Philosophy 146

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.