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PHIL3020 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

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 are explored in some depth.

Learning Outcomes

Knowledge and Understanding

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

  • demonstrate familiarity with the arguments advanced by the adherents of the main schools in the philosophy of mathematics – Platonism, constructivism, empiricism, logicism and formalism.
  • develop and defend views of your own on the nature of mathematical truth and knowledge.
  • demonstrate an understanding of the influence that these arguments have had on other areas of philosophy, for example, in the philosophy of language and philosophical logic.
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.
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, both orally and in writing, in an open minded and rigorous way.

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?). In this module you can expect to explore topics such as: 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
Teaching33
Independent Study117
Total study time150

Resources & Reading list

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

Assessment

Formative

Essay

Summative

MethodPercentage contribution
Assessment  (90 minutes) 50%
Essay  (1500 words) 50%

Referral

MethodPercentage contribution
Assessment  (120 minutes) %

Repeat Information

Repeat type: Internal & External

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