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Module descriptions

7AAN2056 Philosophy of Mathematics

THIS MODULE IS RUNNING IN 2017-18          

Credits: 20
Module tutor: Dr Tamsin De Waal


  • Summative assessment: one 4,000-word essay (100%)
  • Formative assessment: one 2,000–3,000-word essay


  • Summative assessment: one 4,000-word essay (100%)
  • Formative assessment: one 2,000–3,000-word essay

Students are reassessed in the failed elements of assessment and by the same methods as the first attempt.

Teaching pattern: one one-hour weekly lecture and one one-hour weekly seminar over ten weeks. 
Additional information: The initial lecture hour will be shared with students taking 6AANA022 Philosophy of Mathematics, but they will otherwise be subject to different requirements.
Pre-requisites: none
Sample syllabus: 7AAN2056 module syllabus 2016-17

What is the subject matter of mathematics? Is it abstract mathematical objects, or can apparent facts about mathematical objects be reduced to facts about something else? Assuming we have knowledge of mathematical facts, how is this knowledge acquired? Despite being essential to the sciences (and often thought of as one of the sciences), the non-empirical nature of mathematics raises epistemological and metaphysical questions quite distinct from those that arise in, say, physics. This course will examine approaches to answering these questions, including varieties of Platonism, and various forms of nominalism. We’ll also take a close look at the role of mathematics in the sciences, with the aim of evaluating one of the key arguments in the debate between the Platonist and the nominalist: the indispensability argument.

Further information

Module aims

The students will be introduced to and receive training in certain key ideas from the Philosophy of Mathematics. In particular, students will gain some or all of the following:

  • An understanding of early twentieth century schools in philosophy of mathematics, including logicism, formalism, and intuitionism.
  • An understanding of the arguments against these positions, including arguments based in Gödel’s incompleteness theorems. 
  • Familiarity with the Quine-Putnam indispensability argument and the more recent ‘enhanced’ indispensability argument.
  • An understanding of contemporary nominalist positions, including fictionalism.
Learning outcomes

By the end of the module, the students will be able to demonstrate intellectual, transferable and practicable skills appropriate to a level-7 module and in particular will be able to demonstrate:

  • Knowledge of the main positions in the philosophy of mathematics.
  • The ability to assess and develop these positions,
  • To exercise their powers of intellectual criticism by critically commenting upon the views discussed.
Past syllabi

7AAN2056 module syllabus 2015-16 (pdf)

Please note that module syllabus and topics covered may vary from year to year.Blank space

More detailed information on the current year’s module (including the syllabus for that year) can be accessed on KEATS by all students and staff. 

The modules run in each academic year are subject to change in line with staff availability and student demand so there is no guarantee every module will run. Module descriptions and information may vary depending between years.

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