This essay neither examines a mathematical equation, nor does it analyze a distinguished mathematician. This essay explores a few philosophical aspects of math. Particularly, this essay covers the confound subjects covered by Zeno of Elea.

Authors Avatar

Mathematical Paradox

Has Anyone Figured This Out Yet?

Table of Contents:

Introduction                                                                Page

Background:                                                                Page

Problems and Solutions:                                                Page

Implications and Uses:                                                Page

Conclusion:                                                                Page

Abstract:  This essay neither examines a mathematical equation, nor does it analyze a distinguished mathematician.  This essay explores a few philosophical aspects of math.  Particularly, this essay covers the confound subjects covered by Zeno of Elea.  

The math world has been disturbed, agitated, and even titillated by the mysteries of Zeno of Elea’s paradoxes in questioning the laws of math and science.  A Paradox, defined by Webster’s dictionary, is “A statement that seems contrary to common sense and yet is perhaps true.”  In taking his arguments at face value, they may seem very logical.  But they have each been repeatedly refuted, then stereotyped as nonsense or a mathematical incredulity by many a renowned mathematician.

Zeno was a philosopher and logician, not a mathematician.  He was the inventor of Dialectic and his greatest fame was for his Paradoxes.  Zeno’s Paradoxes have several complex philosophical aspects.  But just as they have a philosophical and scientific approach, Zeno’s paradoxes each have a profound mathematical twist.

This essay will explain and analyze Zeno’s paradoxes, as well as show arguments against them, as well as try and unravel the perplexity of Zeno’s Paradoxes.  So let’s see what sense we can make out of the chaos that has puzzled mathematicians for centuries:

Introduction

        The subject of motion signifies the four most famous of Zeno’s arguments.  The Dichotomy and The Achilles are two arguments perceived as critiques of the idea of continuous motion of space and time infinitely divisible.  The other two of Zeno’s arguments repudiate discontinuity.  The more famous is The Arrow, which analyzes the flight of an arrow.  Finally, The Stadium has remained the most controversial of the four.   When merely seen at face value, the paradoxes seem logical.  When looked into a bit more deeply, they’re mind-boggling as well as difficult to explain.  And when closely analyzed, they are rather confusing and illogical.  These have baffled many mathematicians.

Join now!

Greeks, who had no concrete understanding of convergence or infinity, found such reasoning incomprehensible.  Aristotle even discarded them as “fallacies” (Salmon 13).  These paradoxes were hidden in the “math closet” for some 2500 years and just referred to as “novelties of philosophy.”  

In the 19th century, they were brought out again by such people as Bertrand Russel and Lewis Carrol.  But today Zeno’s paradoxes can be merely explained in minor detail.  Nonetheless, controversies still arise of such a prevalent issue even today.  Although many of Zeno’s Paradoxes have been continuously refuted, many even proven wrong, they are still very interesting ...

This is a preview of the whole essay