The Dennes Room

Philosophy 146

Fall 2003

Number Title Instructor Days/time Room
146 Philosophy of Mathematics Mancosu TBA TBA

This is an introduction to the classics of philosophy of mathematics with emphasis on the debates on the foundations of mathematics. Topics to be covered: infinitist theorems in seventeenth century mathematics; the foundations of the Leibnizian differential calculus and Berkeley’s ‘Analyst’; Kant on pure intuition in arithmetic and geometry; the arithmetization of analysis (Bolzano, Dedekind); Frege’s logicism; the emergence of Cantorian set theory; Zermelo’s axiomatization of set theory; Hilbert’s program; Russell’s logicism; Brouwer’s intuitionism; Gödel’s incompleteness theorems. Prerequisites: Phil 12A or equivalent. Textbooks: Frege, The Foundations of Arithmetic, Northwestern University Press. Dedekind, Essays on the Theory of Numbers, Dover. Kenny, Frege, Penguin. Recommended: P. Mancosu, ed., From Brouwer to Hilbert, OUP, 1998.