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Foundations of Mathematics - PHI00032M

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  • Department: Philosophy
  • Module co-ordinator: Prof. Mary Leng
  • Credit value: 20 credits
  • Credit level: M
  • Academic year of delivery: 2020-21
    • See module specification for other years: 2019-20

Module will run

Occurrence Teaching cycle
A Spring Term 2020-21

Module aims

Subject Content

  • To explore some key issues in the philosophy of mathematics, including the foundations of mathematics;
  • To provide a research-led approach to understanding and participating in contemporary debates in the philosophy of mathematics.

Academic and Graduate Skills

  • To develop students' abilities to apply philosophical tools and techniques, in order to advance understanding of intellectual problems.

Module learning outcomes

Subject content
Students will be able to:

  • Display an understanding of the mathematical and philosophical context (particularly the so- called 'crisis' in foundations of mathematics) that led to the development of the three foundationalist programmes (logicism, intuitionism, and formalism) at the start of the 20th century;
  • Describe and evaluate the three foundationalist programmes, particularly in the light of formal results such as Russell's paradox and G ¶del's incompleteness theorems;
  • Understand and evaluate contemporary debates over Platonism and anti-Platonism in mathematics, particularly in the light of Benacerraf's epistemological challenge (to Platonism) and the challenge raised (for anti-Platonism) by the indispensability of mathematics in science.

Academic and graduate skills
Students will be able to:

  • read and critically engage with a wide range of complex and difficult philosophical material;
  • develop and defend a considered view on complex and difficult material;

Module content

Students attend relevant UG lectures and seminars (which are research-led) to provide a background in the general area of research, while working with the module convener over the course of the term to define and develop a topic for independent research, on which they will write their assessed essay, which they will work on in parallel with the lecture/seminar course. They will be expected to produce a topic proposal and reading list by week 7, and a plan for their essay by week 10, and will have a minimum of two meetings with the module convener to discuss ideas for an essay topic (before producing the proposal) and to discuss the essay plan (on production of the plan). These meetings are an absolute minimum, and it is expected that in practice students will make use of staff office hours regularly throughout the term to discuss their project with the module convener. Module conveners may also choose to provide feedback on the essay proposal and reading list in person in a further one-to-one meeting, or to meet MA students as a group at the start of term to discuss the subject area and suggest topics for independent research.


Task Length % of module mark
Essay - 4000 words
N/A 100

Special assessment rules



Task Length % of module mark
Essay - 4000 words
N/A 100

Module feedback

Students will receive written or verbal feedback on the essay proposal and reading list at two weeks after they submit it.

Students will meet their module tutor in week 10 to discuss their essay plan in person.

Students will receive feedback on the 4000 word summative assessment and reassessment four weeks after they submit it.

Indicative reading

Paul Benacerraf and Hilary Putnam, eds., Philosophy of Mathematics: Selected Readings (2nd edition) (CUP, 1983)

Marcus Giaquinto, The Search for Certainty (OUP, 2002)

Stewart Shapiro, Thinking about Mathematics (OUP, 2000)

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.