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Advanced Topics in the Philosophy of Mathematics - PHI00092M

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  • Department: Philosophy
  • Module co-ordinator: Prof. Mary Leng
  • Credit value: 20 credits
  • Credit level: M
  • Academic year of delivery: 2022-23

Module summary

This module introduces some contemporary debates in the philosophy of mathematics, with a particular focus on the philosophy of applied mathematics.

Module will run

Occurrence Teaching cycle
A Autumn Term 2022-23

Module aims

  • This module aims to introduce students to some contemporary debates in the philosophy of mathematics, and to engage with these debates in depth through consideration of recent literature.

  • To develop students’ abilities to apply philosophical tools and techniques, in order to advance understanding of intellectual problems, and to provide a grounding for further independent research.

Module learning outcomes

By the end of this module students should be able to:

  • Articulate central issues relating to mathematics and its applications, including accounting for the so-called ‘miracle’ of applied mathematics; understanding and responding to the explanatory indispensability argument; and considering the mathematical acceptability of the use of ‘empirical’ methods (including computer proofs) to establish mathematical results;

  • Work autonomously and self-critically to produce a substantial piece of writing engaging with contemporary discussions of at least one of these issues;

  • Analyse complex areas of knowledge, displaying critical awareness; synthesise information and ideas from a variety of sources at the forefront of the discipline; evaluate research critically; and show originality in the discussion and application of ideas from the philosophical literature in developing their own arguments.

Module content

  • The ‘miracle’ of applied mathematics (3 weeks)

  • The explanatory indispensability argument and fictionalist responses (3 weeks)

  • Further topics (chosen from a list provided to students at the start of the term, and updated on an annual basis, based on recent literature). E.g. enumerative induction in mathematics; computer proofs; mathematical ‘beauty’ and mathematical depth (3 weeks)


Task Length % of module mark
Summative Essay
N/A 100

Special assessment rules


Additional assessment information

  • A formative essay proposal and reading list of 1,200 words is to be submitted in Week 8 of the Autumn Term.
  • A formative essay plan is to be submitted in Week 10 of the Autumn Term.
  • A summative essay of 4,000 words is to be submitted by 12 noon on Monday, Week 2 of the Spring Term.


Task Length % of module mark
Summative Essay
N/A 100

Module feedback

  • Students will receive written feedback on the formative essay proposal and reading list at least two weeks after they submit it.
  • Students will meet their module tutor in week 10 to discuss their formative essay plan in person.
  • Students will receive feedback on the 4000 word summative assessment and re-assessment four weeks after they submit it.

Indicative reading

  • Mark Steiner, The Applicability of Mathematics as a Philosophical Problem
  • Alan Baker, 'Are there mathematical explanations of physical phenomena?', Mind 2005
  • Penelope Maddy, Defending the Axioms (OUP, 2011)

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.