Foundations of Probability & Statistics

University of Utah, Department of Philosophy, Fall 2013

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 strong 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 evaluation 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 optional, supplementary material, then any homework, review sessions, exams, and the like.

 

Week 1 (Aug 26-30)

NO CLASSES ON WEDNESDAY AND FRIDAY

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

• Hacking, chs. 1-2
• OLI, pp. 86-93 (Module 5)

• McGrew, "From Truth Tables to Joint Probability Distribution" [CANVAS]

Enroll in our OLI course (instructions)
Week 2 (Sep 2-6)

NO CLASS ON MONDAY (Labor Day)

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

• Hacking, chs. 3-4
• OLI, pp. 94-99

• Hájek, SEP: "Interpretations of Probability," section 1
• Kolmogorov, "Foundations of the Theory of Probability" [CANVAS]
• Lyon, "Kolmogorov's Axiomatisation and its Discontents" [CANVAS]

OLI checkpoint 6.1 (all checkpoints must be completed by 5pm on the Friday of the assigned week)
Week 3 (Sep 9-13)

NO LAB ON FRIDAY

Theorems and Basic Rules, Conditional Probability

• Hacking, chs. 5-6
• OLI, pp. 100-106

• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 66-74
• Myrvold, "You Can't Always Get What You Want"
Week 4 (Sep 16-20)

Bayes's Theorem, Bayes's Rule, Introduction to Interpreting Probabilities

• Hacking, ch. 7
• OLI, pp. 107-111

• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 74-77

OLI checkpoint 6.2
Week 5 (Sep 23-27)

Interpretations of Probability, Physical versus Epistemic Interpretations

• Hacking, chs. 11-12
• OLI, pp. 112-117

• Hájek, SEP: "Interpretations of Probability," (through section 3.1)
• Bulmer, Principles of Statistics, chs. 1-2 [CANVAS]

OLI checkpoint 7.1
Week 6 (Sep 30 - Oct 4)

Credences and Probabilities, Dutch Book Argument 1

• Hacking, chs. 13-14
• OLI, pp. 118-123

• Vineberg, SEP: "Dutch Book Arguments"

OLI checkpoint 7.2
Week 7 (Oct 7-11)

Dutch Book Argument 2, Probabilism versus Personalism

• Hacking, ch. 15
• OLI, pp. 124-132

• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 81-84
Week 8 (Oct 14-18)

NO CLASSES THIS WEEK (Fall Break)

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Week 9 (Oct 21-25)

TEST WEEK

REVIEW SESSION: Monday, Oct 21, regular class time
MIDTERM EXAM: Wednesday, Oct 23, regular class time
Week 10 (Oct 28 - Nov 1)

The Subjective-Objective Spectrum, Regularity, Principle of Conditionalization

• OLI, pp. 133-137

OLI checkpoint 8.1
Week 11 (Nov 4-8)

Principle of Indifference, Principal Principle, Reflection

• Eagle, Philosophy of Probability, pp. 284-295 [CANVAS]
• OLI, pp. 138-140

• van Fraassen, "Indifference: The Symmetries of Probability" [CANVAS]
• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 85-89
• Briggs, "Distorted Reflection" [CANVAS]

OLI checkpoint 8.2
Week 12 (Nov 11-15)

Frequencies and Probabilities, Stability

• Hacking, ch. 16-17
• OLI, pp. 141-144

• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 77-81
• Hájek, "Fifteen Arguments Against Finite Frequentism" [CANVAS]

OLI checkpoint 8.3
Week 13 (Nov 18-22)

Significance Testing and Induction, Power, Confidence and Induction

• Hacking, ch. 18-19
• OLI, pp. 145-150

• Hájek, "Fifteen Arguments Against Hypothetical Frequentism" [CANVAS]
Week 14 (Nov 25-29)

NO LAB ON FRIDAY (Thanksgiving Break)

The Problem of Induction

• Hacking, ch. 20
• OLI, pp. 151-155

• Hume, An Enquiry Concerning Human Understanding; section IV, part I [CANVAS]
• Vickers, SEP: "The Problem of Induction"
Week 15 (Dec 2-6)

Probability and the Problem of Induction

• Hacking, chs. 21-22
• OLI, pp. 156-159

• Earman and Salmon, "The Confirmation of Scientific Hypotheses," pp. 55-66
• McGrew, "Direct Inference and the Problem of Induction" [CANVAS]

OLI checkpoint 8.4
Week 16 (Dec 9-13)

TEST WEEK

REVIEW SESSION: Monday, Dec 9, regular class time
CUMULATIVE FINAL EXAM: Wednesday, Dec 11, regular class time