Phil 151/251: Metalogic

Winter 2023, Mon/Wed 3pm-4:20pm, 370-370

Instructor: Thomas Icard

TAs:

  • Robert Bassett
  • Benjamin Sparkes
  • Declan Thompson
  • Syllabus: Syllabus

    Canvas: Class Homepage

    Ed Discussion : Ed Discussion

    In this course we will go through some of the seminal ideas, constructions, and results from modern logic, focusing especially on classical first-order (''predicate'') logic. After introducing general ideas of induction and recursion, we will study a bit of elementary (axiomatic) set theory before then covering basic definability theory, viz. assessing the theoretical limits of what can and cannot be expressed in a first-order language. The centerpiece result of the class is the completeness---and closely related compactness---of first-order logic, a result with a number of momentous consequences, some useful, some philosophically puzzling. We will then study a connection with game theory, whereby a certain type of game characterizes precisely the expressive power of first-order logic. Further topics may include: the 0-1 law in finite model theory, second-order logic, and the algebraic approach to logic.