Phil 146
Philosophy of Mathematics
Spring 2006
Professor Paolo Mancosu
Office: 233 Moses Hall
Phone: 642-5033
E-mail: mancosu@socrates.berkeley.edu
Class meets: T.Th. 9.30-11.00
Office hours: T. 11-12.30
Course Description
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) and another course in philosophy
Syllabus
Week 1: Infinitistic theorems in XVIIth century mathematics.
Week 2: The foundations of the Leibnizian differential calculus and Berkeley's Analyst.
Week 3: Kant on pure intuition in arithmetic and geometry.
Week 4: The arithmetization of analysis: Bolzano's proof of the intermediate value theorem
Week 5: Dedekind's theory of irrational numbers.
Week 6: Dedekind's theory of natural numbers.
Week 7: Frege's Begriffsschrift.
Week 8: Frege's The Foundations of Arithmetic.
Week 9: Frege's The Foundations of Arithmetic.
Week 10: Frege's The Foundations of Arithmetic.
Week 11: The emergence of Cantorian set theory and the mathematical theory of the infinite; Zermelo's axiom of choice and his axiomatization of set theory; semi-intuitionism.
Week 12: Hilbert's program I (axiomatization).
Week 13: Russell's type theory
Week 14: Brouwer's intuitionism
Week 15: Hilbert's program II (proof theory); Gödel's results
Textbooks
Frege, The Foundations of Arithmetic, Northwestern University Press.
Dedekind, Essays on the Theory of Numbers, Dover.
P. Mancosu, ed., From Brouwer to Hilbert: The debate on foundations of mathematics in the 1920s, Oxford University Press, 1998.
Updated on Tue Aug 15 16:59:08 -0700 2006 by Paolo Mancosu