1. Zeno Of Elea [Internet Encyclopedia Of Philosophy] Life and work of the Eleatic philosopher, from the Internet Encyclopedia of Philosophy.Category Society Philosophy Philosophers zeno of elea......zeno of elea. Zeno was an Eleatic philosopher, a native of Elea (Velia) inItaly, son of Teleutagoras, and the favorite disciple of Parmenides. http://www.utm.edu/research/iep/z/zenoelea.htm

Zeno of Elea Paradoxes of Multiplicity and Motion Kant's, Hume's, and Hegel's Solutions to Zeno's Paradoxes. The Contemporary Solution to Zeno's Paradoxes. Zeno was an Eleatic philosopher, a native of Elea (Velia) in Italy, son of Teleutagoras, and the favorite disciple of Parmenides. He was born about 488 BCE., and at the age of forty accompanied Parmenides to Athens. He appears to have resided some time at Athens, and is said to have unfolded his doctrines to people like Pericles and Callias for the price of 100 minae. Zeno is said to have taken part in the legislation of Parmenides, to the maintenance of which the citizens of Elea had pledged themselves every year by oath. His love of freedom is shown by the courage with which he exposed his life in order to deliver his native country from a tyrant. Whether he died in the attempt or survived the fall of the tyrant is a point on which the authorities vary. They also state the name of the tyranny differently. Zeno devoted all his energies to explain and develop the philosophical system of Parmenides . We learn from Plato that Zeno was twenty-five years younger than Parmenides, and he wrote his defense of Parmenides as a young man. Because only a few fragments of Zeno's writings have been found, most of what we know of Zeno comes from what

2. CATHOLIC ENCYCLOPEDIA: Zeno Of Elea Article from the Catholic Encyclopedia. http://www.newadvent.org/cathen/15756b.htm

Home Encyclopedia Summa Fathers ... Z > Zeno of Elea A B C D ... Z Zeno of Elea Greek philosopher, born at Elea, about 490 B.C. At his birthplace Xenophanes and Parmenides had established the metaphysical school of philosophy known as the Eleatic School. The chief doctrine of the school was the oneness and immutability of reality and the distrust of sense-knowledge which appears to testify to the existence of multiplicity and change. Zeno's contribution to the literature of the school consisted of a treatise, now lost, in which, according to Plato, he argued indirectly against the reality of motion and the existence of the manifold. There were, it seems, several discourses, in each of which he made a supposition, or hypothesis, and then proceeded to show the absurd consequences that would follow. This is now known as the method of indirect proof, or reductio ad absurdum , and it appears to have been used first by Zeno. Aristotle in his "Physics" has preserved the arguments by which Zeno tried to prove that motion is only apparent, or that real motion is an absurdity. The arguments are fallacious, because as Aristotle has no difficulty in showing, they are founded on on false notions of motion and space. They are, however, specious, and might well have puzzled an opponent in those days, before logic had been developed into a science. They earned for Zeno the title of "the first dialectician," and, because they seemed to be an unanswerable challenge to those who relied on the verdict of the senses, they helped to prepare the way for the skepticism of the Sophists. Besides, the method of indirect proof opened up for the sophist new possibilities in the way of contentious argument, and was very soon developed into a means of confuting an opponent. It is, consequently, the forerunner of the Eristic method, or the method of strife.

3. John Burnet: Early Greek Philosophy -- Zeno Of Elea John Burnet details the life and works of the preSocratic Greek philosopher revered as the inventor of dialectic. http://plato.evansville.edu/public/burnet/ch8a.htm

Introduction The Life of Plato The Crito The Phaedo ... Credits and E XPLORING P LATO'S D IALOGUES A Virtual Learning Environment on the World-Wide Web Early Greek Philosophy Zeno of Elea John Burnet Life Writings Dialectic Zeno and Pythagoreanism ... Motion 155. Life According to Apollodorus Zeno flourished in 01. LXXIX. (464-460 B.C.). This date is arrived at by making him forty years younger than Parmenides , which is in direct conflict with the testimony of Plato. We have seen already ( ) that the meeting of Parmenides and Zeno with the young Socrates cannot well have occurred before 449 B.C., and Plato tells us that Zeno was at that time "nearly forty years old." He must, then, have been born about 489 B.C., some twenty-five years after Parmenides . He was the son of Teleutagoras, and the statement of Apollodorus that he had been adopted by Parmenides is only a misunderstanding of an expression of Plato's Sophist . He was, Plato further tells us, tall and of a graceful appearance. Like Parmenides Zeno played a part in the politics of his native city. Strabo, no doubt on the authority of Timaeus , ascribes to him some share of the credit for the good government of Elea , and says that he was a Pythagorean. This statement can easily be explained.

