Mathematical Philosophy

                What is mathematics, really? I would say “Thank you for that wonderful question. Next please!” Reuben Hersh on the other hand has a different perspective. Even before he became a mathematician, Hersh already read the book “What is mathematics?” written by Richard Courant and Herbert Robbins. He was a bit disappointed by their explanation and thus inspired him to write “What is Mathematics, Really?” In his own book, he makes two major points. First, is to respond to the question of Robbins and Courant, philosophy must seek to be more than just a trial in order to create a foundation for mathematics, Second is that the people who spreads or promotes math should be a major contributor in the development of its philosophy. Hersh also explores the three main mathematical philosophy: Platonism, formalism, and intuitionism or constructivism.

               

                Platonism’s definition is that “mathematical entities exist outside space and time, outside thought and matter, in an abstract realm independent of any consciousness, individual or social.”  Mathematics is Hersh, points out that Platonism is not enough as a philosophy of mathematics and rejects the notion. Formalism on the other hand is that mathematics was just a manipulation of symbols made by arbitrary rules, though these rules as Hersh argued are not arbitrary but is instead dictated by the society that evolved under pressure. He also argues that “strictly following rules without any judgement” is misleading to apply in real life. Intuition or constructivism on the other hand had the most thorough point of view. Mathematics is a set of natural numbers and is its fundamental data. Hersh again though opposes and explains that natural numbers are simply not universal.

                This book presents valuable data of the philosophical view of mathematics. The ideas of Reuben Hersh towards the three main mathematical philosophy was interesting. It was a bit hard and boring to read though.