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Unit information: Philosophy of Mathematics in 2018/19

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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
Pre-requisites

None

Co-requisites

None

School/department Department of Philosophy
Faculty Faculty of Arts

Description

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

On successful completion of this unit, students will be able to:

  1. 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

22 one-hour lectures and 11 one-hour seminars

Assessment Details

All assessment is summative:

15 minute presentation (15%)

4500 word essay (85%)

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

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