Belief and Probability
Phil 139a, Spring 2016
Mon., Wed., Thur.: 10:00am - 10:50am
Instructor: Ben Sherman
Office: Rabb Graduate Center rm. 306
Email: shermanb@brandeis.edu
Office Hours: Monday 2:00-3:00, Wednesday 11:00-12:00
Course Description
When we cannot be certain, we can regard our beliefs as more or less probable. This course
offers an introduction to formal epistemology, which uses probabilistic reasoning to evaluate
uncertain beliefs.
Four-Credit Course (with three hours of class-time per week)
Success in this 4 credit hour course is based on the expectation that students will spend a
minimum of 9 hours of study time per week in preparation for class (readings, papers, discussion
sections, preparation for exams, etc.).
Learning Goals
1. Introduce students to the terminology and techniques of formal epistemology and inductive
logic
2. Enable students to use and understand the basic symbolic notation of probabilistic reasoning
3. Develop probabilistic reasoning skills, including analyzing belief sets for probabilistic
coherence, and conditional updating
4. Familiarize students with some central problems and debates about when and whether
probabilistic reasoning is a good representation of reasonable thought
Laptop Policy
No laptops, please; it will be both easier and less distracting if you take notes on paper instead.
Academic Integrity
All material submitted for a grade should be the student’s own original, independent work. All
uses of others’ work should be properly documented through notes and citations. Unauthorized
collaboration, plagiarism, and any other violation of University policies on academic integrity
will result in disciplinary action, which can include grading penalties, suspension, or dismissal.
If you have questions about what constitutes academic dishonesty, please consult the Rights and
Responsibilities Handbook, contact the Office of Student Development and Conduct, or ask the
instructor. More information can be found at http://www.brandeis.edu/studentaffairs/srcs/index.html.
Disability
Please let me know as soon as possible if you have a documented disability on record at
Brandeis. I will be glad to make the appropriate arrangements.
Course Texts
The required textbook for the course is An Introduction to Probability and Inductive Logic, by
Ian Hacking. All other required readings will be made available through Latte.
Requirements
All students are expected to participate in class discussion and take responsibility for
understanding key materials. Grades will be based largely on two exams and on regular
homework assignments, but participation will be taken into account as a salient factor when
calculating final grades.
Homework: 25%
Mid-term Exam: 20%
Three short (3 page) papers: 10% each
Final Exam: 25%
Schedule
Readings from Ian Hacking’s Introduction to Probability and Inductive Logic will be listed as
“Hacking, ch. ##.” All other readings will be posted on Latte.
Any changes or additional readings will be announced in class. Updates will be posted on the
course Latte site.
Week 1 (Jan 13-14)
Introduction: Epistemology and Logic
Joseph Butler, excerpt from The Analogy of Religion
Hacking, ch. 1-2
Week 2 (Jan 20-21)
Note: No class Monday on account of Martin Luther King Day. Wednesday follows a Monday
schedule.
Basic Probabilistic Math
Hacking, ch. 3-4
Amos Tversky and Daniel Kahneman, “Extensional Versus Intuitive Reasoning: The
Conjunction Fallacy in Probability Judgment”
Week 3 (Jan 25-28)
Conditional Probability
Hacking, ch. 5-7
Amos Tversky and Daniel Kahneman, “Evidential Impact of Base Rates”
Optional reading:
Thomas Bayes/Richard Price, “An Essay towards Solving a Problem in the Doctrine of Chances”
S. P. Laplace, excerpt from A Philosophical Essay on Probabilities
“Less Wrong”, excerpt from Harry Potter and the Methods of Rationality
Week 4 (Feb 1-4)
Decision Theory: Maximizing Expected Utility
Hacking, ch. 8-9
Week 5 (Feb 8-11)
Decision under Uncertainty
Hacking, ch. 10
John Rawls, excerpt from A Theory of Justice
February Break: Feb 15-19
Week 6 (Feb. 22-26)
First short paper due
Interpretations of Probability
John Venn, excerpt from The Logic of Chance
Frank P. Ramsey, excerpt from “Truth and Probability”
Hacking, ch. 11-12
Week 7 (Feb 29-March 3)
Mid-term exam, Monday March 8
Subjective Probability and Coherence
Hacking, ch. 13-14
Lonard Savage, excerpt from “Elicitation of Personal Probabilities and Expectations”
Bruno de Finetti, excerpt from Theory of Probability
Week 8 (March 7-10)
Updating on Evidence
Hacking, ch. 15
Week 9 (March 14-17)
Application: Miracles as Evidence
David Hume, “Of Miracles” from An Enquiry Concerning Human Understanding
Richard Price, excerpt from Four Dissertations
Jordan Sobel, “On the Evidence of Testimony for Miracles: A Bayesian Interpretation of David
Hume’s Analysis”
David Owen, “Hume Versus Price on Miracles and Prior Probabilities: Testimony and the
Bayesian Calculation”
Philip Dawid and Donald Gillies, “A Bayesian Analysis of Hume’s Argument Concerning
Miracles”
Week 10 (March 21-24)
Application: Reasonable Disagreement
Keith Lehrer and Carl Wagner, excerpt from Rational Consensus in Science and Society
Adam Elga, “Reflection and Disagreement”
March Recess: Friday March 25- Monday March 28
Week 11 (March 30-31)
Second short paper due
Open Question: How Do Probabilities Square with Conventional Beliefs?
Henry Kyburg, excerpt from Probability and the Logic of Belief
David Makinson, “Paradox of the Preface”
Jane Friedman, “Rational Agnosticism and Degrees of Belief”
Week 12 (April 4-7)
Probability as Frequency
Hacking, ch. 16-18
Week 13 (April 11-14)
Open Questions: Subjective Probability vs. Frequency
Hacking, ch. 19
Daniel Kahneman and Amos Tversky, “On the Study of Statistical Intuitions”
Gert Gigerenzer, “How to Make Cognitive Illusions Disappear: Beyond ‘Heuristics and Biases’”
Week 14 (April 18-20)
Open Questions: Should Probabilities Be Precise?
James M. Joyce, “How Probabilities Reflect Evidence”
Roger White, “Evidential Symmetry and Mushy Credence”
James M. Joyce, “A Defense of Imprecise Credences in Inference and Decision Making”
Note: Thursday April 21 follows a Friday schedule
Passover Break: Friday April 22-Friday April 29
Week 15
Third short paper due
Final class meeting (Monday May 2)
Final Exam: TBA