Topics in Logic

Metalogic

Metalogic is the study of formal logical systems with the methods of mathematics. It asks what properties such systems have: Are they complete? Decidable? What is their expressive power? There has been extensive philosophical debate about what sort of lessons we should draw from certain metalogical results. In this course, we will focus on first-order predicate logic. The aim is to familiarize students with key concepts and results about first-order predicate logic, as well as to introduce them to some of the philosophical discussion of these results. By the end of the course, students will be able to: state the definitions of central notions of model theory (model, truth in a model, validity, etc); explain in what sense first-order logic is complete, and sketch, in broad outline, a proof of its completeness; critically discuss some limitations of first-order logic.