Time Schedule:
Bob Alan Dumas
PHIL 473
Seattle Campus
Study of the traditional accounts of the nature of mathematical entities and mathematical truth given by logicism, intuitionism, and formalism, and the impact of Godel's incompleteness theorems on these accounts.
Class description
Study of the traditional accounts of the nature of mathematical entities and mathematical truth given by logicism, intuitionism, and formalism, and the impact of Godel's incompleteness theorems and modern advances in Mathematical Logic on these accounts. We will investigate the epistemology of mathematics, contrasting Platonist, empiricist and structural conceptions and focusing on the role of proof in mathematical understanding. We will cover Tarski's definition of truth, model theory and structuralism. Finally, we will take up some special topics, including recent discussions by Woodin, Maddy and others regarding set theory as a foundation for mathematics, the Axiom of Choice, the Continuum Hypothesis, generic absoluteness and constructability. TEXTS: Philosophy of Mathematics, Paul Benacerraf and Hilary Putnam; Transition to Higher Mathematics, Dumas-McCarthy.
Student learning goals
General method of instruction
Recommended preparation
Class assignments and grading
