Humanist’s Insight towards Mathematics

In the book that Reuben Hersh wrote, he explored the nature of mathematics and its philosophical development. Hersh considered and rejected the three common mathematical philosophy namely—Platonism, formalism and intuitionism. He debunked this and pushed his idea of humanism.

                While reading the first few pages of the book, I cannot fathom why a 12-year old girl can have a conversation with an adult something about the philosophy of mathematics. When I was her age, I only cared about Naruto. But anyways, having such conversation about mathematics will make my mind boggling.

                In part one, a problem was proposed; the existence of the 4-dimensional cube was questioned. It was stated that if existed, where we could find it. If there’s no a perfect 3-dimensional cube as a physical object, where could we find a 4-cube one?

                Hersh pointed out that mathematics is something that is out there, out in the space. This was his view about that Platonism. For him, formalism states that mathematics is a meaningless game that is played with arbitrary rules. For me, it might be some sort of game but mathematics is never useless. In intuitionism the mathematics must be obtained through a process of finite construction.  In humanism, 4-cube exists ‘at the social-cultural-historic level in the shared consciousness of people; we humans use mental images to understand this kind of concept.

                In the book the twelve philosophy of mathematics was stated which was subdivided into two parts; the essential and desired. The first three are the essential ones namely the breadth, links to epistemology and philosophy of science and valid against practice. The desirable philosophies are the elegance, economy, comprehensibility, precision, simplicity, consistency, originality, certitude and indubitability, applicability and acceptability.

                According to Hersh, mathematics has a front and back. The front, which are the results of the problems that are solved and the back, which we do to achieve the results. And mathematics has four myths which are the unity, universality, certainty and objectivity.

                Honestly, I had difficulty in reading this book.  When I read the statement, “This book aims to be easily comprehensive to anyone,” I really don’t know what to feel because most of the subject matter that is being discussed is not so understandable for a reader like me. Some points are not explained well or not totally explained at all.

                I only stated the points and views of the author which I somewhat understood and what he really wants to tell his readers about his perception about mathematics.

Reference:

    Hersh, R. 2004. What is Mathematics, Really? pp. 29 retrieved 11 December 2013