Set Theory and Further Logic

This information is for the 2022/23 session.

Teacher responsible

Dr Wesley Wrigley


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 and to General Course students.


Introduction to Logic (PH111) with a grade of at least 65, or Mathematical Proof and Analysis (MA102) with a grade of at least 65, or MA103 Abstract Mathematics with a grade of at least 65. Taking PH112 before PH217 is recommended (but not required).

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 (i) what is needed for use in formal reasoning, and (ii) what is of philosophical interest (Russell Paradox, elementary theory of cardinals and ordinals, transfinite induction, Axiom of Choice, Continuum Hypothesis). From logic, it covers the basic metatheory of sentential and first-order predicate logic (up to the completeness theorems), continues with Gödel's famous incompleteness theorems concerning the limitations of mathematical provability and ends with exploring extensions of classical logic.



15 hours of lectures and 10 hours of classes in the MT. 15 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: Cameron, Peter: Sets, Logic and Categories (Springer, 1999); Sider, Theodore: Logic for Philosophy (Oxford University Press, 2010). Specific sections of these texts that are relevant to weekly topics will be indicated in the detailed course description and in the Moodle page of the course.   

Additional reading: Halmos, Paul: Naive Set Theory (Springer reprint 2011); Crossley, John: What is Mathematical Logic? (Dover reprint 1991); Goble, Lou ed.: The Blackwell Guide to Philosophical Logic (Blackwell, 2001); Boolos, G., Burgess, J., & Jeffrey, R.: Computability and Logic (Cambridge University Press, 2007). Additional material on special topics will be made available on Moodle.


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

Student performance results

(2019/20 - 2021/22 combined)

Classification % of students
First 33.3
2:1 51.3
2:2 15.4
Third 0
Fail 0

Key facts

Department: Philosophy, Logic and Scientific Method

Total students 2021/22: 2

Average class size 2021/22: 2

Capped 2021/22: No

Lecture capture used 2021/22: Yes (LT)

Value: One Unit

Guidelines for interpreting course guide information

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.