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## ECMM415 - Logic and Philosophy of Mathematics (2015)

MODULE TITLE | Logic and Philosophy of Mathematics | CREDIT VALUE | 15 |
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MODULE CODE | ECMM415 | MODULE CONVENER | Dr Antony Galton (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
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DURATION: WEEKS | 0 | 11 weeks | 0 |

Number of Students Taking Module (anticipated) | 15 |
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Most mathematics modules aim for the sky, exploring ever more advanced and complex structures that build upon previously learnt material to extend your knowledge towards ever higher levels in the vast edifice that is modern mathematics. This module is different: it digs down into the very foundations, and looks closely at the nuts and bolts of mathematical reasoning and and the basic logic that underpins it. You will learn that all is not what it seems: it can be proved, mathematically, that there is a clear sense in which mathematics cannot be reduced to pure logic or formal reasoning. This calls into question the whole nature of the enterprise, leading to philosophical questions about the nature of mathematics and the status of the abstract entities, which form its subject matter.

The aim of this module is to introduce you to formal logic in the form of classical first-order predicate calculus. This module also explores the logical underpinnings of mathematical thought and examines a range of philosophical viewpoints concerning the nature of mathematics.

On successful completion of this module, **you should be able to**:

**Module Specific Skills and Knowledge:**

1 express propositions in logical notation and test the validity of inferences formally;

2 understand the logical basis for mathematical proof and the nature of axiomatisation;

3 appreciate the role of logic in the development of mathematics;

4 critically evaluate different points of view regarding the nature of mathematics.

**Discipline Specific Skills and Knowledge:**

5 apply the logical skills acquired in the module to improving the quality of mathematical proofs you produce.

**Personal and Key Transferable/ Employment Skills and Knowledge:**

6 use the logical and analytical skills acquired in the module to improve your reasoning abilities in more general contexts.

- logic: propositional calculus, predicate calculus, proof theory, model theory, soundness, completeness and semi-decidability;

- foundations of mathematics: axiomatic set theory, Peano arithmetic, Gödel's incompleteness theorems;

- philosophy of mathematics: platonism, formalism and constructivism.

Scheduled Learning & Teaching Activities | 32.00 | Guided Independent Study | 118.00 | Placement / Study Abroad |
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Category | Hours of study time | Description |

Scheduled learning and teaching activities | 20 | Lectures |

Scheduled learning and teaching activities | 10 | Tutorials |

Scheduled learning and teaching activities | 2 | Class tests |

Guided independent study | 30 | Individual assignments |

Guided independent study | 88 | Lecture and assessment preparation; wider reading |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
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Two class tests | 1 hour each | 1,2 | In-class |

Coursework | 20 | Written Exams | 80 | Practical Exams |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
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Written exam – closed book | 80 | 2 hours | 1,3, 4 | None |

Coursework – CA1 | 10 | 10 hours | 1,2,5 | Feedback sheet |

Coursework – CA2 | 10 | 10 hours | 1,2,6 | Feedback sheet |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-reassessment |
---|---|---|---|

All above | Written exam (100%) | All | August Ref/Def period |

Referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Chiswell I and Hodges W | Mathematical Logic, Oxford Texts in Logic 3 | Oxford University Press | 2006 | [Library] | ||

Set | Smith P | Introduction to Goedel's Theorems | Cambridge University Press | 2008 | [Library] | ||

Set | Brown JR | Philosophy of Mathematics: A contemporary Introduction to the World of Proofs and Pictures | Routledge | 2008 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
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PRE-REQUISITE MODULES | None |
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CO-REQUISITE MODULES | None |

NQF LEVEL (FHEQ) | 7 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Friday 09 January 2015 | LAST REVISION DATE | Tuesday 31 March 2015 |

KEY WORDS SEARCH | Mathematical logic; philosophy of mathematics. |
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