Mathematical Logic and Philosophy of Mathematics (P01285)

? Credit Points : 20 ? SCQF Level : 11 ? Acronym : PPL-P-MSCMLPM

Mathematical Logic: A self-contained, rigorous account of: (i) cardinality (finite and infinite, Cantor's Theorem) (ii) computability (Turing machines, recursive functions, their equivalence); (iii) formal theories of arithmetic. It culminates in proofs of G'del's Incompleteness Theorems. Philosophy of Mathematics: This course concerns topics the epistemology and the ontology of mathematics. (i) Is mathematical knowledge possible? Is such knowledge a priori? How could pure reason give us knowledge of mathematical objects? What is the role of proof? (ii) What are numbers and sets? How do they relate to the physical world we inhabit? What is truth in mathematics and how does it relate to proof?

Entry Requirements

? Pre-requisites : An good grasp of propositional logic.

Subject Areas

Home subject area

Philosophy, (School of Philosophy, Psychology and Language Sciences, Schedule I)

Delivery Information

? Normal year taken : Postgraduate

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 10 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
19/09/2006	14:00	15:00	Room 13.07, David Hume Tower	Central

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	14:00	15:50	Central
Lecture	Tuesday	14:00	14:50	Central

? Additional Class Information : Seminars: Tues, 1400 - 1550

Summary of Intended Learning Outcomes

The coursework involves close and critical analysis of central issues in the philosophy of maths and logic. Students are asked to read, critically assess and discuss some of the most important texts in these fields. Students are encouraged to develop their skills in individual research through the writing of essays, and to develop their critical, analytic and communication skills through informal discussion and oral presentations in tutorial groups.