4. 10.12. Zeno Of Elea (495?-435? B.C.) 10.12. zeno of elea (495?435? B.C.) IRA zeno of elea was the first great doubter in mathematics. His paradoxes stumped mathematicians for millennia and provided enough aggravation to lead to numerous discoveries in the attempt to solve them. Zeno http://www.shu.edu/projects/reals/history/zeno.html

10.12. Zeno of Elea (495?-435? B.C.) IRA Zeno of Elea was the first great doubter in mathematics. His paradoxes stumped mathematicians for millennia and provided enough aggravation to lead to numerous discoveries in the attempt to solve them. Zeno was born in the Greek colony of Elea in southern Italy around 495 B.C. Very little is known about him. He was a student of the philosopher Parmenides and accompanied his teacher on a trip to Athens in 449 B.C. There he met a young Socrates and made enough of an impression to be included as a character in one of Plato's books Parmenides . On his return to Elea he became active in politics and eventually was arrested for taking part in a plot against the city's tyrant Nearchus. For his role in the conspiracy, he was tortured to death. Many stories have arisen about his interrogation. One anecdote claims that when his captors tried to force him to reveal the other conspirators, he named the tyrant's friends. Other stories state that he bit off his tongue and spit it at the tyrant or that he bit off the Nearchus' ear or nose. Zeno was a philosopher and logician, not a mathematician. He is credited by Aristotle with the invention of the dialectic, a form of debate in which one arguer supports a premise while another one attempts to reduce the idea to nonsense. This style relied heavily on the process of

5. Zeno Page 112 zeno of elea, son of Teleutagoras, was born early in thefifth century B.C. He was the pupil of Parmenides, and his relations with him were so intimate that Plato calls him Parmenides's son (Soph. http://history.hanover.edu/texts/presoc/zeno.htm

Zeno Commentary Arthur Fairbanks, ed. and trans. The First Philosophers of Greece (London: K. Paul, Trench, Trubner, 1898), Page 112-119. Hanover Historical Texts Project Scanned and proofread by Aaron Gulyas, May 1998. Proofread and pages added by Jonathan Perry, March 2001. Fairbanks's Introduction Simplicius's account of Zeno's arguments, including the translation of the Fragments Zeno's arguments as described by Aristotle Passages relating to Zeno in the Doxographists Fairbanks's Introduction [Page 112] Zeno of Elea, son of Teleutagoras, was born early in the-fifth century B.C. He was the pupil of Parmenides, and his relations with him were so intimate that Plato calls him Parmenides's son (Soph. 241 D). Strabo (vi. 1, 1) applies to him as well as to his master the name Pythagorean, and gives him the credit of advancing the cause of law and order in Elea. Several writers say that he taught in Athens for a while. There are numerous accounts of his capture as party to a conspiracy; these accounts differ widely from each other, and the only point of agreement between them has reference to his determination in shielding his fellow conspirators. We find reference to one book which he wrote in prose (Plato, Parm. 127 c), each section of which showed the absurdity of some element in the popular belief. Literature: Lohse, Halis 1794; Gerling, de Zenosin Paralogismis, Marburg 1825; Wellmann, Zenos Beweise, G.-Pr. Frkf. a. O. 1870; Raab, D. Zenonische Beweise, Schweinf. 1880; Schneider, Philol. xxxv. 1876; Tannery, Rev. Philos. Oct. 1885; Dunan, Les arguments de Zenon, Paris 1884; Brochard, Les arguments de Zenon, Paris 1888; Frontera, Etude sur les arguments de Zenon, Paris 1891

