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Unit information: Philosophy of Mathematics in 2021/22

Unit name Philosophy of Mathematics
Unit code PHIL30090
Credit points 20
Level of study H/6
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Dr. Catrin Campbell-Moore
Open unit status Not open
Pre-requisites

None

Co-requisites

None

School/department Department of Philosophy
Faculty Faculty of Arts

Description including Unit Aims

In this unit two or three of the following topics will be covered:

1. The mathematical universe as a whole (the set theoretic universe) cannot be understood in the same way as the elements in it (the sets). This raises the questions: what is the ontological nature of the mathematical universe as a whole? What is the nature of the relation between the mathematical universe as a whole and the sets that populate it?

2. Gödel's theorem tells us that a sufficiently strong consistent mathematical theory can express but cannot prove its own consistency. Nonetheless, when we accept a mathematical theory, we are implicitly commitment to its consistency. Therefore the implicit commitment of a mathematical theory outstrips its explicit commitment. What is the nature and scope of implicit commitment associated with the acceptance of a mathematical theory?

3. Recently probability theories have been proposed that make use of infinitesimal (i.e., infinitely small) probability values. But philosophical objections have been raised by prominent philosophers (Williamson, Easwaran, Pruss,...) against the use of infinitesimals in probability theory. How cogent are these objections?

Intended Learning Outcomes

On successful completion of this unit, students will be able to:

  1. discuss and critically engage with questions about the nature and prospects for some of the main programmes which are being pursued in contemporary philosophy of mathematics, in particular: the neo-Fregean programme of Bob Hale and Crispin Wright; the structuralist programme of Michael Resnik and Stewart Shapiro; and the fictionalist programme of Stephen Yablo.

Teaching Information

Lectures, small group work, individual exercises, seminars and virtual learning environment.

Assessment Information

FORMATIVE: digital presentation + Summative: 4500 word essay - 100%

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. PHIL30090).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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