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PHIL6060 Philosophy of Mathematics

Module Overview

“Irrefragibility, thy name is mathematics.” From the very earliest days of the subject, philosophers have always been fascinated by mathematics, partly because it seemed to offer the best example of a body of knowledge that was certain and immutable and partly also because its “objects” (numbers, points, lines, etc.) seemed to be philosophically mysterious. This module aims to introduce students to the central issues in the philosophy of mathematics, centring on the questions of what mathematical objects are and what the nature of mathematical knowledge is. Those issues are situated in the context of their connections with other areas of philosophy, and the strengths and weaknesses of the various responses to them offered by the main schools in the philosophy of mathematics - Logicism, Platonism, Constructivism and Intuitionism – are explored in some depth.

Aims and Objectives

Module Aims

To explore and critically discuss central theories and issues in the philosophy of mathematics.

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

  • the arguments advanced by the adherents of the main schools in the philosophy of mathematics – Platonism, constructivism, empiricism, logicism and formalism.
  • the influence that these arguments have had on other areas of philosophy, for example, in the philosophy of language and philosophical logic.
  • how to develop and defend views of your own on the nature of mathematical truth and knowledge.
Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

  • interpret, synthesise and criticise complex texts and positions.
  • present and debate ideas in writing, in an open minded and rigorous way.
Transferable and Generic Skills

Having successfully completed this module you will be able to:

  • undertake, with adequate supervision, independent work, including identifying and using appropriate resources.
  • work effectively to deadlines.
  • think independently and supporting your views with arguments.
  • take notes from talks and written materials.

Syllabus

The central questions in the philosophy of mathematics, divided into two broad classes: metaphysical questions (What are mathematical objects? In what sense do they exist? What is mathematical truth?); and epistemological questions (How do we know the truth of mathematical propositions? What is mathematical understanding?). While the syllabus may vary, topics typically include: 1. Transfinite set theory, as created by the German mathematician Georg Cantor. 2. Logicism, as presented by its two most influential exponents: Gottlob Frege and Bertrand Russell. 3. Intuitionism, represented through the work of the Dutch mathematician L.E.J.Brouwer. 4. The Formalist philosophy of mathematics advanced by the German mathematician, David Hilbert. 5. Gödel’s incompleteness theorem. 6. Wittgenstein’s Philosophy of Mathematics

Learning and Teaching

Teaching and learning methods

Teaching methods include - Lectures - In-class discussion - One-on-one consultation with module co-ordinator Learning activities include - Attending lectures - Contributing to in-class discussion - Doing research for and writing the assessed essay and exam - Applying techniques and skills learnt to your reading and writing inside and outside the module

TypeHours
Wider reading or practice25
Tutorial2
Preparation for scheduled sessions30
Independent Study40
Follow-up work20
Lecture33
Total study time150

Resources & Reading list

Benacerraf and Putnam (1989). ilosophy of Mathematics: Selected Readings. 

Assessment

Assessment Strategy

For MA students taking this module, expectations will be significantly higher than those for year 3 undergraduate students attending the same lectures, and the assessment criteria will accordingly by stricter. In particular students will be required to demonstrate extremely high levels of detailed and accurate exposition, critical engagement, organisation and presentation, with scholarship that draws on appropriate primary literature.

Formative

Business case or Essay plan

Summative

MethodPercentage contribution
Essay  (4000 words) 100%

Referral

MethodPercentage contribution
Resubmit assessments 100%

Repeat Information

Repeat type: Internal & External

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