This course covers some of the most important metalogical results that are of interest to philosophers. It is divided into three parts. The first two parts are mathematical in style whereas the last part is philosophical. In the first part we will cover the basic notions of computability theory and study in detail the Turing machine approach to computability. The second part of the course will give a detailed presentation of Gödel’s incompleteness theorems and related results. Finally, we will look at the philosophical relevance of these logical results to various areas of philosophy.
Prerequisite: 12A (or equivalent) or permission from the instructor.
Course requirements: exercise sets approximately every ten days (counting for 60% of final grade) and a philosophical paper due at the end of the semester (40% of final grade).