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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 A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...
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; these re ...
and a member of the Eleatic School 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 of Elea, from a wealthy and illustrious family. His dates a ...
.
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
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 ...
. 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, ...
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 institution ...
's ''
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 of Elea, from a wealthy and illustrious family. His dates a ...
'' 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 r ...
''. In the dialogue of ''Parmenides'', Plato describes a visit to
Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates ...
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 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 sourc ...
'', 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 Diogenes Laërtius, 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 Phalaris ( el, Φάλαρις) was the tyrant of Akragas (now Agrigento) in Sicily, from approximately 570 to 554 BC. History Phalaris was renowned for his excessive cruelty. Among his alleged atrocities is cannibalism: he was said to have e ...
, 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 ''P ...
, 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
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
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 i ...
. 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 philosophers ...
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'',
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
says that an ''epicheirema'' is "a dialectical syllogism". 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 Stoic philosopher of Ancient Rome, a statesman, dramatist, and, in one work, satirist, from the post-Augustan age of Latin literature. Seneca was born in ...
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 amo ...
. According to Sir William Smith, 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 Christian ...
quoting Aristocles of Messene says that Zeno was part of a line of philosophy that culminated in Pyrrhonism.


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


See also

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Notes


References

* * * *


Further reading

* Barnes, Jonathan. 1982. ''The Presocratic Philosophers.'' 2d ed. London: Routledge & Kegan Paul. * Lewis, Eric. 1999. "The Dogmas of Indivisibility: On the Origins of Ancient Atomism. In ''Proceedings of the Boston Area Colloquium in Ancient Philosophy.'' Vol. 14. Edited by John J. Cleary and Gary M. Gurtler, S. J., 1–21. Leiden, The Netherlands: Brill. * McKirahan, Richard. 2001. "Zeno’s Dichotomy in Aristotle." ''Philosophical Inquiry'' 23.1–2: 1–24. * Navia, Luis. E. 1993. ''The Presocratic Philosophers: An Annotated Bibliography.'' New York and London: Garland. * Owen, G. E. L. 1958. "Zeno and the Mathematicians." ''Proceedings of the Aristotelian Society'' 58:199–222. * Papa-Grimaldi, Alba. 1996. "Why Mathematical Solutions of Zeno’s Paradoxes Miss the Point: Zeno’s One and many Relation and Parmenides’ Prohibition." ''Review of Metaphysics'' 50.2: 299–314. * Sainsbury, Mark. 1988. ''Paradoxes''. Cambridge: Cambridge University Press. * Salmon, Wesley C., ed. 1970. ''Zeno’s Paradoxes.'' Indianapolis, IN, and New York: Bobbs-Merrill. * Vlastos, Gregory. 1967. "Zeno of Elea." In ''The Encyclopedia of Philosophy.'' Vol. 8. Edited by Paul Edwards, 369–379. New York and London: Macmillan. * White, Michael J. 1992. ''The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective.'' Oxford: Clarendon.


External links

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Zeno's Paradoxes
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Fragments of Zeno
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