Gödel's Theory

(3 Credit Hours) · Undergraduate

This course looks at some of the famous incompleteness and undecidability results from the first half of the twentieth century. We'll start by discussing the notion of computability and then use this notion to examine the limitations of (even ideal) computers. We'll then move on to look at Goedel's first and second incompleteness theorems, the undecidability of arithmetic and of second-order logic, and the undefinability of truth. Finally, if there's time, we will discuss some of the technical and philosophical ramifications of this material.