## PHILOSOPHY OF MATHEMATICS

Course Aims:

This course explores some of the different programmes that are being pursued in contemporary philosophy of mathematics. We will discuss questions about the existence of mathematical objects, the status of mathematical truths, as well as questions about the infinite.

Course Texts:

Thinking About Mathematics, by Stewart Shapiro

Additional readings will be made available.

An optional recommended text is the anthology Philosophy of Mathematics: Selected Readings, second edition, edited by Benacerraf and Putnam.

Assessment:

An essay of 2,000 - 3,000 words, to be handed in at the end of the semester.

Course Schedule:

Weeks 1-2: Logicism

Frege Foundations of Arithmetic

Russell An Introduction to Mathematical Philosophy

Weeks 3-4: Intuitionism

Heyting "The Intuitionist Foundations of Mathematics'' (in B & P)

Weeks 5-6: Formalism

Hilbert "On the Infinite" (in B & P)

Zach "Hilbert's Program"

Weeks 7-8: Neo-Logicism

Heck "An Introduction to Frege's Theorem"

Wright "On the Philosophical Significance of Frege's Theorem"

Weeks 9-10: Structuralism

Benacerraf "What Numbers Could Not Be"

Parsons "The Structuralist View of Mathematical Objects"

Weeks 11-12: Nominalism

Field "Realism and Anti-Realism about Mathematics"

Yablo "The Myth of the Seven"