6. Zeno zeno of elea. by Kristen Riley. zeno of elea, born approximately 490485BC, was a follower of Parmenides, said to be his favorite. http://www.perseus.tufts.edu/GreekScience/Students/Kristen/Zeno1.html

Zeno of Elea by Kristen Riley Look at the comments on this paper. Zeno of Elea , born approximately 490-485 BC , was a follower of Parmenides, said to be his favorite. He published a book on philosophical puzzles and paradoxes, which is a defense of Parmenides' theory of oneness (Kirk, Raven, Schofield, p. 248) According to Aristotle, Zeno was the first to use dialectic, the method of interrogation and analysis used later by Socrates. His method was to challenge a person's beliefs by reducing them to absurdity or showing that they conflicted with other beliefs. Zeno is most well-known for his four paradoxes of motion, which argue against the possibility of motion as we see it. The Dichotomy , otherwise known as the Stadium, argues that a runner going from point A to point B will never be able to reach his goal because he must traverse an infinite distance. Similarly, the paradox of Achilles and the Tortoise shows that the faster Achilles can never catch up to the slower tortoise as long as the tortoise has had a head start of a certain distance, because Achilles can only reach as far as the last place the tortoise has been. These two paradoxes refute the assumption that space and time are infinitely divisible. The second pair of paradoxes, the

7. Zeno Of Elea (495?-435? B.C.) zeno of elea was the first great doubter in mathematics. His paradoxes stumped mathematicians for millennia and provided enough aggravation to lead to numerous discoveries in the attempt to solve them. http://pirate.shu.edu/projects/reals/history/zeno.html

Zeno of Elea (495?-435? B.C.) Zeno of Elea was the first great doubter in mathematics. His paradoxes stumped mathematicians for millennia and provided enough aggravation to lead to numerous discoveries in the attempt to solve them. Zeno was born in the Greek colony of Elea in southern Italy around 495 B.C. Very little is known about him. He was a student of the philosopher Parmenides and accompanied his teacher on a trip to Athens in 449 B.C. There he met a young Socrates and made enough of an impression to be included as a character in one of Plato's books Parmenides . On his return to Elea he became active in politics and eventually was arrested for taking part in a plot against the city's tyrant Nearchus. For his role in the conspiracy, he was tortured to death. Many stories have arisen about his interrogation. One anecdote claims that when his captors tried to force him to reveal the other conspirators, he named the tyrant's friends. Other stories state that he bit off his tongue and spit it at the tyrant or that he bit off the Nearchus' ear or nose. Zeno was a philosopher and logician, not a mathematician. He is credited by Aristotle with the invention of the dialectic, a form of debate in which one arguer supports a premise while another one attempts to reduce the idea to nonsense. This style relied heavily on the process of

8. Biography Of Zeno Of Elea Kristen Riley presents a paper on the philosopher known for introducing the dialectic. zeno of elea, born approximately 490485 BC, was a follower of Parmenides, said to be his favorite. http://www.andrews.edu/~calkins/math/biograph/199899/biozeno.htm

Back to the Table of Contents Biographies of Mathematicians-Zeno Zeno of Elea Very little is known about Zeno, the first great doubter of mathematics. Zeno was born in Elea, a Greek colony in southwestern Italy, around 495 B.C. In 449 B.C. Zeno accompanied his teacher, philosopher Parmenides, on a trip to Athens. Zeno taught in Athens for several years before returning to Elea and joining a conspiracy to overthrow the city's tyrant, Nearchus. For his part in this conspiracy, Zeno was tortured to death. Many stories are told about his interrogation. One claims that he named the tyrant's friends as conspirators. Others say he bit off his own tongue and spit it at the tyrant, or that he bit off the Nearchus' ear or nose. Zeno was a philosopher and logician, not a mathematician. He is credited by Aristotle with the invention of the dialectic, a form of debate. Zeno wrote only one known work called Epicheiremata , where he attacks the opponents of his teacher, Parmenides. His most famous achievement came from his paradoxes. With very little remaining from his only work, the only records of his work come from secondary sources, mainly Aristotle. Only eight have survived from around forty of these paradoxes. The purpose of these arguments was to defend his teacher's ideas. Parmenides believed that reality was one, immutable and unchanging. Motion, change, time, and plurality were all mere illusions. Many critics were attracted by this. Zeno's paradoxes attempted to show that holding the opposite position, that reality was many, was contradictory and absurd. Therefore, "the one" must be correct philosophy. Curiously, using Zeno's methods, his own position can also be shown to be contradictory.

