Zeno's Paradoxes and Empiricism: A Comparative Study

Introduction

This research paper attempts to provide some insights into the life of Zeno of Elea and his paradoxes — arguments against plurality, motion, place, and hearing. The paper also provides information regarding Empiricism and its relation to these same concepts. By comparing and contrasting these two philosophical traditions, the paper aims to better understand the empirical argument and Zeno's paradoxes.

Historians have noted that Zeno did not actually contribute original doctrines to the Eleatic school of philosophy; rather, his primary objective was to devote all of his philosophical efforts to refuting the opponents of his mentor. That mentor was Parmenides, who taught that motion and multiplicity are illusions. His teachings revolved around the basic concept of a "True Being" — an absolute unity that entails a complete lack of plurality or change. In other words, the "True Being" represented anything that was static or unchangeable.

Who Was Zeno of Elea?

Zeno was considered an Eleatic school philosopher by virtue of his native home of Elea. "The main source of our knowledge of Zeno comes from the dialogue Parmenides" (O'Connor & Robertson). Unfortunately, very little else is known of Zeno of Elea other than that he was the son of Teleutagoras and that he is assumed to have been born in approximately 490 BC in Elea, Lucania — now modern-day southern Italy. It is also assumed that he died there around 425 BC.

Historians believe that he was the favorite disciple of Parmenides, who was born around 488 BCE. Historians have placed Zeno as a resident of Athens for some period of his life, based on references to an attempt to overthrow a tyrant in his native region. It is not known whether Zeno survived this episode or died during the uprising.

Zeno seems to have devoted his life to explaining and developing the philosophical system of his mentor Parmenides. Most of the information known about Zeno is based on the writings of Plato and on works by Aristotle. For example, Plato is credited with establishing that there was a twenty-five-year age difference between Zeno and Parmenides. Parmenides founded the Eleatic School, which has been considered one of the leading pre-Socratic schools of Greek philosophy. Zeno was greatly influenced by this movement and was thought to have written extensively on the subject, though very few fragments of his actual writings have survived.

Our typical assumptions lead us to accept that both motion and plurality exist in our lives. This is precisely the idea that the Pythagoreans, and later Zeno, focused all of their arguments on. Zeno demonstrated how basic common sense gives rise to various paradoxical problems. He is said to have written some forty different paradoxes based on the assumptions of plurality and motion. "The book Zeno wrote before his visit to Athens was his famous work which, according to Proclus, contained forty paradoxes concerning the continuum" (O'Connor & Robertson).

Zeno's Paradoxes of Motion and Plurality

Each of these paradoxes focused on the unique difficulties that arise from analyzing a continuum. The basic premise is that if something is divided, it can be divided again — in fact, it can be divided an infinite number of times. In addition, Zeno argued that if something had no scale or magnitude, it would be impossible for that thing to exist.

Zeno's argument regarding the impossibility of existence without magnitude runs as follows: adding a thing of no magnitude to something else does not make the receiving thing larger, and subtracting a thing of no magnitude does not make the receiving thing smaller. Since a magnitude-less item makes things neither bigger nor smaller, such an item must be nothing. Although Zeno's argument about plurality is perplexing, his ideas about motion are even more complicated.

Consider walking down a hall. Before you reach the end, you must first reach the midpoint. Before you reach the midpoint, you must reach the quarter-point. There is always a prior point to be reached, which means you can never actually complete the journey — because you are always required to reach a midpoint before the next. "On the one hand Zeno can argue that the sum 1/2 + 1/4 + 1/8 + … never actually reaches 1, but more perplexing to the human mind is the attempt to sum 1/2 + 1/4 + 1/8 + … backwards" (O'Connor & Robertson).

Zeno argued that this sum never reaches 1 and that, no matter how we approach the problem, motion can never truly begin or end. Modern philosophers still consider Zeno's paradoxes deeply challenging. The underlying premise is that Zeno uses paradox to discredit both movement and pluralism, since once something is divisible it must continue to be divisible without end.

Conclusion

This research paper attempted to provide insights into the life of Zeno of Elea and the paradoxes he is thought to have created concerning plurality, motion, place, and hearing. The paper also provided information about Empiricism and the Empiricists' views on plurality, motion, place, and hearing. By comparing and contrasting these notions, the paper aimed to help clarify both the empirical argument and Zeno's paradoxes.