Many philosophical debates have been enhanced by the use of mathematical tools. The purpose of this course is to introduce students to those tools, and enhance their skills in using them. Any student who is interested in the use of mathematical tools in reasoning, either because they want to use those tools themselves, or because they want to critically examine others' usage of the tools, will benefit from the course. We will start with propositional and predicate logic, which is presupposed in everything else we do, and is relevant to the analysis of arguments. Then we will look at modal logic, the logic of 'must'. This is relevant to the theory of necessity in metaphysics, to the theory of knowledge in epistemology, and to the theory of obligation in ethics. We will look at 'non-classical' logics, and why some logician have thought that we need to modify logic itself to solve philosophical puzzles. The final part of the course will look at probability, decision making and game playing. We will go over the orthodox theory of how rational agents think and act under uncertainty. And we will look at applications of this theory to explaining puzzles from the history of science and from economics. Then we will look at the theory of games, the theory of how agents act when their outcomes depend on what they do, and on what other rational agents do. We will explain the fundamental notion of game theory, Nash equilibrium, and show how game theory can be used to explain puzzling behavior.

Course Requirements:

The course assessment will be based largely on problem sets throughout the course, with a final exam.