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PH217

Set Theory and Further Logic

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

**Teacher responsible**

Prof Miklos Redei

**Availability**

This course is available on the BSc in Philosophy and Economics, BSc in Philosophy, Logic and Scientific Method 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.

**Pre-requisites**

Students must have completed Logic (PH101).

**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 8 hours of classes in the MT. 15 hours of lectures and 10 hours of classes in the LT.

**Formative coursework**

Students are required to write one essay each term on a topic from a list and are supposed to hand in solutions for two sets of problems.

**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**

(2010/11 - 2012/13 combined)

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

First | 41.9 |

2:1 | 25.8 |

2:2 | 19.4 |

Third | 3.2 |

Fail | 9.7 |

** Key facts **

Department: Philosophy

Total students 2012/13: 14

Average class size 2012/13: 15

Value: One Unit