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PH419

Set Theory and Further Logic

**This information is for the 2013/14 session.**

**Teacher responsible**

Prof Miklos Redei LAK5.04

**Availability**

This course is available on the MPhil/PhD in Philosophy of the Social Sciences, 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**

Introductory level logic.

**Course content**

The aim of the course is to make students of philosophy familiar with the elements of naive and axiomatic set theory, classical mathematical logic and propositional modal logic. From set theory, two types of facts and results are covered: (i) the ones needed to understand the basic notions, constructions and the mode of thinking in mathematical logic (ii) the ones that have philosophical-conceptual significance in themselves (elementary theory of ordinals and cardinals, transfinite induction, Axiom of Choice and its equivalents, Continuum Hypothesis, Russell paradox). Formal languages, syntactic-semantic, theorem-metatheorem, soundness and completeness and some model theory are the main topics covered from classical first-order logic, together with an outline of Peano arithmetic, decidability and Gödel's incompleteness theorems. The idea of possible world semantics and the semantic characterization of the basic types of modal propositional logics are covered from modal logic. In both set theory and logic, emphasis is on the conceptual-structural elements rather than on technical-computational details. Not all theorems are proven and not all proofs are complete.

**Teaching**

15 hours of lectures and 10 hours of seminars in the MT. 15 hours of lectures and 10 hours of seminars in the LT.

**Formative coursework**

Students are required to write three 1,500 word essays during the year on a topic from a list and are to hand in two problem solutions each term.

**Indicative reading**

Peter J. Cameron. Sets, Logic and Categories. Springer undergraduate mathematics series. Springer, London, Berlin, Heidelberg, 1999.(main text for set theory); Sider, Theodore. Logic for Philosophy. Oxford University Press 2010. (main text for logic); J. Crossley. What is Mathematical Logic? Oxford University Press, Oxford, 1972.; H.B. Curry. Foundations of Mathematical Logic. McGraw-Hill, New York, 1963;. L. Goble, editor. The Blackwell Guide to Philosophical Logic, Oxford, 2001. Blackwell.; G.E. Hughes and M.J. Cresswell. A New Introduction to Modal Logic. Routledge, New York, 1996. (main text for modal logic).; D. Lewis. Counterfactuals. Blackwell, Oxford, 2nd edition, 2001. First edition: 1979.; D. Makinson. Sets, Logic and Maths for Computing. Springer, London, 2008.

**Assessment**

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

**Student performance results**

(2009/10 - 2011/12 combined)

Classification | % of students |
---|---|

Distinction | 45.8 |

Merit | 16.7 |

Pass | 8.3 |

Fail | 29.2 |

** Key facts **

Department: Philosophy

Total students 2012/13: 11

Average class size 2012/13: 11

Value: One Unit

**Personal development skills**

- Problem solving
- Application of information skills
- Application of numeracy skills
- Specialist skills