Reuben
Hersh started his book with a conversation made with Laura, a 12- year old girl
who’s pecking at his work. Their conversation started with the introduction of
the Philosophy of Math by asking Laura, what is the biggest number she can
think of. Laura answered there is no biggest number; their conversation goes on
and on. Reuben asking seemingly endless questions to Laura, while Laura
answered him, trying to understand his point. The ending statement of Reuben is
that even if Laura haven’t seen a gazillion, yet she was sure about it compared
to the pencil that she can perceive by her five senses. Reuben Hersh, unlike
other philosophers of Mathematics believed that Mathematics must be understood
as a part of human life. A human activity, a social experience, as a part of
human culture and should evolve historically.
Mathematics
is a huge network of interconnected problems and solutions as Reuben described.
In the nature of mathematics, there are two principle views, Platonism and
formalism. Platonism is the most dominant philosophy of mathematics, wherein
their standard version is that mathematical entities is outside space and time,
outside thought and matter, in an abstract realm independent of any
consciousness, individual or social. On the other hand, The philosophy of
mathematics under formalism is reduced to a short slogan; “Mathematics is a
meaningless game” In general, in considering games and rules, this only shows
that one can’t understand mathematics by simply finding rules that it follows.
The idea of following rules without any need for judgment is fiction. It
misleads us to apply it literally to real life. Most mathematicians are half
consciously Platonist, for instance inside a classroom where all of the
students must get the right answer, that is what the teacher wants to believe,
that right answers are right because they are right. A naïve uncritical
Platonism.
Reuben exposed many mathematical myths, He
revealed mathematics as seen by professionals. He introduced the humanist idea
of the nature mathematics wherein, it closely resembles how mathematicians
actually work. He contends that Platonism have the same perspective that of
elitism or superiority in which Platonism justified that mathematics are for
people who understands math, it claims that “some people just can’t learn
math”. It is totally different with the humanist philosophy, wherein it
connects mathematics to people, to society and history. It fits the
ant-elitism, it strives for universal literacy, universal higher education and
universal access to knowledge and culture. It is true, Mathematics are for all
of the people who are willing to study and learn. Mathematics is part of human
culture, a social historic work of reality. Views of mathematics should fit in
with our views about physical science and a part of our lives.
The author's conversation with the little kid was absolutely comedic (as for me). On the other hand, it also made me think of the idea that he was trying to explain. It really made sense.
ReplyDeleteDo you agree with Hersh that the right philosophy for the nature of math should be humanism?
ReplyDeletei was quite amazed with the first part when you talked about the conversation between the author and laura. honestly, i skipped that part since i find it hard to understand.
ReplyDeleteall in all. it was a job well done!
Its well stated about the principles of math- platonism and fomalism. Seems like you really did read the whole book. (which I hardly did) :D Good Job!
ReplyDeleteThe conversation with Laura was adorable. Hersh was able to gain my attention because of it hahaha. i liked how you included platonism and formalism and compared it to humanism. (i find Hersh's humanism approach in explaining math more 'user friendly' than the others.) :)
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ReplyDeleteyou did a good job in making the review; you even mentioned platonism and formalism. :) im quite speechlss. >_<
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