Zeno of Elea
Portretbuste van Zeno van Elea Paradigmata graphices variorum artificum (serietitel), RP-P-1907-4495.jpg
Portrait of Zeno of Elea by Jan de Bisschop (1628–1671)
Bornc. 495 BC
Diedc. 430 BC (aged around 65)
Elea or Syracuse
EraPre-Socratic philosophy
RegionWestern philosophy
SchoolEleatic
Main interests
Metaphysics, ontology
Notable ideas
Zeno's paradoxes
Influences

Zeno of Elea (/ˈzn ...ˈɛliə/; Ancient Greek: Ζήνων ὁ Ἐλεᾱ́της; c. 495 – c. 430 BC)[1] was a pre-Socratic Greek philosopher of Magna Graecia (southern Italy) and a member of the Eleatic School founded by Parmenides. Plato and Aristotle called him the inventor of the dialectic.[2] He is best known for his paradoxes.

Life

Little is known for certain about Zeno's life. The primary source of biographical information about Zeno is Plato's dialogue Parmenides, which recounts a fictionalized account of a visit that Zeno and Parmenides made to Ancient Athens in 450 BC,[3] at a time when Parmenides is "about 65", Zeno is "nearly 40", and Socrates is "a very young man".[4][5] 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".[4]

According to Sir William Smith, in the Dictionary of Greek and Roman Biography and Mythology (1870)[6]

Others content themselves with reckoning Parmenides as well as Zeno as belonging to the Pythagorean school, or with speaking of a Parraenidean life, in the same way as a Pythagorean life is spoken of; and even the censorious Timon allows Parmenides to have been a high-minded man; while Plato speaks of him with veneration, and Aristotle and others give him an unqualified preference over the rest of the Eleatics.

Other perhaps less reliable details of Zeno's life are given by Diogenes Laërtius in his Lives and Opinions of Eminent Philosophers,[7] 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.[8] Eventually, Zeno was arrested and tortured.[9] According to Valerius Maximus, 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."[10][11] Within Men of the Same Name, Demetrius said that the nose was bitten off instead.[12] 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".[13][5]

Your noble wish, O Zeno, was to slay

A cruel tyrant, freeing Elea
From the harsh bonds of shameful slavery,
But you were disappointed; for the tyrant
Pounded you in a mortar. I say wrong,

He only crushed your body, and not you.

— Diogenes Laërtius, Life of Zeno, the Eleatic[14][15]

Zeno may have also interacted with other tyrants. According to Laërtius, Heraclides Lembus, within his Satyrus, these events occurred against Diomedon instead of Nearchus.[8] Valerius Maximus recounts a conspiracy against the tyrant Phalaris, but this would be impossible as Phalaris had died before Zeno was even born.[11][16] According to Plutarch, 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".[17]

Works

According to Plato,[4] Zeno wrote a book of paradoxes, however, this has unfortunately not survived.[3] Plato says that Zeno's writings were "brought to Athens for the first time on the occasion of" the visit of Zeno and Parmenides.[4] Plato also has Zeno say that this work "meant to protect the arguments of Parmenides",[4] 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."[4]

The main sources on the nature of Zeno's arguments on motion come from Aristotle's Physics.[18] and the commentary on that work by Simplicius of Cilicia.[19]

Zeno's paradoxes

Main article: Zeno's paradoxes

Zeno's paradoxes have puzzled, challenged, influenced, inspired, infuriated, and amused philosophers, mathematicians, and physicists for over two millennia. According to Proclus in his Commentary on Plato's Parmenides, Zeno produced "not less than forty arguments revealing contradictions",[20] but only nine are now known. The most famous are the arguments against motion described by Aristotle in his Physics, Book VI.[21]

Legacy

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum, literally meaning to reduce to the absurd. Parmenides is said[citation needed] 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 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 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."[22]

Zeno shows the Doors to Truth and Falsity (Veritas et Falsitas). Fresco in the Library of El Escorial, Madrid.
Zeno shows the Doors to Truth and Falsity (Veritas et Falsitas). Fresco in the Library of El Escorial, Madrid.

Bertrand Russell described Zeno's paradoxes as "immeasurably subtle and profound".[23]

"In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity's lack of judgment is the Eleatic Zeno. Having invented four arguments all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments to be one and all sophisms. After two thousand years of continual refutation, these sophisms were reinstated and made the foundation of a mathematical renaissance..."[24]

Zeno is also regarded as the first philosopher who dealt with the earliest attestable accounts of mathematical infinity.[25]

See also

Notes

  1. ^ Zeno of Elea - Greek philosopher and mathematician.
  2. ^ Diogenes Laërtius, 8.57, 9.25
  3. ^ a b Huggett, Nick (2002). "Zeno's Paradoxes". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
  4. ^ a b c d e f Plato, Parmenides 127b–e.
  5. ^ a b "Suda, Zeno of Elea". Suda On Line: Byzantine Lexicography. Stoa Consortium. Archived from the original on September 17, 2019. (at footnote n. 2)
  6. ^ Public Domain Smith, William, ed. (1870). "Parmenides". Dictionary of Greek and Roman Biography and Mythology. p. 125.
  7. ^ Diogenes Laërtius. The Lives and Opinions of Eminent Philosophers, translated by C. D. Yonge. London: Henry G. Bohn, 1853. Scanned and edited for Peithô's Web Archived 2010-12-12 at the Wayback Machine.
  8. ^ a b Diogenes Laërtius, Lives of Eminent Philosophers. Book IX.5.26.
  9. ^ Boethius, The Consolation of Philosophy. Book 1.III.
  10. ^ Valerius Maximus, Memorable Deeds and Sayings. Foreign Stories 3. ext. 3.
  11. ^ a b Maximus, Valerius; Walker, Henry J. (2004). Memorable Deeds and Sayings: One Thousand Tales from Ancient Rome. Hackett Pub. p. 97. ISBN 978-0-87220-674-8.
  12. ^ Diogenes Laërtius, Lives of Eminent Philosophers. Book IX.5.27.
  13. ^ "Zeno of Elea". Suda. Topostext.org. Archived from the original on January 24, 2019. Retrieved June 11, 2021.
  14. ^ "The paradox ideas of Zeno of Elea, is motion an illusion or even impossible?". Archived from the original on 2015-06-07. Retrieved 2015-04-12.
  15. ^ "Diogenes Laertius, Lives of Eminent Philosophers, Book IX, Chapter 5. Zeno of Elea".
  16. ^ Valerius Maximus, Memorable Deeds and Sayings. Foreign Stories 3. ext. 2.
  17. ^ Plutarch, Against Colotes.
  18. ^ Aristotle (c. mid 4th century BC), Physics 233a and 239b.
  19. ^ Cajori, Florian (1920). "The Purpose of Zeno's Arguments on Motion". Isis. 3 (1): 7–20. doi:10.1086/357889.
  20. ^ Proclus, Commentary on Plato's Parmenides, p. 29.
  21. ^ Aristotle. Physics, translated by R.P. Hardie and R.K. Gaye. Internet Classics Archive.
  22. ^ Zeno in The Presocratics, Philip Wheelwright ed., The Odyssey Press, 1966, pp. 106–107.
  23. ^ Russell (1996 [1903]), p. 347
  24. ^ Russell (1996 [1903]), p. 347
  25. ^ Boyer, Carl B.; Merzbach, Uta C. (2011). A History of Mathematics (Third ed.). Hoboken, New Jersey: John Wiley & Sons. p. 538. ISBN 978-0-470-52548-7. Ever since the days of Zeno, men had been talking about infinity,...

References

Further reading