PH419
Set Theory and Further Logic
This information is for the 2022/23 session.
Teacher responsible
Dr Wesley Wrigley
Availability
This course is available on the 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.
Pre-requisites
Students taking this course should already have taken a year-long introductory course in logic in a Philosophy Department, or a mathematical course that covers the basics of set theory and logic. If in doubt whether you satisfy this prerequisite, consult the instructor.
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.
Teaching
15 hours of lectures and 15 hours of seminars in the MT. 15 hours of lectures and 15 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: 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.
Assessment
Exam (100%, duration: 3 hours) in the summer exam period.
Student performance results
(2018/19 - 2020/21 combined)
| Classification | % of students |
|---|---|
| Distinction | 36.4 |
| Merit | 59.1 |
| Pass | 4.5 |
| Fail | 0 |
Key facts
Department: Philosophy, Logic and Scientific Method
Total students 2021/22: 10
Average class size 2021/22: 8
Controlled access 2021/22: No
Lecture capture used 2021/22: Yes (LT)
Value: One Unit
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.
Personal development skills
- Problem solving
- Application of information skills
- Application of numeracy skills
- Specialist skills
