Philosophy 148

The sun has risen every day in the past. Will it rise tomorrow? A gambler just lost ten bets in a roll. Should they be more confident that they will win the next one? More generally, how should we make predictions and generalizations based on data collected in the past? Probability theory is a powerful tool for studying such questions. This course is an introduction to the fundamental concepts of probability and inductive logic (the axioms of probability, conditional probability, Bayes’ rule, and expected value) and their application to the problem of induction and theory confirmation. Along the way, we will look at two dominant schools of statistical inferences, Bayesian and frequentist, and critically examine their philosophical foundations and limitations. We will also discuss the ethics of statistics and investigate questions such as: Is it acceptable to base high-stakes decisions (e.g. whether to convict someone) on merely statistical evidence or algorithm’s predictions? What does it mean for an algorithm to be “unbiased”? Is it possible for a machine learning program to be value-free?

Prerequisites: 12A (or equivalent) or consent of the instructor