Dr Xinhe Wu

This course is available on the MSc in Philosophy of Economics and the Social Sciences and MSc in Philosophy of Science. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission.

Students taking this course should already have taken a year-long introductory course in logic in a Philosophy Department, or a mathematical course that covers the basics of logic. If in doubt whether you satisfy this pre-requisite, consult the Teacher Responsible.

Students who have completed a BSc at LSE are not permitted to take this course if they have taken the equivalent course as part of their BSc. If this course is a core course for their chosen MSc programme, they can receive an exception for prior learning, which would allow them to take an alternative course approved by the programme director.

This course will focus mainly on restrictive meta-theoretic results in mathematical logic: in particular, the compactness theorem, Gödel’s incompleteness theorems, and the halting problem. Along the way, the course also cover the soundness and completeness theorems of classical logic.

In this course, we will also discuss the plethora of deep philosophical implications of these results, including but not limited to:

• Can we possibly obtain mathematical knowledge, or even just talk about the mathematical objects?

• How can we be certain that our knowledge of any formal system is reliable?

• Can mathematicians be replaced by machines/computers?

• Are human minds machines (computers)?

15 hours of seminars and 15 hours of lectures in the Winter Term.

This course has a reading week in Week 6 of Winter Term.

10 x 1.5 hours of lectures and 10 x 1.5 hours of seminars in the Winter Term. 

• Zach, R (2021). Sets, Logic, Computation. Available online.
• Smith, P. (2016). Godel Without (Too Many) tears. Available online.

Exam (100%), duration: 180 Minutes in the Spring exam period.

The exam questions are chosen from a list of questions that are made available at the beginning of the academic year ("seen exam").