Set Theory and Further Logic

This information is for the 2017/18 session.

Teacher responsible

Dr Owen Griffiths, LAK 3.01


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.


Students must have completed Logic (PH101).

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 ‘working’ set theory as a tool for use in formal reasoning, and also some ‘conceptual’ set theory of philosophical interest in its treatment of infinite sets, cardinals and ordinals. From classical logic, it 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 modal propositional 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 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 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 texts that are relevant to 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 Naive Set Theory (Springer reprint 2011); Smith, Peter 2015 Gödel without (too many) tears; Stanford Encyclopedia of Philosophy 


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

Student performance results

(2014/15 - 2016/17 combined)

Classification % of students
First 59.4
2:1 9.4
2:2 12.5
Third 6.2
Fail 12.5

Key facts

Department: Philosophy

Total students 2016/17: 19

Average class size 2016/17: 11

Capped 2016/17: No

Value: One Unit

Guidelines for interpreting course guide information

Course survey results

(2014/15 - 2016/17 combined)

1 = "best" score, 5 = "worst" score

The scores below are average responses.

Response rate: 79%



Reading list (Q2.1)


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