief.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2012.

  Compares the probabilistic representation of belief (the basis of Bayesianism) with various other representations that have been proposed, including full belief, as well as alternative formal theories of uncertainty.

• Joyce, James. “Bayes’ Theorem.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2003.

  A helpful discussion of Bayes’ theorem about conditional probabilities, showing why it is so useful in various applications in epistemology and philosophy of science.

• Talbott, William. “Bayesian Epistemology.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2008.

  Has useful discussions of the probability axioms, Dutch book arguments, and Bayesian confirmation theory.