A
Communication Arts student should know the elements in writing a substantial
book review. It should be descriptive and evaluative as possible. It should
contain points on the author’s style of writing and parts of what you loved or
hated in the book.
However, as much as I want to
write a substantial book review, I just can’t. I have to admit that I have not
finished reading the book. And honestly, I do not even fully understand and
grasp the parts that I have read. Well, perhaps, it’s because I do not have a
Math or Math-related subject for two years. All thanks to Math1 for watering my
‘Math-barren’ heart and mind, and for giving me such a challenging read.
To start off, one could not get a
simple reply from asking a short yet thought-provoking question, “What is
Mathematics, Really?” The same question was the title of the book Reuben Hersh
wrote. In his book, Mathematics was not just defined, described and explained;
it was presented with the help of Philosophy. Or, it was more of the
Philosophies of Math. The book was divided into two parts. The part one was
about the three main streams of Mathematical philosophy: Platonism, formalism
and intuitionism and constructivism, and how he rejected those three and
offered a new one, which he called, humanism. I do not have any idea what the
part two has to offer since, unfortunately, I have not finished the entire
book.
Hersh began by introducing and
presenting a problem on counting a 4-dimensional cube and even doubting its
existence. But then, this problem was faced with possible answers which Hersh
also presented. Later on, he explains the mainstream philosophies of maths
which he still rejects anyway.
Formalism, the first principal view
of the nature of mathematics, is more known and understood when related to the
slogan, “Mathematics is a meaningless game”, in which both the words
meaningless and game were undefined. It was further mentioned that Mathematics
is partly a rule-governed game. However, in reality, there are no such things
as rule-governed activities. According to Hersh, “It is misleading to apply it
in real life.” The belief of following rules without judgment is pure nonsense.
Platonism, on the other hand, asserts
that mathematical entities exist in an abstract world and are independent of our
rational activities. But as Hersh would say, this platonic view does not
suffice the philosophy of mathematics. He rejects this idea because he thinks
it goes against the empiricism of modern science and does not even relate to
mathematical reality.
Lastly, Intuitionism acknowledges
that natural numbers are the fundamental datum of mathematics. Still, Hersh
rejects this idea since, according to him, intuitionism is not universal.
Because of that, he proposed humanism. In this, Hersh adds, aside from the
mental and physical, social to the standard kinds of existence as discussed by
philosophers.
Hersh also lists criteria for the
philosophy of mathematics. These are the first three essential elements:
Breadth, or recognizing the scope and variety of math; Links to epistemology
and philosophy of science, and should be valid and compatible into mathematical
practice. The next five elements in the criteria are not necessarily essential
but are desirable: elegance, economy, comprehensibility, precision and
simplicity. Another element is Consistency. It is essential but it is not as
difficult to attain as the first three elements. However, he rejects novelty
and originality since it is inessential and unattainable, and certainty and
indubitability because it is misleading.
Overall, I’d like to think that
Hersh has written such an appealing book but I just couldn’t take that much
information on philosophy and mathematics all at once. It didn’t interest me
that much. Well, if, at least, he has written in such a way that even high
school students would understand, I bet I could appreciate it. But, that’s not
the case. He wrote it for those who are in the field of Mathematics and
Philosophy, apparently. For if, as he writes the book, expects the ‘greater
public’ to understand, he should’ve written it simply and slowly, without
shoving the philosophies and mathematics all at once in our throats.
It’s such a shame that I have
written such an unfair review on Hersh’s book. I honestly think that I am not
the appropriate ‘target audience or reader’ for the book. I know that book
reviews should be as substantial as possible, but you could not blame me if I’d
rather read articles on Intercultural Communication than a book on the
Philosophy of Mathematics.
