Zeno of Elea
Zeno of Elea
Velia is the Italian name of the ancient town of Elea located on the territory of the comune of Ascea, Salerno, Campania, Italy in a geographical sub-area named Cilento...

(icon; ; ca. 490 BC – ca. 430 BC) was a pre-Socratic Greek philosopher of southern Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

 and a member of the Eleatic School founded by Parmenides
Parmenides of Elea was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy. The single known work of Parmenides is a poem, On Nature, which has survived only in fragmentary form. In this poem, Parmenides...

. Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 called him the inventor of the dialectic
Dialectic is a method of argument for resolving disagreement that has been central to Indic and European philosophy since antiquity. The word dialectic originated in Ancient Greece, and was made popular by Plato in the Socratic dialogues...

. He is best known for his paradoxes
Zeno's paradoxes
Zeno's paradoxes are a set of problems generally thought to have been devised by Greek philosopher Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is...

, which Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...

 has described as "immeasurably subtle and profound".


Little is known for certain about Zeno's life. Although written nearly a century after Zeno's death, the primary source of biographical information about Zeno is the dialogue of Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

 called the Parmenides. In the dialogue, Plato describes a visit to Athens
History of Athens
Athens is one of the oldest named cities in the world, having been continuously inhabited for at least 7000 years. Situated in southern Europe, Athens became the leading city of Ancient Greece in the first millennium BCE and its cultural achievements during the 5th century BCE laid the foundations...

 by Zeno and Parmenides, at a time when Parmenides is "about 65," Zeno is "nearly 40" (Parmenides 127b) and Socrates
Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...

 is "a very young man" (Parmenides 127c). Assuming an age for Socrates of around 20, and taking the date of Socrates' birth as 469 BC gives an approximate date of birth for Zeno of 490 BC.

Plato says that Zeno was "tall and fair to look upon" and was "in the days of his youth … reported to have been beloved by Parmenides" (Parmenides 127b).

Other perhaps less reliable details of Zeno's life are given by Diogenes Laërtius
Diogenes Laertius
Diogenes Laertius was a biographer of the Greek philosophers. Nothing is known about his life, but his surviving Lives and Opinions of Eminent Philosophers is one of the principal surviving sources for the history of Greek philosophy.-Life:Nothing is definitively known about his life...

 in his Lives and Opinions of Eminent Philosophers
Lives and Opinions of Eminent Philosophers
Lives and Opinions of Eminent Philosophers is a biography of the Greek philosophers by Diogenes Laërtius, written in Greek, perhaps in the first half of the third century AD.-Overview:...

, where it is reported that he was the son of Teleutagoras, but the adopted son of Parmenides, was "skilled to argue both sides of any question, the universal critic," and that he was arrested and perhaps killed at the hands of a tyrant of Elea.

According to Plutarch
Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...

, Zeno attempted to kill the tyrant Demylus, and failing to do so, "with his own teeth bit off his tongue, he spit it in the tyrant’s face."


Although many ancient writers refer to the writings of Zeno, none of his writings survive intact.

Plato says that Zeno's writings were "brought to Athens for the first time on the occasion of" the visit of Zeno and Parmenides (Parmenides 127c). Plato also has Zeno say that this work, "meant to protect the arguments of Parmenides" (Parmenides 128c), was written in Zeno's youth, stolen, and published without his consent (Parmenides 128e). Plato has Socrates paraphrase the "first thesis of the first argument" of Zeno's work as follows: "if being is many, it must be both like and unlike, and this is impossible, for neither can the like be unlike, nor the unlike like" (Parmenides 127d,e).

According to Proclus
Proclus Lycaeus , called "The Successor" or "Diadochos" , was a Greek Neoplatonist philosopher, one of the last major Classical philosophers . He set forth one of the most elaborate and fully developed systems of Neoplatonism...

 in his Commentary on Plato's Parmenides, Zeno produced "not less than forty arguments revealing contradictions" (p. 29), but only nine are now known.

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum
Reductio ad absurdum
In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction...

, literally meaning to reduce to the absurd. Parmenides is said to be the first individual to implement this style of argument. This form of argument soon became known as the epicheirema (ἐπιχείρημα). In Book VII of his Topica, Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 says that an epicheirema is a dialectical syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

. It is a connected piece of reasoning which an opponent has put forward as true. The disputant sets out to break down the dialectical syllogism. This destructive method of argument was maintained by him to such a degree that Seneca the Younger
Seneca the Younger
Lucius Annaeus Seneca was a Roman Stoic philosopher, statesman, dramatist, and in one work humorist, of the Silver Age of Latin literature. He was tutor and later advisor to emperor Nero...

 commented a few centuries later, If I accede to Parmenides there is nothing left but the One; if I accede to Zeno, not even the One is left.

Zeno's paradoxes

Zeno's paradoxes have puzzled, challenged, influenced, inspired, infuriated, and amused philosophers, mathematicians, and physicists for over two millennia. The most famous are the so-called "arguments against motion" described by Aristotle in his Physics
Physics (Aristotle)
The Physics of Aristotle is one of the foundational books of Western science and philosophy...


Further reading

  • Early Greek Philosophy Jonathan Barnes
    Jonathan Barnes
    Jonathan Barnes is a British philosopher, translator and historian of ancient philosophy.-Education and career:He was educated at the City of London School and Balliol College, Oxford University....

    . (Harmondsworth, 1987).
  • "Zeno and the Mathematicians" G. E. L. Owen
    Gwilym Ellis Lane Owen
    Gwilym Ellis Lane Owen was a Welsh philosopher, concerned with the history of Ancient Greek philosophy. From 1973 until his death he was the fourth Laurence Professor of Ancient Philosophy at the University of Cambridge...

    . Proceedings of the Aristotelian Society (1957-8).
  • Paradoxes Mark Sainsbury
    Mark Sainsbury (philosopher)
    R. Mark Sainsbury is a philosopher from the United Kingdom who has worked in the areas of philosophical logic, philosophy of language, and the philosophies of Bertrand Russell and Gottlob Frege....

    . (Cambridge, 1988).
  • Zeno's Paradoxes Wesley C. Salmon
    Wesley C. Salmon
    Wesley C. Salmon was a metaphysician and contemporary philosopher of science concerned primarily with the topics of causation and explanation....

    , ed. (Indianapolis, 1970).
  • Zeno of Elea Gregory Vlastos
    Gregory Vlastos
    Gregory Vlastos was a scholar of ancient philosophy, and author of several works on Plato and Socrates. He was also a Christian and has written on Christian faith as well.-Life and works:...

     in The Encyclopedia of Philosophy (Paul Edwards
    Paul Edwards (philosopher)
    Paul Edwards, born Paul Eisenstein, was an Austrian American moral philosopher.-Life and career:Edwards was born in Vienna in 1923 to assimilated Jewish parents, the youngest of three brothers....

    , ed.), (New York, 1967).
  • De compositie van de wereld Harry Mulisch
    Harry Mulisch
    Harry Kurt Victor Mulisch was a Dutch author. He wrote more than 80 novels, plays, essays, poems and philosophical reflections. These have been translated into more than 20 languages....

    . (Amsterdam, 1980).

External links

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