Probability is the central concept in statistics, and hence, it is employed in every quantitative scientific discipline that uses statistical methods. Despite its ubiquity, there is substantial disagreement among philosophers, scientists, and statisticians about the interpretation of probability and how it ought to be employed in inductive inferences. This course is an introduction to philosophical issues surrounding probability. Time permitting, we will discuss why such issues are important in scientific practice.
We will begin by discussing various interpretations of probability (e.g., logical, frequentist, and subjective). In particular, we will concentrate on the subjective interpretation of probability and arguments for probabilism, which is the thesis that one's degrees of belief ought to be represented by a probability measure. We will also discuss arguments for conditionalization, which is the conjunction of probabilism and the thesis that one's beliefs ought to be updated by Bayes' Rule. In the final section of the course, we will briefly discuss the relationship between probability and induction.
Philosophical thinking is a skill, not unlike playing the piano, riding a bike, or dancing. Learning a new skill requires practice, and the best way to practice philosophical thinking is to write and engage in spirited (but polite) debates with other philosophers. Thus, the central requirement for this course is to write a term paper in which you explicate a particular interpretation of probability and defend it from objections.
However, as noted above, one cannot study the philosophy of probability without knowing a bit about mathematical probability theory. As such, for the first four weeks of the course, I will assign a short problem set that contains several exercises that require you to perform short calculations or to write short proofs. Students should complete the problems and submit them to me at the beginning of class. There will be a short in-class exam on May 27th in which students will be tested on the concepts introduced in these four weeks.
Your final grade will be calculated via a weighted average using the following weights:
Below is a table indicating readings and assignments that are due each class. If you are a registered student in the class, then you can download the readings in .pdf format here. A few abbreviations are employed throughout the course schedule:
| Date | Topic | Readings | Assignment |
|---|---|---|---|
| 15/4 |
Criteria for Interpretations of Probability and Kolmogorov's Axioms
Lecture 1 Slides |
Optional Readings: • SEP. Introduction. Sections 1 and 2. • Carnap. Logical Foundations of Probability. Chapter 1. • For advanced students - Suppes. Chapter 3. Pages 51-70. |
None |
| 22/4 |
History of Probability, The Classical Concept, and The Principle of Indifference
Lecture 2 Slides |
• SEP. Introduction. Sections 1, 2, and 3.1. • Suppes. Section 5.2. Pages 157-167. • DeGroot. Sections 1.1-1.5. Recommended: Keynes. A Treatise on Probability. Chapter 4. Reading Questions 1 |
Problem Set 1 |
| 29/4 | Frequency Interpretations: Finite Frequencies
Lecture 3 Slides |
• SEP. Section 3.4. "Frequency Interpretations" • Suppes. Pages 167-171. • Hajek. "Mises Redux. Redux." • DeGroot. Sections 1.6-1.7. |
Problem Set 2 |
| 6/5 | Frequency Interpretations: Randomness and Infinite Sequences
Lecture 4 Slides |
• Suppes. Pages 171-178. • DeGroot. Sections 1.8-1.11. |
Problem Set 3 |
| 13/5 | The Propensity Interpretation
Lecture 5 Slides |
• Gillies. "Varieties of Propensity" • Suppes. Chapter 5. Section 6. Pages. 202-225. • DeGroot. Sections 2.1-2.2. |
Problem Set 4 |
| 20/5 | No class | None | None |
| 27/5 | The Propensity Interpretation | Eagle. "Twenty One Arguments Against Propensity Analyses of Probability.'' | Quiz on Probability Theory |
| 3/6 |
Logical Theories: Keynes
Lecture 6 Slides |
Keynes. A Treatise on Probability. Chapters 1, 2, 3, 10, 12, and 13. You may skim the proofs in chapters 12 and 13. | None |
| 10/6 |
Survey of Logical Theories
Lecture 7 Slides |
• SEP. Section 3.4. "Logical Interpretations." • Suppes. Chapter 5. Section 5. Pages 184-202. |
None |
| 17/6 |
Personal Probabilities, Scoring Rules, and Dutch Book Arguments
Lecture 8 Slides |
• Lindley. Understanding Uncertainty. Chapters 3, 4, and 5.0-5.9 (inclusive). • Kadane. Principles of Uncertainty. Section 1.1. • de Finetti. Philosophical Lectures on Probability. Chapter 2. Section "Why Proper Scoring Rules are Proper" |
None |
| 24/6 | Personal Probabilities: Savage's Theory
Lecture 9 Slides |
Savage. Foundations of Statistics. Pages 1-20. | None |
| 1/7 | Personal Probabilities: Savage's Theory
Lecture Notes on Savage |
Savage. Foundations of Statistics. Pages 20-40. | None |
| 8/7 | Dynamic Coherence |
• Skyrms. "Dynamic Coherence and Probability Kinematics" Section 1. Pages 1-5. • Levi. "The Demons of Decision" Pages 193-199. |
None |
| 15/7 | Criticisms of Subjective Probability
Lecture 10 Slides |
• Kyburg. "Subjective Probability: Criticisms, Reflections, and Problems" • Savage. Foundations of Statistics. Pages 56-67. |
None |