Philosophy of Mathematics and Mathematical Practice

Philosophy of Mathematics and Mathematical Practice
from Descartes to Bolzano
Summer School, University of Copenhagen
September 15-19, 2008
Prof. Paolo Mancosu, U.C. Berkeley

A common criticism of contemporary analytic philosophy of mathematics is its apparent irrelevance to mathematical practice both in the sense on not speaking to the concerns of practicing mathematicians and in the sense of ignoring the vast phenomenology offered by mathematics by limiting itself to logic, elementary number theory, and basic set theory. A new generation of philosophers of mathematics is now attempting to redress the imbalance by tackling a variety of issues of relevance to the relation between philosophy of mathematics and mathematical practice (see P. Mancosu, ed., The Philosophy of Mathematical Practice, OUP, 2008).

The summer school will study the interaction between philosophy of mathematics and mathematical practice using five different episodes of central importance:

· Descartes' analytic geometry and the mechanical/geometrical divide
· Torricelli's infinitely long solid and problems of infinity in the seventeenth century
· Berkeley's criticisms of the infinitesimal calculus
· Kant's philosophy of mathematics
· Bolzano's anti-Kantian philosophy of mathematics and the philosophical role of the intermediate value theorem.

Structure of the summer school: The summer school will consist of five two-hour meetings in seminar style. Paolo Mancosu will present the material for approximately 1.20 or 1.30 minutes and then there will be a discussion of approximately half an hour. Each section will present both the philosophical topics and the mathematical results that bear on the philosophical discussion.
Time and Place: Monday 3-5 pm.; Tuesday to Friday 2-4 pm. In Room D317, HCØ, Copenhagen
More information: http://www.phis.ruc.dk/FrameSet/mainFrameset_new.htm
Registration: Jesper Lützen: lutzen [@] math.ku.dk Participation is free