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 |
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?
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.
11 one-hour lectures and 11 one-hour seminars
Formative: one 2,500 word essay
Summative: 3 hour unseen examination