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Unit information: Philosophy of Mathematics in 2016/17

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Unit name Philosophy of Mathematics
Unit code PHIL30090
Credit points 20
Level of study H/6
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Horsten
Open unit status Not open




School/department Department of Philosophy
Faculty Faculty of Arts


In this unit two or three of the following topics will be covered:

1. The mathematical universe as a whole (the set theoretic universe) cannot be understood in the same way as the elements in it (the sets). This raises the questions: what is the ontological nature of the mathematical universe as a whole? What is the nature of the relation between the mathematical universe as a whole and the sets that populate it?

2. Gödel's theorem tells us that a sufficiently strong consistent mathematical theory can express but cannot prove its own consistency. Nonetheless, when we accept a mathematical theory, we are implicitly commitment to its consistency. Therefore the implicit commitment of a mathematical theory outstrips its explicit commitment. What is the nature and scope of implicit commitment associated with the acceptance of a mathematical theory?

3. Recently probability theories have been proposed that make use of infinitesimal (i.e., infinitely small) probability values. But philosophical objections have been raised by prominent philosophers (Williamson, Easwaran, Pruss,...) against the use of infinitesimals in probability theory. How cogent are these objections?

Intended learning outcomes

Students will be able to discuss and critically engage with questions about the nature and prospects for some of the main programmes which are being pursued in contemporary philosophy of mathematics, in particular: the neo-Fregean programme of Bob Hale and Crispin Wright; the structuralist programme of Michael Resnik and Stewart Shapiro; and the fictionalist programme of Stephen Yablo.

Teaching details

11 one-hour lectures and 11 one-hour seminars

Assessment Details

Formative: one 2,500 word essay

Summative: 3 hour unseen examination

Reading and References

  • Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology, OUP 1997
  • Stephen Yablo, The Myth of the Seven (available from his home page)
  • Demopoulos (ed.), Frege's Philosophy of Mathematics, Harvard UP 1995
  • Shapiro, The Oxford Handbook of Philosophy of Mathematics and Logic, OUP 2005