Philosophy of Mathematics

Learning Outcomes

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.

Knowledge and Understanding

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

• how to develop and defend views of your own on the nature of mathematical truth and knowledge.
• 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.

Transferable and Generic Skills

Having successfully completed this module you will be able to:

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

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 may 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

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

Formative

This is how we’ll give you feedback as you are learning. It is not a formal test or exam.

Essay

• Assessment Type: Formative
• Feedback: Students will receive written feedback on the essay plan, essay, and exam. Students have the opportunity to receive further feedback from the module co-ordinator in office hours or by appointment.
• Final Assessment: No
• Group Work: No

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.