Foundations of Probability & Statistics

University of Utah, Department of Philosophy, Fall 2012

Syllabus | Schedule | Professor

Course Schedule

In the schedule below, you'll see that the course is broken into three main sections. The first, yellow section is devoted to the mathematics of probability theory. Here, we focus on developing a sound, working understanding of the basic axioms and rules of probability. The second, blue section is devoted to the philosophical issues that lie at the foundations of probability and statistics; these issues mostly regard alternative interpretations of the notion of probability. In the third, purple section, we will examine some of the applications of the probability theory to philosophical issues (including inductive reasoning and scientific confirmation).

The pace of our course will be determined in part by my evaluations of student progress. Thus, the schedule below should be thought of as tentative and subject to change throughout the term. Make sure you visit this page regularly in order to keep track of the reading and homework assignments. Below, in the right column, I list your assigned reading for the week, then supplementary material, then any homework, review sessions, exams, and the like. (In the schedule below, the notation "E<#>" generally refers to chapter number <#> in our textbook.)

Week 1 (Aug 20-24)

Course Introduction, Logic Refresher, From Logic to Probability Theory, Basic Notation

• Hacking, ch. 4 [CANVAS]
• McGrew, "From Truth Tables to Joint Probability Distributions" [CANVAS]

• Hacking, chs. 1-3 [CANVAS]
• Fitelson, "A Decision Procedure for Probability Calculus with Applications" [CANVAS]

Enroll in our OLI course (instructions); register for course wiki (instructions); sign-up on wiki to be primary contributor for one reading

Week 2 (Aug 27-31)

The Mathematics of Probability Theory, σ-Algebras, Events and Propositions, Kolmogorov's Axioms

• Eagle, pp. 1-4
• Strevens, "Notes on Bayesian Confirmation Theory," section 3.1 [CANVAS]
• Hájek, SEP: "Interpretations of Probability," section 1

• Kolmogorov, "Foundations of the Theory of Probability" [CANVAS]
• Weisberg, "Varieties of Bayesianism," section 1.1 [CANVAS]
• Williamson, "How Probable is an Infinite Sequence of Heads?" [CANVAS]
• Weintraub, "Reply to Williamson" [CANVAS]
• Pruss, "Infinite Lotteries, Perfectly Thin Darts, and Infinitesimals" [CANVAS]

OLI, Module 5

Week 3 (Sep 3-7)

NO CLASS ON MONDAY (Labor Day); Theorems and Basic Rules

• Eagle, pp. 4-13
• Hacking, chs. 5-6 [CANVAS]
• Strevens, "Notes on Bayesian Confirmation Theory," sections 3.2-3.3 [CANVAS]

• Hacking, ch. 7 [CANVAS]
• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 66-74
• Weisberg, "Varieties of Bayesianism," section 1.2 [CANVAS]
• Hájek, "What Conditional Probability Could Not Be" [CANVAS]
• Easwaran, "What Conditional Probability Must (Almost) Be" [CANVAS]
• Hájek, "What Conditional Probability Also Could Not Be" [CANVAS]

Module 6, pp. 95-99

Week 4 (Sep 10-14)

Interpretations of Probability, Physical versus Epistemic Interpretations, Classical Interpretation

• Hájek, SEP: "Interpretations of Probability" (through section 3.1)
• Laplace, Philosophical Essay on Probabilities (1814), chs. 2-3 [CANVAS]

• Weatherford, ch. 2 [CANVAS]
• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 74-77

Module 6, pp. 100-111 (checkpoint; all checkpoints must be completed by 5pm on the Friday of the assigned week)

Week 5 (Sep 17-21)

Relative Frequency Interpretation

• Venn, Logic of Chance (1866), ch. 1 [CANVAS]
• Keynes, Treatise on Probability (1921), ch. 8 [CANVAS]
• Bulmer, Principles of Statistics, pp. 1-5 [CANVAS]

• Eagle [E21]
• Bulmer, Principles of Statistics, chs. 1-2 [CANVAS]
• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 77-81
• Giere, "Objective Single-Case Probabilities and the Foundations of Statistics" [E29]

Module 7, pp. 112-117 (checkpoint)

Week 6 (Sep 24-28)

Relative Frequency Interpretation; Criticisms

• von Mises, "The Definition of Probability" [E22], pp. 355-369
• Hájek, "Fifteen Arguments Against Finite Frequentism" [E24]

• Jeffrey, "Mises Redux" [E23]
• Hájek, "Fifteen Arguments Against Hypothetical Frequentism" [E25]
• Eagle [E26], pp. 443-449
• Popper, "The Propensity Interpretation of Probability" [E28]
• Humphreys, "Why Propensities Cannot Be Probabilities" [E30]

