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Foundations of Maths - PHI00017H

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  • Department: Philosophy
  • Module co-ordinator: Prof. Mary Leng
  • Credit value: 20 credits
  • Credit level: H
  • Academic year of delivery: 2024-25

Module summary

This module considers philosophical questions about the nature of mathematics, starting with the early 20th century controversies concerning the new transfinite set theory, and resultant philosophical efforts to put mathematics on firm foundations, before moving on to more contemporary discussions of the ontology and epistemology of mathematics.

Module will run

Occurrence Teaching period
A Semester 2 2024-25

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

  • 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 Gödel’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

  • 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;


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 feedback on the 1500 word essay two weeks after they submit it.

Students will receive feedback on the 4000 word summative assessment and re-assessment 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.