Matthew Gerstbrein

Professor Johns

English Comp 0200

19 November 2014

Project Proposal

The argument I intend on making and defending is that
thinking about scenarios in a mathematical sense will always yield a correct
result or answer. Whether this line of thinking exists in pure computations, or
in simply a philosophical viewpoint, or most often of all, a mixture of both, by
adjusting your analysis of problems to a more mathematically skewed one, you
can be correct regarding problems in an absolute sense.

A plausible counter-argument is that mathematical
reasoning, while useful in particular situations, is not applicable to many
problems. It really has no place in trying to alter viewpoints, since math can
only encompass problems that were predetermined to fit into it.

This argument (not the counter-argument) is relevant
because it can persuade readers to attempt to re-evaluate problems in a new
way, taking a method of approach that will yield desirable and correct results,
in an absolute sense.

Math that has been proven to be true can be applied to a
variety of situations that one might not originally expect them to be. More
importantly, it is not necessarily math as a list of equations and computations
that need to be made, but math as a way of thinking. It can be viewed as more
of a type of philosophical thinking. I do not want people to think of the term
mathematics and automatically associate it with a series of equations, sets of
algebraic problems, and values of “x” that need to be computed. Or even if
people do continue to associate it in that manner, at least recognize that
there is much more to it than that. The “tip of the iceberg” metaphor is not
the exact correlation that I have in mind, but it is nonetheless true that
there is much more to mathematics than meets the eye.

Bibliography

Abbey, Edward. Desert
Solitaire: A Season in the Wildernerness. New York: Ballantine, 1968. Print.

Ellenberg, Jordan. How
Not to Be Wrong: The Power of Mathematical Thinking. New York: Penguin, 2014.
Print.

Lewontin, Richard C.
Biology as Ideology: The Doctrine of DNA. New York, NY: HarperPerennial, 1992.
Print.

Lewontin, Richard C. It
Ain't Necessarily So: The Dream of the Human Genome and Other Illusions. New
York: New York Review of, 2000. Print

The second book listed here strongly correlates to my argument.
The author’s stance is one I would like to morph into my own. I will likely
incorporate some of the questions/scenarios that he introduces and explain how
or why math can be utilized here to both understand and answer the problem.

In the paper, I would like to discuss how math can be
viewed as philosophy, and not just a bunch of computations, and in doing so, it
may be useful to utilize Abbey’s philosophy. I am not exactly sure how, or if I
will even do so, but it is a thought for now.

Finally, Lewontin makes great arguments regarding science
and its varying validity. I am considering contrasting science and math, to
show where math may outshine science.

Outline

·
Introduction

o
Differentiate
math as it is generally regarded, and assert a new view of it.

·
Examples
of problems

o
Why
these can be solved by thinking mathematically

·
What
relevance would these have towards other, potentially specific problems

·
Why
mathematical thinking is a better approach than science in certain situations

·
Counter-argument

·
Conclusion

If you are seriously interested in this topic, you need to do some basic, ground-level research before anything. I'm not a mathematician or philosopher of mathematics, but I'm not quite totally ignorant here, so I have some very, very basic suggestions.

ReplyDeleteFirst - if you haven't read about Godel's proof, do so! A book like this would be a good starting point: http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/0814758371/ref=sr_1_1?ie=UTF8&qid=1416697986&sr=8-1&keywords=godel%27s+proof

Godel's proof concerns the inherent limitations of arithmetic systems - that is, the bounds of mathematical thinking. It's relevant to your argument, and if you have no grounding (yet) in the relevant fields of mathematics, learning about Godel is a decent start.

I guess my short version is that I'm fine with the general topic, but you need to do some reading before you can even begin to pin down a particular argument (for instance, attacking or defending Edward Abbey on the basis of your understanding of the theory/philosophy of mathematics).

Let me know if this leads to further questions.