| 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. Everett |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
None |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | Department of Philosophy |
| Faculty | Faculty of Arts |
Why is this unit important?
The unit gives a sophisticated overview of the key issues and main theories in contemporary philosophy of mathematics. We take mathematics for granted and regularly employ it in our everyday lives without even being aware we are doing so. But mathematics raises a range of challenging philosophical questions and
has long puzzled philosophers. What exactly is mathematics about; are there such things as numbers and sets and mathematical functions and if so, what sort of things are they? We feel certain of mathematical truths, such as 1+1=2, but how do we come to know them? And how can truths about the mathematical realm be of such critical importance in the non-mathematical concrete world? We will explore these questions in detail, they way philosophers have mathematics have responded to them, and the way answers to these responses have shaped broader philosophical debates in metaphysics and epistemology.
How does this unit fit into your programme of study?
The unit brings together both sides of our JH degrees in Philosophy and Mathematics, allowing students to apply the philosophical techniques they have learned in their philosophy units to the subject matter of their mathematics units. As such it is a core must-pass unit for these JH. For our SH and other JH degrees the unit complements the curriculum’s core units in analytic philosophy, exploring key issues and thinkers which have shaped, not merely philosophy of mathematics, but methodology and debates within analytic philosophy more generally.
An overview of content
The unit will critically explore the arguments in favour of mathematical realism and the arguments against it. The former will typically include arguments based upon the indispensability of mathematics for science. The latter include epistemological arguments that mathematical realism precludes the possibility of mathematical knowledge and semantic arguments that it not possible to determinately refer to the mathematical. We will explore a number of views developed in response to these arguments including various forms of nominalism which deny the existence of mathematical entities, forms of realism which understand mathematical entities as arising via abstraction, and forms of realism which take mathematics to be concerned with patterns or structures .
How will students, personally, be different as a result of the unit
Students will leave the unit with the skills to critically analyse and assess questions concerning the nature of the mathematical, the epistemology of mathematics, and the applicability of mathematics to the physical world. Students will also acquire the ability to apply the ideas they have studied and the methodologies they have acquired in the unit to other areas of philosophy.
Learning Outcomes
On successful completion of this unit students will be able to:
1. Critically analyse and evaluate contemporary positions concerning the metaphysics, epistemology, and semantics, of mathematics.
2. Critically analyse and evaluate contemporary positions concerning themetaphysics, epistemology, and semantics, of mathematics.
3. Present and explain technical material in a manner accessible to a wider audience.
Lectures, small group work, individual exercises, seminars and virtual learning environment.
Tasks which help you learn and prepare you for summative tasks (formative):
None
Tasks which count towards your unit mark (summative):
When assessment does not go to plan
When required by the Board of Examiners, you will normally complete reassessments in the same formats as those outlined above. However, the Board reserves the right to modify the form or number of reassessments required. Details of reassessments are normally confirmed by the School shortly after the notification of your results at the end of the academic year.
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 University Workload statement relating to this unit for more information.
Assessment
The assessment methods listed in this unit specification are designed to enable students to demonstrate the named learning outcomes (LOs). Where a disability prevents a student from undertaking a specific method of assessment, schools will make reasonable adjustments to support a student to demonstrate the LO by an alternative method or with additional resources.
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. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
