Topics in Mathematical Logic (PHIL 356.001)

Philosophy 356 is a second course in logic, and follows directly on from Philosophy 155. I will assume that you are familiar with sentential logic and the monadic predicate calculus, though we will review those systems at the beginning of the course. There are four parts to the course. (1) Building on what we did in Phil 155, we’ll study the full predicate calculus, its syntax and its semantics, along with a related special topic — set theory and the logical paradoxes. (2) We’ll study identity theory, the logic obtained by adding of the identity relation to the predicate calculus. We’ll study the identity calculus from the syntactic and the semantic point of view, and explore Russell’s theory of descriptions. (3) We’ll cover the metalogic of the propositional calculus, and show the close connections between proof and truth: we will prove the soundness and thecompleteness of the propositional calculus. (4) In the final part of the course, we’ll broaden our scope and move on to modal logic, the logic of possibility and necessity. We’ll study the syntax and semantics of several different systems of modal logic.

Keith Simmons’s webpage