Zeno of Elea
Zeno of Elea (classical Greek: Ζήνων ὁ Ελεάτης) was a Greek philosopher born in Elea, belonging to the Eleatic school (c. 490-430 BC). He was a direct disciple of Parmenides of Elea. He did not establish or conform any positive doctrine at his own hand. He is famous for his intricate paradoxes that discuss the plurality of entities and in some cases movement —among other things. Aristotle called him the inventor of dialectics and the philosopher and mathematician Bertrand Russell described him as "immensely subtle and profound".
Biography
As with most pre-Socratic philosophers, the life of Zeno of Elea remains largely unknown.
It is thought that he spent his entire life in Elea and was concerned with the education of men in virtue. In principle he was a Pythagorean and Strabo attributed a political activity to him. In the only context in which he is quoted several times, it is an account of his participation in a plot against a tyrant, the details are so divergent that it is impossible to reconstruct what happened.
The sources that shed light on this are Plato's dialogue Parmenides, the work Life of Illustrious Philosophers by the historian and ancient philosopher Diogenes Laertius, and Aristotle's Physics.
In Plato's dialogue, Zeno is said to be around 40 and Parmenides is said to be close to 65 at the time they both meet a "very young" Socrates; data that can help us to place his birth around the year 480 or 490 a. C. Plato describes him as & # 34; tall and beautiful to look at & # 34;, as well as esteemed by his teacher.
Diogenes Laertius indicates that he was the natural son of a man named Telentagoras, but that Parmenides took him up for adoption. Laertius also underlines his skill when it comes to analyzing both sides of each question or dilemma, a capacity that earned him the title of & # 34; inventor of dialectic & # 34; from the hand of Aristotle.
Like his teacher, he probably had a great political activity: Laertius himself affirms that Zeno supported the overthrow of the Eleatian tyrant who ruled, under threat of death:
Having carried out the overthrow of the Nearco tyrant (others say Diomedon), he was arrested (...) Interrogated about his accomplices and the weapons he had given to Lipara, he quotes the names of all the tyrant's friends, with the intention of hiding their own. Then, under the promise of confidential revelations about certain people, he cruelly bit the tyrant in his ear and does not release him until he is wounded in death (...) In the end, he cut his tongue with his own teeth and spit it in his face.Diogenes Laercio, Life of the illustrious philosophers, IX, 26-27
Laertius does not specify the identity of the tyrant, since he indicates that it could be both Nearchus and Diomedon, also giving two possible endings to the story: in one the tyrant is finally stoned by the people who rebel and in another it is Zeno who is executed Tertullian reports several centuries later on Zeno's death:
Zenon of Elea, whom Dionisio asked what the superiority of philosophy is, replied: "In the contempt of death!" and at the hands of the tyrant he maintains, impassive, his purpose until death.Tertullian, Apologeticum, 50
In the passage Tertullian makes the wrong tyrant, since it is impossible for Zeno, a philosopher born in the V century, to. C. was tortured by Dionisio I, tyrant of Syracuse a century later.
The works of Zeno have been lost. Plato writes that during his youth he had already written to defend the theories of his teacher, since such documents were brought to Athens on the occasion of his visit with Parmenides; they were stolen there and subsequently published without his consent.
As usual in the pre-Socratic sphere, the largest and almost the only source from which we can extract information about his work and thought is the citation of later authors, particularly Aristotle himself.
Works and controversies
From Plato's aforementioned writing, it can be inferred that what was written by Zeno constituted a volume that consisted of a collection of arguments, each of which attempted against the thesis of the plurality of entities; however, in the quoted fragments, Zeno does not show them either as antinomies or as explicitly directed against the plurality of entities. More than anything, the paradoxes of motion that we see in Aristotle's writings.
In short, we do not know exactly what was the organizing principle that Zeno followed for the ordering of his arguments. The scholars G. S. Kirk, J. E. Raven and M. Schofield, test three possibilities:
A: Zeno wrote a play, the way Plato describes it, but Zeno wrote at least one other play, which included other paradoxes that did not attack the plurality of things.
B: The philosopher wrote only one book, but Plato does not describe well his arguments or their form.
C: Zeno wrote a single work, and all the paradoxes originally attacked the plurality of entities, and have been distorted by different authors and their interpretations over time.
Zeno's influence through time
It is not known with certainty whether Zeno's work preceded and influenced the philosophy of Melissus and Anaxagoras or vice versa. It is evident that he strongly influenced the atomism of Leucippus and Democritus. The curious work of Gorgias.
When Protagoras intercedes for the construction of contradictory arguments on any matter, it is evident that he drew inspiration from Zeno.
Plato's philosophical interest in Zeno was reflected in his antinomies that fill the last thirty pages of Parmenides with reasoning about movement, place and time, which would later stimulate Aristotle...
In our time is when the paradoxes of Zeno have been discussed -and are being discussed- with greater intensity, who is the pre-Socratic who exerts the most influence.
Paradoxes
Zenón, in the line of his teacher, tries to prove that being has to be homogeneous, unique and, consequently, that space is not made up of discontinuous elements but that the entire cosmos or universe is a single unit.
His aporias are designed under the following argumentative axes:
- Against plurality as the structure of the real.
- Against the validity of space.
- Against the reality of the movement.
- Against the reality of the passing of time.
Applying this scheme, he has been considered the first to use the demonstration called ad absurdum (reduction to absurdity), which assumes the opposite of what is considered true (in his case, the adversary's statements) and shows the inconsistencies that derive from considering this as true, forcing the interlocutor to reject the premises and accept the opposite theses, which were the ones that were initially wanted to be demonstrated. This procedure is carried out by means of his aporias.
As an example of (1) we have in Fr. 3, Simplicio, Physics., where he probably argues that, for one thing to be one and not another, between both members within a set, there must be something separating them. We could refute it by claiming that the statement is valid only if it were applied to systematically ordered sets -such as series of points- and that in reality, being objects in three dimensions, they behave in a very different way, but Zeno could well continue "inquiring" about this, and asking ourselves questions that we could not answer until we have resolved through philosophical reflection what it is that makes one thing itself and not another or many.
Achilles and the Tortoise, Aristotle, Phys., is a clear example of (3), but it also creates difficulties for us in (2) and (4); It consists of a race between Achilles -the one with the light feet- against a tortoise, but starting the tortoise from a more advanced distance...
The problem is to show how it is impossible for the fastest runner to overtake the slowest, since in order to even catch up with Achilles the tortoise must first go through half the distance of that run, and to reach that distance, before it should reach half that distance, and so on infinitely, in a series of numbers converging towards zero, where it not only poses a problem of how we measure and perceive time and space, but also makes the idea of motion rationally impossible.
Infinitesimal thinking
Zenón's reasoning constitutes the oldest surviving testimony of the infinitesimal thought developed many centuries later in the application of the infinitesimal calculus that will be born from the hand of Leibniz and Newton in 1666. However, Zenón was oblivious to any possible mathematization, presenting a conceptualization of such a style as a necessary instrument to be able to formulate its paradoxes.
Fonts
- Aristotle, Metaphysics (trad. and notes by T. Calvo Martínez): Editorial Gredos. 2007.
- Plato, Dialogues V, Parmenides, Teeteto, Sophist, Political (Trad. and notes by M. Isabel Santa Cruz). Madrid: Editorial Gredos. 1988.