Set Theory and Further Logic

This information is for the 2018/19 session.

Teacher responsible

Prof David Makinson, LAK 3.03


This course is available on the BSc in Philosophy and Economics, BSc in Philosophy, Logic and Scientific Method, BSc in Philosophy, Politics and Economics and BSc in Politics and Philosophy. This course is available with permission as an outside option to students on other programmes where regulations permit. This course is available to General Course students.


Logic (PH101) or Formal Methods of Philosophical Argumentation (PH104), with a grade of at least 65.

Course content

The aim of the course is to familiarize students of philosophy with the essentials of set theory and formal logic. From set theory, the course covers both ‘working’ set theory as a tool for use in formal reasoning, and also ‘conceptual’ set theory of philosophical interest in its treatment of infinite sets, cardinals and ordinals. From logic, it begins by reviewing and extending basic material on propositional and first-order logic from both semantic and axiomatic viewpoints, continues with the celebrated limitative theorems of Tarski and Godel, and ends with introductions to modal, intuitionistic, and relevance logics. Throughout, a balance is sought between formal proof and intuition, as also between technical competence and conceptual reflection.


20 hours of lectures and 10 hours of classes in the MT. 20 hours of lectures and 10 hours of classes in the LT.

Formative coursework

In each term, students are required to submit solutions to two problem-sets, and write one essay on a topic selected from  a list or proposed by the student and approved by the instructor.

Indicative reading

Textbooks: Makinson, David Sets, Logic and Maths for Computing (2nd edition Springer 2012); Halmos, Paul Naive Set Theory (Springer reprint 2011); Sider, Theodore 2010 Logic for Philosophy (OUP 2010). Remark: Specific sections of these three texts that are relevant to weekly topics will be indicated on the Moodle page for the course.

Complementary reading : Cameron, Peter Sets, Logic and Categories (Springer 1999); Crossley, John What is Mathematical Logic? (Dover reprint 1991); Goble, Lou ed 2001 The Blackwell Guide to Philosophical Logic (Blackwell). Additional material on special topics (notably Gödel's theorem, relevance logics) will be made available on Moodle.


Exam (100%, duration: 3 hours) in the summer exam period.

Student performance results

(2015/16 - 2017/18 combined)

Classification % of students
First 59.1
2:1 11.4
2:2 13.6
Third 6.8
Fail 9.1

Key facts

Department: Philosophy, Logic and Scientific Method

Total students 2017/18: 17

Average class size 2017/18: 9

Capped 2017/18: No

Value: One Unit

Guidelines for interpreting course guide information