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.
What happened? heheh
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