Mathematical metaphors and philosophical structures

The purpose of this study was to examine relationships between mathematics and philosophy. The first part of the study examined the history and basic doctrines of idealism, realism, pragmatism, and existentialism. This was a basic overview which would familiarize the reader with the teachings of each philosophical system. Mathematical topics and structure were then used to model and evaluate each of the philosophies. By using mathematical metaphors to evaluate each philosophical structure, the reader could decide which beliefs would have worth to his or her life. The second part of the study addressed the problem of choice. The belief that humans have few choices and that only one of those choices would bring success was evaluated using the binomial distribution to mathematically model the Greek dialectic. The belief that humans have an infinite number of choices was evaluated using Georg Cantor's mathematical argument that there are infinitely many decimal fractions on the finite line segment between zero and one