Zeno of Elea (; grc, Ζήνων ὁ Ἐλεᾱ́της; ) was a

pre-Socratic Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of thes ...

Greek philosopher of

Magna Graecia Magna Graecia (, ; , , grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Romans to the coastal areas of Southern Italy in the present-day Italian regions of Calabria, Apulia, Basilicata, Campania and Sicily; the ...

and a member of the

Eleatic School The Eleatics were a group of pre-Socratic philosophers in the 5th century BC centered around the ancient Italian Greek colony of Elea ( grc, Ἐλέα), located in present-day Campania in southern Italy. The primary philosophers who are associa ...

founded by

Parmenides Parmenides of Elea (; grc-gre, Παρμενίδης ὁ Ἐλεάτης; ) was a pre-Socratic Greek philosopher from Elea in Magna Graecia. Parmenides was born in the Greek colony Greek colonization was an organised Colonies in antiquity ...

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...

called him the inventor of the

dialectic Dialectic ( grc-gre, διαλεκτική, ''dialektikḗ''; related to dialogue; german: Dialektik), also known as the dialectical method, is a discourse between two or more people holding different points of view about a subject but wishing to ...

. He is best known for his

paradoxes A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

, which

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...

described as "immeasurably subtle and profound".

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

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institutio ...

's ''

'' and he is also mentioned in Aristotle's ''

Physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...

''. In the dialogue of ''Parmenides'', Plato describes a visit to

Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital city, capital and List of cities and towns in Greece, largest city of Greece. With a population close to four million, it is also the seventh List ...

by Zeno and Parmenides, at a time when Parmenides is "about 65", Zeno is "nearly 40", and

Socrates Socrates (; ; –399 BC) was a Greek philosopher from Athens who is credited as the founder of Western philosophy and among the first moral philosophers of the ethical tradition of thought. An enigmatic figure, Socrates authored no te ...

is "a very young man".Plato, ''Parmenides'
127b–e
(at footnote n. 2) 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". Other perhaps less reliable details of Zeno's life are given by

Diogenes Laërtius Diogenes Laërtius ( ; grc-gre, Διογένης Λαέρτιος, ; ) was a biographer of the Greek philosophers. Nothing is definitively known about his life, but his surviving ''Lives and Opinions of Eminent Philosophers'' is a principal sour ...

in his ''

Lives and Opinions of Eminent Philosophers Diogenes Laërtius ( ; grc-gre, Διογένης Λαέρτιος, ; ) was a biographer of the Greek philosophers. Nothing is definitively known about his life, but his surviving ''Lives and Opinions of Eminent Philosophers'' is a principal sour ...

'', 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

, Zeno conspired to overthrow Nearchus the tyrant.Diogenes Laërtius, ''Lives of Eminent Philosophers''. Book IX.5.26. Eventually, Zeno was arrested and tortured. According to

Valerius Maximus Valerius Maximus () was a 1st-century Latin writer and author of a collection of historical anecdotes: '' Factorum ac dictorum memorabilium libri IX'' ("Nine books of memorable deeds and sayings", also known as ''De factis dictisque memorabilibus' ...

, when he was tortured to reveal the name of his colleagues in conspiracy, Zeno refused to reveal their names, although he said that he did have a secret that would be advantageous for Nearchus to hear. When Nearchus leaned in to listen to the secret, Zeno bit his ear. He "did not let go until he lost his life and the tyrant lost that part of his body." Within ''Men of the Same Name'', Demetrius said that the nose was bitten off instead. According to the 10th-century ''Suda'', while "Zeno was being interrogated by him, he took his own tongue between his teeth, gnawed it off, and spat it upon the tyrant", and "afterward he was thrown into a mortar and crushed and beaten to a pulp". Zeno may have also interacted with other tyrants. According to Laërtius,

Heraclides Lembus Heraclides Lembus ( grc-gre, Ἡρακλείδης Λέμβος, ''Hērakleidēs Lembos'') was an Ancient Greek statesman, historian and philosophical writer. Heraclides was an Egyptian civil servant who lived during the reign of Ptolemy VI Philom ...

, within his '' Satyrus'', these events occurred against Diomedon instead of Nearchus. Valerius Maximus recounts a conspiracy against the tyrant Phalaris, but this would be impossible as Phalaris had died before Zeno was even born. According to

Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ...

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

Works

Although many ancient writers refer to the writings of Zeno, none of his works survive intact. The main sources on the nature of Zeno's arguments on motion, in fact, come from the writings of

and

Simplicius of Cilicia Simplicius of Cilicia (; el, Σιμπλίκιος ὁ Κίλιξ; c. 490 – c. 560 AD) was a disciple of Ammonius Hermiae and Damascius, and was one of the last of the Neoplatonists. He was among the pagan philosophers persecuted by Justinian ...

. Plato says that Zeno's writings were "brought to Athens for the first time on the occasion of" the visit of Zeno and Parmenides. 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. 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." According to

Proclus Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophe ...

in his ''Commentary on Plato's Parmenides'', Zeno produced "not less than forty arguments revealing contradictions", but only nine are now known. Zeno's arguments are perhaps the first examples of a method of proof called ''

reductio ad absurdum In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical arguments'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absu ...

'', 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 ''Topics'',

says that an ''epicheirema'' is "a dialectical

syllogism A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

". 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 Lucius Annaeus Seneca the Younger (; 65 AD), usually known mononymously as Seneca, was a Stoicism, Stoic philosopher of Ancient Rome, a statesman, dramatist, and, in one work, satirist, from the post-Augustan age of Latin literature. Seneca was ...

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'' in ''The Presocratics'', Philip Wheelwright ed., The Odyssey Press, 1966, pp. 106–107. Zeno is also regarded as the first philosopher who dealt with the earliest attestable accounts of mathematical

infinity Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions am ...

. According to

Sir William Smith Sir William Smith (20 May 1813 – 7 October 1893) was an English lexicographer. He became known for his advances in the teaching of Greek and Latin in schools. Early life Smith was born in Enfield in 1813 to Nonconformist parents. He attended ...

, in the

Dictionary of Greek and Roman Biography and Mythology The ''Dictionary of Greek and Roman Biography and Mythology'' (1849, originally published 1844 under a slightly different title) is an encyclopedia/biographical dictionary. Edited by William Smith, the dictionary spans three volumes and 3,700 p ...

(1870)

Eusebius Eusebius of Caesarea (; grc-gre, Εὐσέβιος ; 260/265 – 30 May 339), also known as Eusebius Pamphilus (from the grc-gre, Εὐσέβιος τοῦ Παμφίλου), was a Greek historian of Christianity, exegete, and Christ ...

quoting Aristocles of Messene says that Zeno was part of a line of philosophy that culminated in

Pyrrhonism Pyrrhonism is a school of philosophical skepticism founded by Pyrrho in the fourth century BCE. It is best known through the surviving works of Sextus Empiricus, writing in the late second century or early third century CE. History Pyrrho of E ...

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 arguments against motion described by Aristotle in his ''Physics'', Book VI.Aristotle
''Physics''
translated by R.P. Hardie and R.K. Gaye. Internet Classics Archive. Zeno Achilles Paradox.png, Achilles and the tortoise Zeno Dichotomy Paradox alt.png, The dichotomy Zeno Arrow Paradox.png, The arrow Zeno Moving Rows Paradox.png, The moving rows

Notes

References

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External links

* * *
Zeno's Paradoxes
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Fragments of Zeno
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