Different philosophies... Different perspectives... United
with one GOAL...
That is to explain a discipline called MATHEMATICS.
PLATONISM... FORMALISM... INTUITIONISM... and HUMANISM.
This is the battle within mathematics...
The evolution of mathematics was one of the magnanimous
contributions of humankind. And over centuries, many people have
tried to explain and unravel the true identity of mathematics. Many
theories and philosophies with different concepts were formed. But
everyday, new questions and dilemmas arise and because of these,
people tried to seek for answers, thus, new ones were born.
In Reuben Hersh's book, he explained different philosophies and
their flaws. These philosophies include Platonism, Formalism, and
Intuitionism. And as he sought imperfections of these three, he is
also introducing the principles of Humanism.
According to Hersh, Platonism is the idea that 'mathematical
entities exist outside space and time, outside thought and matter, in
an abstract realm independent of any consciousness, individual or
social'. And since it does not relate to material reality or have any
contact with flesh-and-blood mathematicians, Platonism is not
competent to be a philosophy of mathematics. He also said that it
violates the empiricism of modern science and is not acceptable since
as it keeps on insisting about the “strange parallel existence of
two realities: the physical and mathematical, it does not explain how
these two interact.
On the other hand, Formalism believes that math is a meaningless
game played by explicit but arbitrary rules. And for him, these rules
are not arbitrary but rather 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. As he said, it is misleading to
apply it to real life because for one, the concept of strictly
following rules without any need for judgment is just impossible.
The third is intuitionism. This philosophy accepts that the set of
real numbers are the fundamental datum of math. And it adopts the
anthropological point of view that the intuition of the natural
numbers is not universal.
Lastly is humanism. This is also called the socio-historical point
of view. It states that 'There is no need to look for a hidden
meaning of definition of mathematics beyond its
socio-historical-cultural meaning”. It also believes that there are
three standard kinds of existence: mental, physical, and the social.
Intuition is also an important issue that every Philosophy of
mathematics has to consider. Different philosophies have their own
opinion about this. In addition, the book also enumerated the 13
criteria for a philosophy of math.
In Part 2, he also mentioned persons who have contributed a lot in the world of math. Some of these are Pythagoras, Plato, Rene Descartes and other religious people.
The challenge of revealing the mystery hidden in mathematics is
really mind-boggling. These people who tried to explain such have
different concepts because they have unique ideas. They see and
perceive things in a different way. Even we have different ideas
about math. Some say they are just numbers, formulas and problems
made to “punish” students for taking their studies so easily. And
I bet, many of us chose not to care because... uuhhmm... how do I
say it?... They just don't care?... Or they're too busy to stress
themselves about defining mathematics?
Neither ways, we define math, or let me say, these people is
striving to explain mathematics because that's what people do! We
we're never contented of things. We always try to seek for more and
have an explanation of everything. We were born to discover and
unravel the secrets this mystical world withholds.
I have come to the end of this article yet the question is still
unanswered. Reuben Hersh has his own definition of mathematics. I
have my own. How about you? What is mathematics really?
First, I would like to commend for the courage of discussing this interesting yet challenging topic. Next is that I would like the writer to expand more the definitions or point out the important notes about a certain philosophy for the readers to understand the concept since the writer introduced Reuben's perspectives of mathematics. I would like also to suggest to change the title for I've recently learned that in writing titles, one should avoid having a similar title to other authors/ writers. I would also suggest that if the writer could lessen the "......" for it weakens an idea. Lastly, my opinion about mathematics is that this discipline was introduced to mankind to have a more stabilize and accurate computations that would simplify work and provide solutions to problems that involves mathematical equations. One of mathematics work is to simplify and it is vital to every individual's existence.
ReplyDeleteI totally agree with what you're saying. This book had a simple goal which is to explain the true nature of mathematics or rather to know what it really is. What made it challenging to read is the methods that the author used to find the true nature of mathematics. And i really agree that each person has his own unique way of defining mathematics. Its just based on what we have experienced with it :)
ReplyDeleteThe writer truly intend to explain the true nature of mathematics. I believe that experience also contributed to the way of mathemathics is right now. :)
ReplyDeleteHehe. truly battle? Hahha..if it is, math has its battle that had won many war, AND IS STILL WINNING!
ReplyDeleteIts nice to spark a question to the readers at the end :)
ReplyDelete