1. 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.

2. 10.12. Zeno Of Elea (495?-435? B.C.) Reviews the legacy and what is known of the life of this Presocratic thinker.Summarizes Zeno s four most famous paradoxes. 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

3. Zeno A short paper by Kristen Riley reviewing Zeno s four paradoxes of motion andtheir import for modern thinkers. 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

4. 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 ... Z This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters last substantive content change MAR The Encyclopedia Now Needs Your Support Please Read How You Can Help Keep the Encyclopedia Free 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 ... 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 of 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

5. Zeno Of Elea [Internet Encyclopedia Of Philosophy] Zeno was an Eleatic philosopher, a native of Elea (Velia) in Italy, son ofTeleutagoras, and the favorite disciple of Parmenides. He was born about 488 BCE. http://www.iep.utm.edu/z/zenoelea.htm

Zeno of Elea 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 Aristotle said about him in Physics , Book 6, chapter 9.

6. Zeno Of Elea [Internet Encyclopedia Of Philosophy] Life and work of the Eleatic philosopher, from the Internet Encyclopedia of Philosophy. http://www.utm.edu/research/iep/z/zenoelea.htm

Zeno of Elea 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 Aristotle said about him in Physics , Book 6, chapter 9.

7. Zeno Of Elea [Internet Encyclopedia Of Philosophy] zeno of elea. Zeno was an Eleatic philosopher, a native of Elea (Velia) in Italy, son of Teleutagoras, and the favorite disciple of Parmenides. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Zeno_of_Elea Biography of zeno of elea (490BC425BC) Zeno returned to Elea after the visitto Athens and Diogenes Laertius claims that he met his death in a heroic 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 Version for printing 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.

9. CATHOLIC ENCYCLOPEDIA Zeno Of Elea zeno of elea. Greek philosopher, born at Elea, about 490 B.C. At his birthplace Xenophanes and Parmenides had established the metaphysical school http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Zeno_of_Elea Portraits Portraits of zeno of elea. zeno of elea. JOC/EFR August 2001. The URL of thispage is, © Copyright information http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Zeno_of_Elea.html

Zeno of Elea JOC/EFR August 2005 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Zeno_of_Elea.html

11. 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. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Zeno Of Elea Glossary of Religion and Philosophy Short Biography of zeno of elea http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Zeno Zeno's arguments as described by Aristotle Passages relating to Zeno in the Doxographists. Fairbanks's Introduction Page 112 zeno of elea http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Zeno Page 112 zeno of elea, son of Teleutagoras, was born early in thefifth centuryBC He was the pupil of Parmenides, and his relations with him were so 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

15. Zeno's Paradoxes Discusses the paradoxes of zeno of elea, e.g., Achilles and the Tortoise; by Nick Huggett. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. Presocratic Philosophers Historical information on the philosophers preceding Socrates. The foundation of the Ionian school in Miletos is considered the startingpoint of http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Zeno Of Elea - Wikipedia, The Free Encyclopedia zeno of elea should not be confused with Zeno of Citium. zeno of elea GregoryVlastos in The Encyclopedia of Philosophy (Paul Edwards, ed. http://en.wikipedia.org/wiki/Zeno_of_Elea

Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Zeno of Elea From Wikipedia, the free encyclopedia. Zeno of Elea should not be confused with Zeno of Citium Zeno of Elea IPA :zɛnoʊ, ɛlɛɑː)(circa 490 BC ? – circa 430 BC ?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides . Called by Aristotle the inventor of the dialectic , he is best known for his paradoxes 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... Bertrand Russell The Principles of Mathematics Contents Life Works Zeno's paradoxes Two other paradoxes as given by Aristotle ... edit 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 of Zeno is the dialogue of

18. Zeno's Race Course, Part 1 The Paradox. Zeno argues that it is impossible for a runner to traverse a race course. His reason is that http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. User TalkZeno Of Elea - Wikipedia, The Free Encyclopedia zeno of elea 0328, 21 July 2005 (UTC) it s taking you quite a while to zeno of elea 1234, 21 July 2005 (UTC). Zeno, that same jihadist guy tries http://en.wikipedia.org/wiki/User_talk:Zeno_of_Elea

20. BBC - Radio 4 - In Our Time In Our Time explores the history of ideas, particularly in philosophy, science, literature, culture and religion http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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