Set Theory and Further Logic

This information is for the 2018/19 session.

Teacher responsible

Professor David Makinson, LAK 3.03


This course is available on the MPhil/PhD in Philosophy of the Social Sciences, MSc in Economics and Philosophy, MSc in Philosophy of Science and MSc in Philosophy of the Social Sciences. This course is available as an outside option to students on other programmes where regulations permit.


Introductory level logic to a level equivalent to a grade of at least 65 in either Logic (PH101) or Formal Methods of Philosophical Argumentation (PH419).

Course content

The aim of the course is to familiarize students of philosophy with the essentials of naive set theory and formal logic. From set theory, the course covers both ‘working’ set theory as a tool for use in formal reasoning, and ‘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 seminars in the MT. 20 hours of lectures and 10 hours of seminars in the LT.

Formative coursework

In each term, students are required to submit solutions to two problem-sets, and write one 1,500 word essay on a topic 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 2012 Springer); Halmos, Paul Naive Set Theory (Springer reprint 2011); Sider, Theodore Logic for Philosophy (OUP 2010). Specific sections of these textbooks that are relevant to the 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) The Blackwell Guide to Philosophical Logic (Blackwell 2001). Additional material on specific topics (notable Gödel's theorem, relevance logic) will be be posted on Moodle.



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

Student performance results

(2014/15 - 2016/17 combined)

Classification % of students
Distinction 57.1
Merit 9.5
Pass 4.8
Fail 28.6

Key facts

Department: Philosophy, Logic and Scientific Method

Total students 2017/18: 12

Average class size 2017/18: 11

Controlled access 2017/18: No

Value: One Unit

Guidelines for interpreting course guide information

Personal development skills

  • Problem solving
  • Application of information skills
  • Application of numeracy skills
  • Specialist skills