# 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 HĂˇjek, "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"

### Bayesian accounts of science and confirmation

**Sep. 30, Successes of Bayesianism**

Reading:

Colin Howson and Peter Urbach, *Scientific Reasoning: the Bayesian Approach*, Chapter 4

**Tuesday, Oct. 5, Grue (NOTE CHANGE IN DATE!)**

Reading:

Branden Fitelson, "Goodman's 'New Riddle' "

Supplementary readings:

Nelson Goodman, "The New Riddle of Induction"

### Problems for Bayesianism

**Oct. 14, Outline of problems**

Reading:

Clark Glymour, "Why I am not a Bayesian"

**Tuesday, Oct. 19, Old Evidence and Logical Omniscience (NOTE CHANGE IN DATE!)**

Reading:

Daniel Garber, "Old Evidence and Logical Omniscience in Bayesian Confirmation Theory"

Supplementary readings:

Ian Hacking, "Slightly More Realistic Personal Probabilities"

Richard Jeffrey, "Bayesianism with a Human Face"

Haim Gaifman, "Reasoning with Limited Resources and Assigning Probabilities to Arithmetical Statements"

**Oct. 28, Old Evidence**

Reading:

Ellery Eells, "Problems of Old Evidence" (reprinted as "Bayesian Problems of Old Evidence")

**Nov. 4, Measuring Confirmation**

Reading:

David Christensen, "Measuring Confirmation"

Ellery Eells and Branden Fitelson, "Measuring Confirmation and Evidence"

Supplementary readings:

Branden Fitelson, "The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity"

**Nov. 11, New Theories**

Reading:

Charles Chihara, "Some Problems for Bayesian Confirmation Theory"

Patrick Maher, "Probabilities for New Theories"

Supplementary readings:

John Earman, *Bayes or Bust?*, Chs. 5 and 8

### Further topics

**Nov. 18, Statistical Methodology**

Reading:

Ian Hacking, "The Foundations of Statistics"

Supplementary reading:

Barnard, "The Meaning of a Significance Level"

**Nov. 25, Thanksgiving**

**Dec. 2, Bayesianism and the Law**

Reading:

Michael Finkelstein and William Fairley, "A Bayesian Approach to Identification Evidence"

Supplementary reading:

Laurence Tribe, "Trial by Mathematics: Precision and Ritual in the Legal Process"

**FINAL PAPER DUE DEC. 14**