Philosophy of
Mathematics:
A study of
mathematical truth and related questions of ontology and epistemology.
We will begin
with the foundations crisis in the early part of the twentieth century, study
GodelŐs Incompleteness theorems and their implications, and move on to
contemporary work in this area.
Studies will
read papers on and discuss the topics listed below and then write a paper of 10
to 20 pages with a specific focus on a related topic.
Topics:
Set theory and
the infinite
Foundations
Crisis
Logicism
Finitism
Intuitionism
Incompleteness
Existence of
Mathematical Objects
The nature of
mathematical truth
Texts:
1)
Philosophies
of Mathematics by ALEXANDER GEORGE and DANIEL VELLEMAN (Blackwell 2001)
2)
What is
Mathematics, Really? by Reuben Hersh, Oxford University Press, 1997.
and selections from
3) Philosophy of Mathematics:
An Anthology, edited by Dale Jacquette (Blackwell 2002)
4
) Philosophy of Mathematics: Selected Readings,
edited by Paul Benacerraf & Hilary Putnam, 2nd edition 1983 (reprinted
1997)