Course Description: | This course explores the power and limits of logic, covering some of the great conceptual advances in logic in the 20th century, which have revolutionized our understanding of logic and language, of models and meaning, and of concepts and computation. Students investigate the conceptual foundations of logic and the ways it can be applied, not only to develop theories in other domains, but to test the limits of logic when applied to itself. They also examine fundamental results such as the soundness and completeness of different proof systems of first-order predicate logic; the boundary between the countably infinite and the uncountably infinite; the boundary between the computable and the uncomputable; and GĂ¶del's incompleteness theorem and its consequences. Concepts and results are approached via both practical exposure to formal techniques and proofs and theoretical and philosophical reflection on those techniques. Students appreciate the philosophical importance of the major logical results and are prepared for further work in logic in philosophy, mathematics, linguistics, computer science, and related fields. |