PH217     
Set Theory and Further Logic

This information is for the 2021/22 session.

Teacher responsible

Professor Miklos Redei, LAK 4.03

Availability

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.

Pre-requisites

Logic (PH101) with a grade of at least 65; or Formal Methods of Philosophical Argumentation (PH104) with a grade of at least 65; or Introduction to Logic (PH111) and Intermediate Logic (PH112) with an average 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 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

20 hours of lectures and 15 hours of classes in the MT. 20 hours of lectures and 15 hours of classes in the LT.

Lectures will be delivered online.

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.

Assessment

Take-home assessment (100%) in the ST.

Exam will be a 48 hour take home exam to be submitted electronically.

Key facts

Department: Philosophy, Logic and Scientific Method

Total students 2020/21: 24

Average class size 2020/21: 12

Capped 2020/21: No

Value: One Unit

Guidelines for interpreting course guide information