Set Theory and Further Logic

This information is for the 2015/16 session.

Teacher responsible

Prof David Makinson LAK3.06


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.

Course content

The aim of the course is to help students of philosophy become familiar with naive set theory, classical logic, and modal logic. From set theory, the course covers both ‘working’ set theory as a tool for use in formal reasoning, and some ‘conceptual’ set theory of philosophical interest in its treatment of infinite sets, cardinals and ordinals. From classical logic, the course deals with propositional and first-order inference from both semantic and axiomatic viewpoints, with also some material on first-order theories including celebrated theorems of Tarski and Godel. The material on propositional modal logic presents the main axiomatic systems and their analysis using relational models. 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 2012 Sets, Logic and Maths for Computing, 2nd edition. Springer; Cameron, Peter 1999 Sets, Logic and Categories. Springer; Sider, Theodore 2010 Logic for Philosophy. Oxford University Press. Remark: Specific sections of these three textbooks that are relevant to the weekly topics will be indicated on the Moodle page for the course.

Complementary reading: Crossley, John 1972 What is Mathematical Logic? Dover reprint 1991; Goble, Lou (ed) 2001 The Blackwell Guide to Philosophical Logic, Blackwell; Halmos, Paul 1960 Naive Set Theory, Springer reprint 2011; Smith, Peter 2015, Gödel without (too many) tears. Internet access:; Stanford Encyclopedia of Philosophy, internet access:



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

Student performance results

(2011/12 - 2013/14 combined)

Classification % of students
Distinction 58.1
Merit 9.7
Pass 9.7
Fail 22.6

Key facts

Department: Philosophy

Total students 2014/15: 10

Average class size 2014/15: 10

Controlled access 2014/15: 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