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Zeno of Elea (Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
: ????? ? ??e?t??) (ca. 490 BC? – ca. 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides
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....
. Aristotle
Aristotle

Aristotle was a Greeks philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, Poetics , theater, music, logic, rhetoric, politics, government, ethics, biology and zoology....
 called him the inventor of the dialectic
Dialectic

Dialectic is a method of argument, which has been central to both Eastern and Western philosophy since ancient times. The word "dialectic" originates in Ancient Greece, and was made popular by Plato's 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 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 nothing but an illusion....
.

le 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

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
 called the Parmenides.






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Zeno of Elea (Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
: ????? ? ??e?t??) (ca. 490 BC? – ca. 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides
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....
. Aristotle
Aristotle

Aristotle was a Greeks philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, Poetics , theater, music, logic, rhetoric, politics, government, ethics, biology and zoology....
 called him the inventor of the dialectic
Dialectic

Dialectic is a method of argument, which has been central to both Eastern and Western philosophy since ancient times. The word "dialectic" originates in Ancient Greece, and was made popular by Plato's 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 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 nothing but an illusion....
.

Life

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

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
 called the Parmenides. In the dialogue, Plato describes a visit to Athens
History of Athens

The History of Athens is one of the longest of any city in Europe and in the world. Athens has been continuously inhabited for over 4,500 years, becoming the leading city of Ancient Greece in the first millennium BC; its cultural achievements during the 5th century BC laid the foundations of western culture....
 by Zeno and Parmenides, at a time when Parmenides is "about 65," Zeno is "nearly 40" and Socrates
Socrates

Socrates was a Classical Greece Philosophy. Credited as one of the founders of Western philosophy, he is an enigmatic figure known only through the classical accounts of his students....
 is "a very young man" (Parmenides 127). Assuming an age for Socrates of around 20, and taking the date of Socrates' birth as 470 BC, gives an approximate date of birth for Zeno of 490 BC. Plato has written that Zeno was about twenty-five years younger than Parmenides.

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 127).

Other perhaps less reliable details of Zeno's life are given in Diogenes Laertius
Diogenes Laertius

Diogenes La?rtius , the biographer of the Greece philosophers, is supposed by some to have received his surname from the town of Laerte in Cilicia, Asia Minor, and by others from the Roman Empire family of the La?rtii....
' Lives of Eminent Philosophers, 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 further that he was arrested and perhaps killed at the hands of a tyrant of Elea.

According to Plutarch, 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."

Works

Although several 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 127). Plato also has Zeno say that this work, "meant to protect the arguments of Parmenides," was written in Zeno's youth, stolen, and published without his consent (Parmenides 128). 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 127).

According to Proclus
Proclus

Proclus Lycaeus , called "The Successor" or "Diadochos" , was a Greek philosophy Neoplatonist philosophy, one of the last major Classical philosophers ....
 in his Commentary on Plato's Parmenides, Zeno produced "not less than forty arguments revealing contradictions" (p. 29).

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum
Reductio ad absurdum

Reductio ad absurdum , also known as an apagogical argument, reductio ad impossibile, or proof by contradiction, is a type of logical argument where one assumes a claim for the sake of argument and derives an absurd or ridiculous outcome, and then concludes that the original claim must have been wrong as it led to an abs...
, 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. In Book VII of his Topica, Aristotle
Aristotle

Aristotle was a Greeks philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, Poetics , theater, music, logic, rhetoric, politics, government, ethics, biology and zoology....
 says that an epicheirema is a dialectical syllogism
Syllogism

A syllogism, or logical appeal, , is a kind of logical argument in which one proposition is Inference from two 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. Zeno is thought to have devised forty different epicheiremata to support aspects of Parmenides' monism
Monism

Monism is any philosophical view which holds that there is unity in a given field of inquiry, where this is not to be expected. Thus, some philosophers may hold that the Universe is really just one thing, despite its many appearances and diversities; or theology may support the view that there is one God, with many manifestations in different...
. 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 Ancient Rome Stoicism philosopher, statesman, dramatist, and in one work humorist, of the Silver Age of Latin literature....
 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, physicists and school children for over two millennia. The most famous are the so-called "arguments against motion" described by Aristotle in his Physics.

See also

  • Incommensurable magnitudes
    Incommensurable magnitudes

    The Greek discovery of incommensurable magnitudes changed the face of mathematics. At its most basic level it shed light on a glaring contradiction within the then current Greek conception of mathematical thought, which eventually resulted in a reformulation of both the methods and practice of mathematics in general....


Further reading

  • Early Greek Philosophy Jonathan Barnes
    Jonathan Barnes

    Jonathan Barnes is a United Kingdom philosopher, translator and historian of ancient philosophy. He taught for 25 years at Oxford University before moving to the University of Geneva....
    . (Harmondsworth, 1987).
  • "Zeno and the Mathematicians" G. E. L. Owen. Proceedings of the Aristotelian Society (1957-8).
  • Paradoxes Mark Sainsbury
    Mark Sainsbury

    Mark Sainsbury may refer to:*Mark Sainsbury , United Kingdom philosopher*Mark Sainsbury , New Zealand current affairs presenter...
    . (Cambridge, 1988).
  • Zeno's Paradoxes Wesley Salmon, 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 believer and has written on Christian faith as well....
     in The Encyclopedia of Philosophy (Paul Edwards
    Paul Edwards (philosopher)

    Paul Edwards, born Paul Eisenstein, was an Austrian-American moral philosopher....
    , ed.), (New York, 1967).


External links

  • - MacTutor


External links to online texts

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