9. Zeno_of_Elea zeno of elea. Born about 490 BC in Elea, Lucania Very little is knownof the life of zeno of elea. We certainly know that he was a http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Zeno_of_Elea.html

Zeno of Elea Born: about 490 BC in Elea, Lucania (now southern Italy) Died: about 425 BC in Elea, Lucania (now southern Italy) Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Very little is known of the life of Zeno of Elea . We certainly know that he was a philosopher, and he is said to have been the son of Teleutagoras. The main source of our knowledge of Zeno comes from the dialogue Parmenides written by Plato Zeno was a pupil and friend of the philosopher Parmenides and studied with him in Elea. The Eleatic School , one of the leading pre-Socratic schools of Greek philosophy, had been founded by Parmenides in Elea in southern Italy. His philosophy of monism claimed that the many things which appear to exist are merely a single eternal reality which he called Being. His principle was that "all is one" and that change or non-Being are impossible. Certainly Zeno was greatly influenced by the arguments of Parmenides and Plato tells us that the two philosophers visited Athens together in around 450 BC.

10. Zeno_of_Elea Read a biography of this early Greek philosopher whose thought influenced Socrates and Plato. zeno of elea. Born about 490 BC in Elea, Lucania (now southern Italy) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Zeno_of_Elea.html

Zeno of Elea Born: about 490 BC in Elea, Lucania (now southern Italy) Died: about 425 BC in Elea, Lucania (now southern Italy) Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Very little is known of the life of Zeno of Elea . We certainly know that he was a philosopher, and he is said to have been the son of Teleutagoras. The main source of our knowledge of Zeno comes from the dialogue Parmenides written by Plato Zeno was a pupil and friend of the philosopher Parmenides and studied with him in Elea. The Eleatic School , one of the leading pre-Socratic schools of Greek philosophy, had been founded by Parmenides in Elea in southern Italy. His philosophy of monism claimed that the many things which appear to exist are merely a single eternal reality which he called Being. His principle was that "all is one" and that change or non-Being are impossible. Certainly Zeno was greatly influenced by the arguments of Parmenides and Plato tells us that the two philosophers visited Athens together in around 450 BC.

11. References For Zeno_of_Elea References for zeno of elea. V Ya Komarova, The teachings of zeno of elea Anattempt to reconstruct a system of arguments (Russian) (Leningrad, 1988). http://www-gap.dcs.st-and.ac.uk/~history/References/Zeno_of_Elea.html

References for Zeno of Elea Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: R E Allen and D J Furley (eds.), Studies in Presocratic Philosophy (2 Vols.) (London, 1975). J Barnes, The Presocratic Philosophers (London, 1979). R Ferber, Zenons Paradoxien der Bewegung und die Struktur von Raum und Zeit, durchgesehene und um ein Nachwort erweiterte Auflage (Stuttgart, l995). A Grunbaum, Modern Science and Zeno's Paradoxes (London, 1968). W K C Guthrie, A History of Greek Philosophy (Vol. 2) (Cambridge, 1962). T L Heath, A history of Greek mathematics (Oxford, 1931). G S Kirk, J E Raven and M Schofield, The Presocratic Philosophers (Cambridge, 1983). V Ya Komarova, The teachings of Zeno of Elea : An attempt to reconstruct a system of arguments (Russian) (Leningrad, 1988). Diogenes Laertius, Lives of eminent philosophers (New York, 1925). H D P Lee, Zeno of Elea. A text with Translation and Commentary (Cambridge, 1936). B Russell

12. John Burnet: Early Greek Philosophy -- Contents a. zeno of elea b. Melissus of Samos 9. Leucippus of Miletus 10. Eclecticism andReaction a. Hippon of Samos b. Diogenes of Apollonia c. Archelaus of Athens. http://plato.evansville.edu/public/burnet/

