Course Title: Philosophy of Mathematics
Course Number: 301H
Course Duration: August to November 2005
Faculty: Dr Sundar Sarukkai

Course Description

This is designed and taught by Dr Sundar Sarukkai.

.No prior knowledge of mathematics is necessary. The course is open to anybody interested in the foundations of mathematics and its relation to other disciplines, including the sciences and philosophy.  This course introduces the basic problems in the philosophy of mathematics. The themes that are discussed in detail in this course include a brief history of mathematics in different civilizations;  logicism: the relation between mathematics and logic, including discussion of  Frege and Russell, nature of logic in both Western and Indian systems;  formalism: Hilbert’s program;  intuitionism: Brouwer and the intuitionists, including discussion of intuitionist logic and the nature of infinity;  realism: dealing with the ontology of mathematics, including issues such as the existence of mathematical entities like numbers; epistemology: dealing with the nature of mathematical knowledge and truth; structuralism: introduction to some influential theories on the structural nature of mathematics; philosophical foundations of set theory;  The nature of mathematical discourse;  philosophical problem of the applicability of mathematics. The course is based on readings handed out every week.