Module 7, pp. 118-123 (checkpoint)

Week 7 (Oct 1-5)

Partial Entailment Interpretation

• Keynes, Treatise on Probability, chs. 1-3 [CANVAS]

• Eagle [E17], pp. 281-283
• Carnap, "Statistical and Inductive Probability" [E19]

Module 8, pp. 124-132

Week 8 (Oct 8-12)

NO CLASSES THIS WEEK (Fall Break)

Week 9 (Oct 15-19)

TEST WEEK; Partial Entailment Interpretation, Evaluating Logical Probabilities, Principle of Indifference, Criticisms

• Keynes, Treatise on Probability, ch. 4 [CANVAS]
• van Fraassen, "Indifference: The Symmetries of Probability" [E18]

• Eagle [E17], pp. 284-295
• Novack, "A Defense of the Principle of Indifference" [CANVAS]
• Stove, "Is the Theory of Logical Probability Groundless?" [E20]
• Williamson, "Motivating Objective Bayesianism" [CANVAS]
• Seidenfeld, "Why I am Not an Objective Bayesian" [CANVAS]

TAKE-HOME MIDTERM: Due Monday, October 22 by 4pm to my mailbox in CTIHB 402F

Week 10 (Oct 22-26)

Degrees of Belief Interpretation, Dutch Books, Conditionalization

• Ramsey, "Truth and Probability" (1926) [E2]
• Lewis, "Why Conditionalize?" [E6]

• Eagle [E1], pp. 27-35
• Eagle [E5], pp. 115-122
• Vineberg, SEP: "Dutch Book Arguments"
• Bradley and Leitgeb, "When Betting Odds and Credences Come Apart" [E12]
• Jeffrey, "Probability Kinematics" [E7]
• Williamson, "Objective Bayesianism, Bayesian Conditionalisation, and Voluntarism" [CANVAS]

Module 8, pp. 133-137 (checkpoint)

Week 11 (Oct 29 - Nov 2)

Degrees of Belief Interpretation, Criticisms

• Kyburg, "Subjective Probability: Criticisms, Reflections, and Problems" [E3]
• van Fraassen, "Belief and the Will" [E8]

• Eagle [E1], pp. 35-38
• Eagle [E5], pp. 122-127
• Joyce, "A Non-Pragmatic Vindication of Probabilism" [E4]
• Maher, "Diachronic Rationality" [E9]
• Briggs, "Distorted Reflection" [CANVAS]

Module 8, pp. 138-140 (checkpoint)

Week 12 (Nov 5-9)

Objectifying Degrees of Belief, Reflection, Principal Principle

• Lewis, "A Subjectivist's Guide to Objective Chance" [E27]

• Eagle [E1], pp. 38-42
• Eagle [E26], pp. 435-443
• Weisberg, "Varieties of Bayesianism," section 3 [CANVAS]
• Loewer, "David Lewis's Objective Theory of Chance" [E31]
• Pettigrew, "A New Epistemic Utility Argument for the Principal Principle" [CANVAS]
• Pettigrew, "Accuracy, Chance, and the Principal Principle" [CANVAS]

Module 8, pp. 141-144 (checkpoint)

Week 13 (Nov 12-16))

Scientific Confirmation, Bayesian Confirmation Theory

• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 42-49, 89-100 [CANVAS]
• Howson and Urbach, "Bayesian versus Non-Bayesian Approaches to Confirmation" [E14]

• Eagle [E13], pp. 209-214

Module 8, pp. 145-153

Week 14 (Nov 19-23)

NO CLASS ON WEDNESDAY OR FRIDAY (Thanksgiving Break); Bayesian Confirmation Theory

• Glymour, "Why I am Not a Bayesian" [E15]
• Eells and Fitelson, "Symmetries and Asymmetries in Evidential Support" [E16]

• Eagle [E13], pp. 214-217
• Fitelson, "The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity" [CANVAS]

Module 8, pp. 154-159 (checkpoint)

Week 15 (Nov 26-30)

The Problem of Induction

• Hume, An Enquiry Concerning Human Understanding; section IV, part I [CANVAS]
• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 55-66

• Vickers, SEP: "The Problem of Induction"

Module 9, pp. 160-165 (checkpoint)

Week 16 (Dec 3-7)

Probability and the Problem of Induction

• McGrew, "Direct Inference and the Problem of Induction" [CANVAS]
• Campbell and Franklin, "Randomness and the Justification of Induction" [CANVAS]

Module 9, pp. 166-170 (checkpoint)

Week 17 (Dec 10-14)

FINALS WEEK

TAKE-HOME FINAL: Due Monday, December 10 by 4pm to my mailbox in CTIHB 402F