This course continues Dr. Corvini's exploration of the objectivity of mathematics, tying together and building on ideas introduced in her earlier courses. The result is an integrated approach to number and infinity, and a solid basis for evaluating the modern theories of number that figure so prominently in modern philosophy and in popular attacks on reason.

This course is a two-fold "sequel", both advancing the positive theory and applying same to the analysis of modern errors. It offers significant new material on the nature and cognitive purpose of number and of measurement and on the relationship of infinity to both; and it uses this framework to explain and evaluate (in laymen's terms) several cornerstones of modern mathematical thought: one-to-one correspondences, the postulational method, and the set-theoretic approach to real numbers. The course examines the deep interrelation among these ideas, identifies the fundamental errors in the modern approach, and demonstrates the significance of a proper theory of concepts for all of the above. It also highlights the essence of an objective approach to number via contrast with other approaches.

This material is very abstract, but does not require specialized background in math. The course assumes familiarity with elementary mathematical ideas such as counting numbers, fractions, and the number line—and offers new perspectives on these basic ideas by connecting them to cognition more generally. It should be of value to students of Objectivist epistemology and to readers of popular treatments of science and mathematics, as well as to those interested in philosophy of math per se.

The course is structured to encourage students to think first-handedly about the issues involved.

Part 1 of this course was presented at OCON 2007