Set Theory and Further Logic

This information is for the 2019/20 session.

Teacher responsible

Professor Miklos Redei, LAK 4.03


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 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 begins by reviewing and extending basic material on propositional and first-order logic from both semantic and axiomatic viewpoints, continues with the basic meta theorems of first order logic (Gödel) and ends with an introduction to propositional modal logic. 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: 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). Additional material on special topics will be made available on Moodle.


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

Key facts

Department: Philosophy, Logic and Scientific Method

Total students 2018/19: 20

Average class size 2018/19: 10

Capped 2018/19: No

Value: One Unit

Guidelines for interpreting course guide information