Introduction The Life of Plato The Crito The Phaedo ... Credits and E XPLORING P LATO'S D IALOGUES A Virtual Learning Environment on the World-Wide Web On-line Scholarship Early Greek Philosophy John Burnet This text is a reprint of the 3rd edition of John Burnet's famous study of Presocratic philosophy, Early Greek Philosophy , originally published in 1920. The spelling has been modernized throughout. To make the text compatible with Internet search engines, Greek names have been Latinized to their common forms and Greek characters have been transliterated to Latin. A. Introduction B. Note on the Sources The Milesian School a. Thales b. Anaximander c. Anaximenes Science and Religion a. Pythagoras of Samos b. Xenophanes of Colophon i. Fragments ii. Discussion Heraclitus of Ephesus a. Fragments b. Discussion Parmenides of Elea a. The Poem b. Discussion c. Alcmaeon of Croton Empedocles of Acragas a. Fragments b. Discussion Anaxagoras of Clazomenae a. Fragments b. Discussion The Pythagoreans The Younger Eleatics a. Zeno of Elea b. Melissus of Samos Leucippus of Miletus Eclecticism and Reaction a. Hippon of Samos b.

13. Zeno's Paradoxes Discusses the paradoxes of zeno of elea, e.g., Achilles and the Tortoise; by Nick Huggett. http://plato.stanford.edu/entries/paradox-zeno/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z content revised APR Zeno's Paradoxes Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides 1. Background 2. The Paradoxes of Plurality 2.1 The Argument from Denseness 2.2 The Argument from Finite Size 2.3 The Argument from Complete Divisibility 3. The Paradoxes of Motion 3.1 The Dichotomy 3.2 Achilles and the Tortoise 3.3 The Arrow 3.4 The Stadium 4. Two more paradoxes 4.1 The Paradox of Place 4.2 The Grain of Millet 5. Zeno's Influence on Philosophy Further Reading Bibliography Other Internet Resources ... Related Entries 1. Background Before we look at the paradoxes themselves it will be useful to sketch some of their historical and logical significance. First, Zeno sought to defend Parmenides by attacking his critics. Parmenides rejected pluralism and the reality of any kind of change: for him all was one indivisible, unchanging reality, and any appearances to the contrary were illusions, to be dispelled by reason and revelation. Not surprisingly, this philosophy found many critics, who ridiculed the suggestion; after all it flies in the face of some our most basic beliefs about the world. (Interestingly, general relativity particularly quantum general relativity arguably provides a novel if novelty is As we read the arguments it is crucial to keep this method in mind. They are always directed towards a more-or-less specific target: the views of some person or school. We must bear in mind that the arguments are

14. Zeno Of Elea zeno of elea. Back to Last Page Glossary Index Related Terms. •paradox. Biography zeno of elea (c. 490 BCE) was a preSocratic http://atheism.about.com/library/glossary/general/bldef_zenoelea.htm

zfp=-1 About Agnosticism/Atheism Search in this topic on About on the Web in Products Web Hosting Agnosticism/Atheism with Austin Cline Your Guide to one of hundreds of sites Home Articles Forums ... Help zmhp('style="color:#fff"') Subjects ESSENTIALS Skepticism, Philosophy, Logic, Fallacies Church / State Separation Evolution vs. Creationism ... All articles on this topic Stay up-to-date! Subscribe to our newsletter. Advertising Free Credit Report Free Psychics Advertisement Zeno of Elea Back to Last Page Glossary Index Related Terms paradox Biography: Zeno of Elea (c. 490 BCE) was a pre-Socratic Greek philosopher and a pupil of Parmenides whose work has not survived directly, but we do know of it from the reports of others. Zeno is most famous for his paradoxes involving time and motion, using reductio ad absurdum to show that neither can be infinitely divisible. Stadium Paradox: Zeno argues that it is impossible to ever reach the finish line when running around a stadium. In order to reach the finish line, you must first reach the halfway point. But before you reach the halfway point, you must reach the halfway point to that - and so on, and so on to infinity. Thus, if space is infinitely divisible then any finite distance must consist of an infinite number of points. It is impossible to reach the end of an infinite series in a finite amount of time. Achilles Paradox: If Achilles races a tortoise and gives the tortoise a head start, then Achilles will never be able to overtake the tortoise. When Achilles reaches the point where the torotise started, the tortoise will have moved on. When Achilles reaches that point, the tortoise will have moved on farther - and so on indefinitely.

