Philosophy 140A

This course covers the most important metalogical results that are of interest to philosophers. It is divided into four parts. The first three 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’s machine approach to computability. We will then move on to the basic metatheoretical results about first order logic (completeness, undecidability, compactness, Löwenheim-Skolem). The third part of the course will give a detailed presentation of Gödel’s incompleteness theorems. 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 readings: Boolos, Burgess, Jeffery, Computability and Logic, 4th edition, 2002 Cambridge UP. Barwise, Etchemendy, Turing’s World, CSLI.