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