Phil 585

Bayesianism in Philosophy of Science

Some philosophers of science have argued that by focusing on probabilistic notions like degree of belief, we can give a good account of the notions of scientific evidence and confirmation, thus giving us a handle on parts of the problem of induction. Defenders, called Bayesians, say this account can additionally help us understand the importance of having evidence from a variety of sources, theories that provide a good explanation of the evidence, and various other features of scientific reasoning. Opponents raise several important problems for Bayesianism, including the problem of the priors, the problem of old evidence, and the problem of new theories.

This seminar will begin with an overview of the probability theory that will be needed for the rest of the class, and then continue with some arguments in favor of Bayesianism and Bayesian accounts of some traditional problems of confirmation. Depending on student interest, we may continue with extended discussion of one or two critics of Bayesianism, or shorter discussion of several distinct criticisms.

Aug. 26, Introduction

No required reading, but we will go over the basics of probability theory in class, and some basic discussion of the interpretation of probability.

Supplementary readings:

Alan Hájek, "Interpretations of Probability", in the Stanford Encyclopedia of Philosophy

Arguments for Bayesianism

Sep. 2, Dutch Book Arguments

Reading:

David Christensen, "Dutch-book Arguments Depragmatized: Epistemic Consistency for Partial Believers"

Supplementary readings:

Paul Teller, "Conditionalization and Observation"

David Christensen, "Clever Bookies and Coherent Beliefs"

Alan Hajek, "Scotching Dutch Books"

Sep. 9, Representation Theorems

Reading:

Frank Ramsey, "Truth and Probability"

Supplementary readings:

You might look up the following books and find the relevant chapters for more modern presentations of versions of this argument

L.J. Savage, The Foundations of Statistics (1972)

Richard Jeffrey, The Logic of Decision (1990)

James Joyce, The Foundations of Causal Decision Theory (1999)

Sep. 16, Accuracy Domination

Reading:

James Joyce, "A Nonpragmatic Vindication of Probabilism"

Supplementary readings:

James Joyce, "Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief"

Hannes Leitgeb and Richard Pettigrew, "An Objective Justification of Bayesianism I: Measuring Inaccuracy", "An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy"

David Lindley, "Scoring Rules and the Inevitability of Probability"

Sep. 23, Cox's Theorem

Reading:

E.T. Jaynes, Probability Theory: the Logic of Science, sections of Chapters 1 and 2 (obtained from Larry Bretthorst's page on Jaynes at http://bayes.wustl.edu/)

Supplementary readings:

http://en.wikipedia.org/wiki/Cox's_theorem

Richard Cox, "Probability, Frequency, and Reasonable Expectation"

Glenn Shafer, "Comments on 'Constructing a Logic of Plausible Inference: A Guide to Cox's Theorem', by Kevin S. Van Horn"

Mark Colyvan, "The Philosophical Significance of Cox's Theorem"