Mathematics is the headquarters of Platonism—the reification of abstractions and the primacy of concepts over percepts. Even Euclid defined “line” as “breadthless length,” something not of this world, and the moderns define “one” in terms of nonbeing (the null set). In this lecture, drawing on a few incisive statements by Ayn Rand, Dr. Binswanger gives perceptually based definitions of key mathematical concepts, such as quantity, measurement, one, number, point, line, infinite, and mathematics itself.

Delivered at OCON 2023 in Miami, Florida on July 3, 2023.