Required Texts:
Ian Hacking, An Introduction to Probability and Inductive Logic, and
George Schlesinger, The Sweep of Probability. Many additional articles
and resources will be made available as they arise in the syllabus, on the web
if at all possible. Students are responsible to download and read all web-based
articles before the relevant class, as indicated on the course schedule. The
course web page is http://homepages.wmich.edu/~mcgrew/gradprob05.htm
Course Description: The aim of this course is to give students a firm understanding of
elementary probability theory, including its basic applications to longstanding
epistemic questions. Along the way we will give considerable attention to
philosophical issues involving the interpretation of the notion of probability,
the interplay between probability and the history and philosophy of science,
and some central epistemological questions regarding evidence, confirmation and
reasonable belief. By the end of the course, students should have a clear sense
of the scope of elementary probability theory, facility in its use, an
understanding of the relations between logic and probability theory, and an
understanding of the epistemological implications of and issues surrounding the
use of Bayes’s Theorem.
Although this course does not have any prerequisites,
it does presuppose a nodding acquaintance with highschool
mathematics. We will move rapidly and the material covered will, at times, be
more difficult than that in the average graduate seminar. Exams will include
proofs and calculations as well as conceptual questions. Students who are
unable or unwilling to do this sort of work will not earn a passing grade and
are strongly urged to take some other course.
Course Requirements: This course meets Tuesday and Thursday of each week at 11:00 a.m. except
for scheduled holidays. Late papers will not generally be accepted without a
medical excuse. Attendance and class participation are taken into account in
the determination of the final grade. In particular, I reserve the right to
subtract five points from the final semester grade for each unexcused absence
beyond the third. Students are expected to come to class having done the
reading indicated on the syllabus and may be asked (with or without advance
warning) to summarize it for the class.
Academic Integrity: You are responsible for making yourself aware of and
understanding WMU's policies and procedures
pertaining to academic integrity, including cheating, fabrication,
falsification and forgery, multiple submission, plagiarism, complicity and computer
misuse. If there is reason to believe you have been involved in academic
dishonesty, you will be referred to the Office of Student Conduct. You will be
given the opportunity to review the charge(s). If you believe you are not
responsible, you will have the opportunity for a hearing. You should consult
with me if you are uncertain about an issue of academic honesty prior to the
submission of an assignment or test.
Grading:
Aside from attendance, the course grade is based on three exams, occasional
quizzes and homework, and the quality (which is not necessarily measurable by
the quantity) of class participation, including demonstrated preparation for
class. The exams will be weighted equally in calculating the final grade, and the quizzes and homework will count for not more
than 25% of the total grade. The grading scale is:
|
A 93-100 |
B 83-87 |
C 73-77 |
D 60-67 |
|
B/A 88-92 |
C/B 78-82 |
D/C 68-72 |
E below 60 |
Note: The following course schedule is tentative. Because
the material is difficult, some of it may take longer than the indicated time.
You are expected to do the readings in accordance with the sequence of topics
even if we are off schedule. Please note that we are not following a direct
path through either of the texts; the order of readings is determined by the
syllabus alone. Any alterations in dates for exams will be announced in class
ahead of time.
Week 1: From
Logic to Probability
Limitations of deductive logic; Probability as a
generalization of logic; Distinction between probabilities of conditionals and
conditional probabilities; Joint probability distributions and their uses; Math
for understanding probability
Week 2:
Interpretations of Probability
Carnap’s two concepts of probability;
Classical, Frequency, Logical and Personalist
conceptions of probability.
Week 3:
Classical Probability and Indifference
Uncertainty and inference; Starting
simple: games of chance and symmetry; Counting equiprobable
events; Pascal’s triangle; The basic rules of the probability calculus;
Conditional probability
Visualizing probability: Venn diagrams and the
probabilistic dart board
Week 4: The Rules of Probability
Visualizing probability: Schlesinger squares and
counterexamples
Week 5: The
Theorem on Total Probability and its Significance
Theorem on total probability; Joint distributions
revisited; Plantinga’s “Principle of Dwindling
Probabilities”
Visualizing probability: Overlapping regions and
non-exclusive events; probability lattices
Weeks 6 and 7:
Bayes’s Theorem
Derivation of Bayes’s
Theorem; Eight Versions of Bayes’s Theorem; The base
rate fallacy; Swamping of the priors; insensitivity to marginal changes in the
base rate;
Sticky priors and special cases; Updating
probabilities; Questions about conditionalization;
Problems with priors and partitions
Visualizing probability: Bayes
nets; McGrew’s square diagrams
Week 8:
Probability, Confirmation, and Old Evidence
Qualitative confirmation theory and its problems;
Defining the concepts of evidence, confirmation, and support; The problem(s) of
old evidence; The measurement of evidential support; Resolution of some
problems of scientific inference
Weeks 9 and 10:
Combined Evidence and Testimony
Combined evidence; Credibility and veracity; Questions
of independence; Hume’s critique of miracles: a Bayesian analysis; Modeling
combined testimony
Visualizing probability: geometric combination of
independent evidence
Week 11: The
Problem of Induction
Hume’s problem; Non-monotonicity:
Hume’s problem reformulated; Solutions to the problem of induction; Bernoulli's
theorem; The fundamental question: success or
rationality?
Weeks 12 and 13:
Inference to the Best Explanation
Claims for IBE by its adherents; IBE and theoretical
virtues; The paucity objection; The guiding challenge; Peirce’s schema for abductive inference; Epistemic accessibility; Ceteris paribus theorems; Theoretical consilience: a Bayesian account
Week 14:
Probability and Decision
Utilities and their ordering; Calculating expected utility;
Probability defined in terms of utilities; Dominance, independence, and choice;
Strategies in decision making (minimax, satisficing, etc.);
Paradoxes of decision theory