Please note: there may be some adjustments to the teaching arrangements published in the course catalogue for 2020-21. Given current circumstances related to the Covid-19 pandemic it is anticipated that some usual arrangements for teaching on campus will be modified to ensure the safety and wellbeing of students and staff on campus; further adjustments may also be necessary, or beneficial, during the course of the academic year as national requirements relating to management of the pandemic are revised.

Philosophy Of Mathematics PHIL5077

  • Academic Session: 2022-23
  • School: School of Humanities
  • Credits: 20
  • Level: Level 5 (SCQF level 11)
  • Typically Offered: Semester 2
  • Available to Visiting Students: Yes
  • Available to Erasmus Students: Yes

Short Description

This course discusses the principal philosophical approaches to the nature of mathematics and mathematical knowledge.


2 lectures per week for 9 weeks, plus 4 seminars. The course may not run every year. Options running this year are available on MyCampus.

Requirements of Entry

Standard entry to Masters at College level

Excluded Courses





Two essays, equally weighted, each with a word limit of 2500 words.

Course Aims

The course aims to:


■ introduce students to the principal philosophical approaches to the nature of mathematics and mathematical knowledge.

■ explain the philosophical significance of some major results in the foundations of mathematics.

■ introduce students to the main positions which constitute the focus of recent and currently active debate in the Philosophy of Mathematics.

Intended Learning Outcomes of Course

At the end of the course, students will be able to:

■ Formulate and discuss central epistemological and ontological questions concerning the nature of mathematics;

■ Explain and critically assess Frege's logicism;

■ Identify the significance of the paradoxes of set theory for the logicist programme, and analyse critically Whitehead and Russell's Logicism;

■ Illustrate and analyse the intuitionist conception of mathematics;

■ Define Hilbert's Programme, and evaluate the significance of the incompleteness theorems for the philosophy of mathematics;

■ Identify and  assess some modern positions in the philosophy of mathematics, such as Platonism, structuralism, mathematical empiricism, nominalism and neo-logicism.


Assessment for this course is at Masters Level.

Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.