Advanced Logic

We explore the limits of what we can know with and about formal systems of reasoning.

Course Description

Folks usually hear about Gödel’s famous incompleteness theorems—slogan-ized as “logic can’t prove its own consistency”—before they ever see them. Some bemoan the results as a fundamental limit on the certainty of our reasoning; others celebrate them as evidence that it’s impossible to reduce human thought to a computer program. We’ll take a close look and decide for ourselves. In addition to building the tools to state and prove Gödel’s theorems, we will assess how second-order logic fares against analogs of Gödel’s arguments.