Intermediate Logic

We explore the power and limitations of formal systems of reasoning.

Course Description

We will explore traditional and contemporary responses to questions that have kept folks across generations up at night, including: Should you believe what you hear? What do we know (if anything)? What does it mean to have a mind? Are our best scientific theories true descriptionsAfter the crisis in mathematics ushered in by Russell’s paradox, developments in formal logic offered renewed hope for foundational security. This course covers its major success stories—namely, the development of a formal notion of syntax and semantics for which the classical rules of inference are sound (everything they prove is true) and complete (everything true is provable). We also face new problems, like Skolem’s paradox, which notes that many logical theories cannot single out their intended models. We’ll conclude by turning to intuitionistic logic, exploring how these sorts of problems afford opportunities to characterize hidden structure in our reasoning.