The Philosophy of Math

            This is just a book review about “What Is Mathematics, Really” by Reuben Hersh. The book talks about the mainstream philosophies of math like Platonism, formalism and intuitionism and deems them inadequate or insufficient and proceeds to highlight his belief on “Humanism” is better or superior. He considers multiple generally accepted properties of math and tries to debunk or discredit them. Platonism in the book, as Hersh defines it, is the idea that “Mathematical entities exists outside time and space, outside thought and matter, in an abstract realm independent of any consciousness, individual or social.”. He combats Platonist ideas against modern science that reality is absolute and there are no “strange and parallel existence of two realities – physical and mathematical” as Platonism insists. Formalism in a nutshell is mathematics is comprised of explicit yet arbitrary rules that must be followed like a game. Hersh objects to this heavily and argues that the rules are “historically determined by the workings of society that evolve under pressure of the inner workings and interactions of social groups and, the physiological and biological environment of earth”. For me the rules in a game can be used as a loophole to win the game and like the rules in math can be used to serve as a loophole to explain or solve problems and equations. Intuitionism to put it simply is that natural numbers is the fundamental datum in any mathematical problem obtained through a process of finite construction.

            Hersh debates that all other philosophies of math are substandard when compared to the “Humanism” philosophy that he believes so hard in. in light of this, math can be explained by anyone may it be a math genius or your everyday individual yet each explanation is different like everyone is unique and math is also unique to them. One can say math to him or her is just a subject and another can say he or she lives and breathes math. Math can live beyond the realm of physical entities like the variable “i”. “i” symbolizes the square root of negative one and there is no integer that can express that so mathematicians use imaginary numbers to be used as variables for such cases. The keyword is imaginary. Imagination is beyond the physical realm. Finally math is complicated enough yet you throw in philosophy and not just one but a bunch of them and you have a debate for only smart people. Why not just let math be math and philosophy be philosophy and end the debates about whose philosophy and ideology is better.