Module description
The module will focus on the Liar Paradox, a puzzle that occupies philosophers and logicians since the birth of philosophy. After presenting the paradox, we will consider contemporary approaches to its resolution. These approaches are based on the theory of truth proposed by Saul Kripke but diverge greatly in some of their key assumptions. We will zoom in two key features: the role of classical logical principles in the theories, and the availability of a conditional suitable to encode theoretical reasoning.
Assessment details
Summative assessment: Essay, 3500 words (100%)
Formative assessment: 4 sets of exercises
Educational aims & objectives
The module aims to provide students with a close understanding of the incompleteness of suitable mathematical axiom systems.
Learning outcomes
Students will acquire foundational knowledge of the tools behind the incompleteness theorems and the related logical and semantic paradoxes, as well as an in depth understanding of their philosophical implications.
They will be able to critically assess philosophical underpinnings of highly abstract techniques such as self-referential logical constructions, the inexhaustibility of mathematical systems, and formal reflection principles.
The assessment pattern of the module is devised to foster individual research on the topics treated in the module. Formative assessment will provide low-stake opportunities to practice such skills.
Students will be exposed to a unique blend of formal and philosophical work, leading to transferable skills such as integrating formal argumentation with conceptual analysis, communicating abstract ideas clearly, and solving structured problems combining precise and imprecise information.
Teaching pattern
One one-hour weekly lecture and one one-hour weekly seminar over ten weeks.
Suggested reading list
- Lecture Notes.
- Hrbacek, K., & Jech, T. (1999). Introduction to Set Theory, 220 of Pure and Applied Mathematics: A Series of Monographs and Textbooks.
- Jech, T. (2003). Set theory: The third millennium edition, revised and expanded. Springer Berlin Heidelberg.