Prof Miklos Redei (LAK.4.03) and Dr Wesley Wrigley (KGS.2.06)

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 as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Students should have taken Introduction to Logic (PH111) and obtained a grade of at least 65.

Students who have not taken PH111 should instead have taken Mathematical Proof and Analysis (MA102) or Introduction to Abstract Mathematics (MA103).

The aim of the course is to make students of philosophy familiar with the elements of naive set theory. 

Two types of concepts and theorems are covered:

1. the ones needed to understand the basic notions, constructions and mode of thinking in modern mathematical logic
2. those that have philosophical-conceptual significance in themselves (elementary theory of ordinals and cardinals, transfinite induction, Axiom of Choice, its equivalents and their non-constructive character, Continuum Hypothesis, set theoretical paradoxes /such as Russell paradox/).

The emphasis is on the conceptual-structural elements rather than on technical-computational details. Not all theorems that are stated and discussed are proven and not all proofs are complete. Students taking this course should tolerate abstract mathematics well but it is not assumed that they know higher mathematics (such as linear algebra or calculus).

10 x 1.5 hours of lectures and 10 x 1 hours of classes during Autumn Term. 

Students are required to submit solutions to two problem-sets, and write one essay (word limit 1,500 words) on a topic selected from a list or proposed by the student and approved by the instructor in the Autumn Term.

• Cameron, Peter: Sets, Logic and Categories (Springer, 1999); 
• Halmos, Paul: Naive Set Theory (Springer reprint 2011)

Specific sections of this text that are relevant to weekly topics will be indicated in the detailed course description and in the Moodle page of the course.  

Exam (100%, duration: 2 hours) in the January exam period.

The exam questions are chosen from a list of questions that are made available at the beginning of the academic year ("seen exam").