.
Zeno of Elea (pron.: /ˈziːnoʊ əv ˈɛliə/; Greek: Ζήνων ὁ Ἐλεάτης; ca. 490 BC – ca. 430 BC) was a preSocratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic.[1] He is best known for his paradoxes, which Bertrand Russell has described as "immeasurably subtle and profound".[2]
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's Parmenides.[3] In the dialogue, Plato describes a visit to Athens by Zeno and Parmenides, at a time when Parmenides is "about 65," Zeno is "nearly 40" and Socrates is "a very young man".[4] 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]
Other perhaps less reliable details of Zeno's life are given by Diogenes Laërtius in his Lives and Opinions of Eminent Philosophers,[5] 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, 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."[6]
Works
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.[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]
According to Proclus in his Commentary on Plato's Parmenides, Zeno produced "not less than forty arguments revealing contradictions", [7] but only nine are now known.
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 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 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."[8]
Zeno is also regarded as the first philosopher who dealt with the earliest attestable accounts of mathematical infinity.
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. The most famous are the socalled "arguments against motion" described by Aristotle in his Physics.[9]
See also
Incommensurable magnitudes
List of speakers in Plato's dialogues
Notes
^ Diogenes Laërtius, 8.57, 9.25
^ Russell, p. 347: "In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity's lack of judgement 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..."
^ Plato (370 BC). Parmenides, translated by Benjamin Jowett. Internet Classics Archive.
^ a b c d e Plato, Parmenides 127be
^ 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.
^ Plutarch, Against Colotes
^ Proclus, Commentary on Plato's Parmenides, p. 29
^ Zeno in The Presocratics, Philip Wheelwright ed., The Odyssey Press, 1966, Pages 106107.
^ Aristotle (350 BC). Physics, translated by R.P. Hardie and R.K. Gaye. Internet Classics Archive.
References
Plato; Fowler, Harold North (1925) [1914]. Plato in twelve volumes. 8, The Statesman.(Philebus).(Ion). Loeb Classical Library. trans. W. R. M. Lamb. Cambridge, Mass.: Harvard U.P. ISBN 9780434991648. OCLC 222336129.
Proclus; Morrow, Glenn R.; Dillon, John M. (1992) [1987]. Proclus' Commentary on Plato's Parmenides. Princeton, N.J.: Princeton University Press. ISBN 9780691020891. OCLC 27251522.
Russell, Bertrand (1996) [1903]. The Principles of Mathematics. New York, NY: Norton. ISBN 9780393314045. OCLC 247299160.
Hornschemeier, Paul (2007). The Three Paradoxes. Seattle, WA: Fantagraphics Books.
Further reading
Early Greek Philosophy Jonathan Barnes. (Harmondsworth, 1987).
"Zeno and the Mathematicians" G. E. L. Owen. Proceedings of the Aristotelian Society (19578).
Paradoxes Mark Sainsbury. (Cambridge, 1988).
Zeno's Paradoxes Wesley C. Salmon, ed. (Indianapolis, 1970).
Zeno of Elea Gregory Vlastos in The Encyclopedia of Philosophy (Paul Edwards, ed.), (New York, 1967).
De compositie van de wereld Harry Mulisch. (Amsterdam, 1980).
External
Zeno
Zeno of Elea entry by John Palmer in the Stanford Encyclopedia of Philosophy
Zeno of Elea  MacTutor
Plato's Parmenides.
Aristotle's Physics.
Diogenes Laërtius, Life of Zeno, translated by Robert Drew Hicks (1925).
Presocratic Philosophers series Thales  Anaximander  Anaximenes  Pythagoras  Philolaus  Archytas  Empedocles  Heraclitus  Parmenides  Zeno of Elea  Melissus  Xenophanes  Anaxagoras  Leucippus  Democritus  Protagoras  Gorgias  Prodicus  Hippias  Pherecydes 
G. S. Kirk, J. E. Raven, M. Schofield , The Presocratic Philosophers: A Critical History with a Selection of Texts , Cambridge University Press;
Ancient Greek and Hellenistic mathematics (Euclidean geometry)
Mathematicians
(timeline)
Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner
Problems
Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Centers
Cyrene Library of Alexandria Platonic Academy
Other
Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction
Ancient Greece

Science, Technology , Medicine , Warfare, , Biographies , Life , Cities/Places/Maps , Arts , Literature , Philosophy ,Olympics, Mythology , History , Images

Medieval Greece / Byzantine Empire

Science, Technology, Arts, , Warfare , Literature, Biographies, Icons, History 
Modern Greece

Retrieved from "http://en.wikipedia.org"
All text is available under the terms of the GNU Free Documentation License