PHIL/LING 455.001 – Symbolic Logic

Symbolic logic has proven to be extremely influential in a variety of 20th century disciplines, like philosophy, linguistics, the foundations of mathematics, and computer science. This course is an introduction to the main topics and results in formal logic. We will first cover the syntax and semantics of various formal languages and a selection of proof systems for them. Then, we will discuss and prove some of the central results in the meta-theory of first order logic: completeness, compactness, the Löwenheim-Skolem theorems, complete theories, notions inexpressible in first order logic, and some applications to first order mathematical theories, like non-standard models of arithmetic. Finally we will discuss the syntax and a variety of semantics for second order logic, the meta-theory of second order logic, and a selection of intentional systems, like modal logic.