This research paper attempts to provide some insights into the life of Zeno of Elea and his paradoxes or arguments against plurality, motion, place, and hearing. The paper also provides information regarding Empiricism and its relation to plurality, motion, place, and hearing. By comparing and contrasting these notions the paper aims to better understand the empirical argument and Zeno's paradoxes.
Historians have noted that Zeno did not actually contribute to the School of Eleatic philosophy but only because his main objective was to devote all of philosophical efforts to refute his mentor's opponents' views. That mentor was said to have been Parmenides who was a teacher on the subjects of the illusions we now know as motion and multiplicity. His teachings revolved around a basic concept that there is a 'True Being' which equates to an absolute one which entails a complete lack of plurality or change. In other words, the 'True Being' represented anything that was static or unchangeable.
Who was Zeno?
Zeno was considered to have been an Eleatic school philosopher because of his native home of Elea. "The main source of our knowledge of Zeno comes from the dialogue Parmenides written by Plato." (O'Connor, J.J. & EF Robertson) Unfortunately, very little else is actually known of Zeno of Elea other than he was the son of Teleutagoras and that it is assumed he was born in approximately 490 BC in Elea, Luciana which is now modern day southern Italy. It is also assumed that he would have 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 in Athens for some period in his life because of references to an attempt to over through his native region from a tyrant of the time. It is not known if Zeno survived a coup or if died during the over through.
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 from other works by Aristotle. For example, Plato was credited with showing 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. Apparently Zeno was greatly influenced by this movement and was thought to have written extensively on the subject. But, very few bits of Zeno's actual writings have been discovered.
One's typical assumptions have us assume that there would have to be both motion and plurality in our lives. This is the exactly the idea that Pythagorean and later Zeno focused all of their arguments on. Zeno may have demonstrated how the basic idea of common sense leads to various paradoxical problems. Zeno was said to have written some forty different paradoxes that were 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, J.J. & EF Robertson)
Each of these paradoxes was focused on unique difficulties that could be derived from an analysis of a gamut. The basic premise of the paradoxes is that if or when something is divided it can therefore be divided again -- in fact, it could be divided an infinite amount of times. In addition, Zeno sufficed to say that if something had no scale or magnitude, it would then be impossible for that something to exist.
Zeno's argument regarding the idea of not being able to exist without magnitude revolves around: adding a thing with no magnitude to something else does not make the receiving thing larger and subtracting a thing of no magnitude will not make the receiving thing smaller. This then entails that since the magnitude-less items do not make things bigger or smaller then the thing of no magnitude most be nothing. Although Zeno's pluralism here is perplexing at the least, his ideas of motion are even more complicated.
Consider your having to walk down a hall. Before you get to the end of the hall you have to reach the middle. Before you reach the middle you have to reach the quarter point. In other words, there is no motion because one must always arrive at the middle and therefore you can never reach an end because you are always reaching points before that. To walk down that hall then you would first have to the middle and prior to that you must first reach the quarter point and so on. "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 attempts to sum 1/2 + 1/4 + 1/8 + ... backwards." (O'Connor, J.J. & EF Robertson)
Consider that Zeno argued that the sum of this equation never reaches 1 and no matter how we approach this we actually never get motion started or ended. Modern day philosophers still consider Zeno's argument as a very perplexing problem. The underlining premise is that Zeno uses a paradox to discredit movement and pluralism since once something is divisible it must continue to be divisible.
Empiricists' doctrine basically states that knowledge must be the result of experience. "Empiricism is a regard to matters of fact as hypotheses liable to modification in the course of future investigation. Radical empiricism implies treating the doctrine of monism as a hypothesis, and, unlike much of the "half-way empiricism that is current under the name of positivism or agnosticism or scientific naturalism," it does not dogmatically affirm monism as something with which all experience has to abide." (James, William) Philosophers that are empiricists also feel that experience must also include what we would consider as an inner experience or an inner reflection. Our mind is constantly at work and throughout these mental operations we create experiences that are just as real as an external experience or perception.
Empiricism is different than rationalism because rationalism does not promote the design of inherent ideas. "If a theologically-driven transcendental metaphysics is inadequate to provide a set of assumptions for science, then so is a subjective rationalism and a radical empiricism. That is to say, neither a transcendental metaphysics nor an experimental epistemology will do to account for the consistency of fact."(Feibleman)
Therefore, empiricist would say that because ideas can only be created or derived from direct experience, the physical world is actually nothing more than a type of generalization. To take this one step further, because the world is a generalization, we as humans can never really be accurate about our world. "Empiricists do acknowledge some mathematical and logical truth but many Empiricists treat even these as generalizations from man's experience." (James, William)
In regard to motion, Empiricists feel that the generalizations of space and time apply. "We need something in effect more substantial than space, which could so to speak be occupied by a point-instant since we have learned of the indissoluble connections of space with time. For there is more in space-time than local regions; space is occupied by more than points and there are things which endure in time beyond its instants. There are elements here, however, which could well be saved for our own account of substance." (Feibleman)
The logic is complicated but it answers the need of the Empiricists. "It is reason which persuades necessity to lead "to the best issue." "most of the things coming into existence." Moreover, there is an irrational as well as a partial ingredient here, represented by the "errant cause," for if the receptacle is responsible for all becoming, and it is the nature of the errant cause to set in motion, then since motion and becoming belong together it is legitimate to associate the errant cause with the receptacle. (Feibleman)
For and pluralism, the Empiricists have their notions as well. "Prima facie the world is a pluralism; as we find it, its unity seems to be that of any collection; and our higher thinking consists chiefly of an effort to redeem it from that first crude form." (James, William)
Compare the empirical argument with Zeno's paradoxes
Empiricists see Zeno's doctrine as a form of Monism and therefore the paradox's on motion and pluralism fail as a philosophical theory. The Empiricists do not concur with Parmenides and therefore Zeno's paradoxes based on the notion that things are both alike and different. "If like means "having qualities in common with," and unlike "not having qualities in common with," then no two things can be at the same time like and unlike. If, on the other hand, unlike merely means "having qualities not shared by," then any two things whatever are both like and unlike. But, in that case also, there is no point in saying that likeness and unlikeness…