15. Xrefer - Zeno Of Elea (c. 470 BC) Article by E.L. Hussey from the Oxford Companion to Philosophy. Briefly reviews the kinds of paradoxes associated with Zeno. http://www.xrefer.com/entry/553917/

home library services showcase about select a topic search all art british history dictionaries encyclopedias health music philosophy place names quotations science shakespeare technology thesaurus Help xreferences heap, paradox of the The Oxford Companion to Philosophy infinite regress The Oxford Companion to Philosophy paradoxes The Oxford Companion to Philosophy Eleatics The Oxford Companion to Philosophy Hussey, E. L., Mr (E.L.H.) The Oxford Companion to Philosophy view all xreferences adjacent entries Zeitgeist Zen Zeno of Citium (334 - 262 BC) Zeno of Elea (c. 470 BC) Ziai, Hossein, Prof (H.Z.) Zoroastrianism About The Oxford Companion to Philosophy from Oxford University Press Zeno of Elea (c. 470 BC Fellow citizen and associate of Parmenides; admired by Plato as 'the Eleatic Palamedes' and by Aristotle as the inventor of philosophical dialectic. Zeno is not known to have advanced any positive views. He devised an arsenal of destructive arguments, directed against opponents of Parmenides. (Some seem to be ad hominem .) These exploit properties of the infinite, and use (perhaps for the first time) infinite regress as an argumentative device. Those for which there is evidence may be grouped as: (1) arguments against plurality (against the thesis 'There are many things'); (2) arguments against the possibility of motion; (3) others.

16. Zeno Of Elea, Greece, Ancient History zeno of elea (5th century BC). Philosopher and mathematician from Elea in Italy.He studied under Parmenides and followed his techer to Athens when he was 40. http://www.in2greece.com/english/historymyth/history/ancient/zeno_elea.htm

Zeno of Elea (5th century BC) Philosopher and mathematician from Elea in Italy. He studied under Parmenides and followed his techer to Athens when he was 40. There he became a teacher, and had several famous students, including Pericles and Callias.Later in life he was to return to Elea, where he is said to have tried to overthrow the tyrant Nearchus. The plan failed, and Zeno was tortured, but couragously gave no information. Zeno worked out a series of paradoxes to demonstrate his ideas, including the logical impossibility of motion and the illusority of the senses. In doing this, he was called the inventor of dialectical reasoning by Aristotle. His best known paradox is the one about Achilles and the turtle. According to Zenon, if the two are put to race and the turtle is given some distance to start before Achilles, there is no way Achilles can pass it as the turtle will move a little while Achilles is running. By moving forward the turtle is always ahead, and so it will be at least a tie. Webmistress V.E.K. Sandels

17. Encyclopædia Britannica zeno of elea Encyclopædia Britannica Article. MLA style zeno of elea. EncyclopædiaBritannica 2003 Encyclopædia Britannica Premium Service. http://www.britannica.com/eb/article?eu=80423

18. Encyclopædia Britannica paradoxes of Zeno statements made by the Greek philosopher zeno of elea, a 5thcentury-BCdisciple of Parmenides, a fellow Eleatic, designed to show that any http://www.britannica.com/search?query=Zeno&ct=

19. CATHOLIC ENCYCLOPEDIA Zeno Of Elea Home Catholic Encyclopedia Z zeno of elea. Join New Advent's Catholicmailing list! Start your FREE subscription today. zeno of elea. http://www.knight.org/advent/cathen/15756b.htm

20. Zeno Of Elea From FOLDOC zeno of elea. history of philosophy, biography follower of Parmenides whose workis known to us only through fragmentary reports from other philosophers. http://lgxserver.uniba.it/lei/foldop/foldoc.cgi?Zeno of Elea

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