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This subject deals with the power and limits of logic. We will cover some of the great conceptual advances in logic in the 20th Century, which have revolutionised our understanding of logic and language, of models and meaning, and of concepts and computation. We will examine the conceptual foundations of logic and the way it can be applied, not only to develop theories in other domains, but how we can learn the limits of logic when we attempt to apply its power to logic itself. In the course we will examine fundamental results such as (1) the soundness and completeness of different proof systems of first-order predicate logic, (2) the boundary between the countably infinite and the uncountably infinite (3) the boundary between the computable and the uncomputable, and (4) Gödel's incompleteness theorem and its consequences. Concepts and results will be approached via both practical exposure to formal techniques and proofs and theoretical and philosophical reflection on those techniques. Students will be able to appreciate the philosophical importance of the major logical results and equipping them for further work in logic in philosophy, mathematics, linguistics, computer science and related fields.
Intended learning outcomes
Students who successfully complete this class should:
- develop and demonstrate an understanding of the core features of first order predicate logic, including soundness and completeness, the compactness theorem, computability, decidability and Gödel’s incompleteness theorems;
- demonstrate an ability to clearly state and prove results in and about first order predicate logic;
- develop a command of the connections between the concepts of proof, model, completeness, computation, decidability, and incompleteness, and their applications to areas inside and outside philosophy;
- critically reflect on the strengths and weaknesses of formal logic and the ways it can be applied and mis-applied in different fields of inquiry;
- work individually, and in groups, to clarify problems, apply reasoning techniques to different issues, and to critically evaluate the results.
Last updated: 1 March 2024