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.) 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. 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 zeno of elea. by Kristen Riley. Look at the comments on this paper. zeno of elea, born approximately 490485 BC, 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

4. 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 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

5. Zeno Page 112 zeno of elea, son of Teleutagoras, was born early in thefifth the credit of advancing the cause of law and order in Elea. Several writers say 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 Of Elea --  Encyclopædia Britannica MLA style " zeno of elea." Encyclopædia Britannica. 2004 APA style zeno of elea. Encyclopædia Britannica. Retrieved May 16, 2004, from Encyclopædia Britannica Premium Service http://www.britannica.com/eb/article?eu=80423

7. Biography Of Zeno Of Elea Biographies of MathematiciansZeno. zeno of elea. Very little is known about Zeno, the first great doubter of mathematics. Zeno was born in Elea, a Greek colony 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.

8. Zeno Of Elea - Famous Mathematicians Pictures, Posters, Gifts Items, Note Cards, zeno of elea, picture, portrait, Zeno's Paradoxes, paradox, Archilles, tortoise, mathematician gifts, Famous mathematician pictures, mathematicians pictures, note cards, mathematician greeting Pythagoras of Samos . zeno of elea . zeno of elea conceived a number of "paradoxes". Zeno conceived these not as mathematical amusement, but as an attempt to http://www.mathematicianspictures.com/Mathematicians/Zeno.htm

Home about The Mathematicians Gift Shop about us ... Cantor Zeno Gift items available include: Zeno Poster All items carry our Total Satisfaction Guarantee . If you are dissatisfied with any item you purchase, simply advise us and return it within 15 days for replacement or refund. Zeno of Elea c. 495 - 430 B.C.E. Zeno of Elea One of Zeno's most famous paradoxes posited a race between the popular Greek hero Achilles, and a tortoise. Zeno set out to logically show that, with the tortoise given a head start, Achilles, speedy as he might be, could, in fact, never overtake the plodding reptile.

9. 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

10. Zeno_of_Elea zeno of elea. Born about 490 BC in Elea, Lucania Very little is known of 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.

11. References For Zeno_of_Elea References for zeno of elea. V Ya Komarova, The teachings of zeno of elea An attempt 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. 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://www.iep.utm.edu/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

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 This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change MAR 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 ... 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

14. Zeno_of_Elea Biography of zeno of elea (490BC425BC) zeno of elea. Born about 490 BC in Elea, Lucania (now southern Italy) little is known of the life of zeno of elea. We certainly know that he 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.

15. Zeno Of Elea - Wikipedia, The Free Encyclopedia Other languages Deutsch Español Français ? Nederlands ? Slovenšcina. zeno of elea. From Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Zeno_of_Elea

Zeno of Elea From Wikipedia, the free encyclopedia. Zeno of Elea (circa 495 BC - circa 430 BC ) was an ancient Greek philosopher of Southern Italy , a member of the Eleatic School founded by Parmenides . He is best known for formulating a number of paradoxes based on Eleatic beliefs of the impossibility of motion . They are known to this day as Zeno's paradoxes Views Article Discussion Edit History Personal tools Log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Special pages Other languages Deutsch Nederlands This page was last modified 02:51, 26 May 2004. All text is available under the terms of the GNU Free Documentation License (see for details). About Wikipedia

16. Zeno Of Elea Search. Agnosticism / Atheism zeno of elea. Back to Last Page Glossary Index . Related Terms. • paradox. Biography zeno of elea http://atheism.about.com/library/glossary/general/bldef_zenoelea.htm

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17. Zeno Of Elea --  Encyclopædia Britannica Visit Britannica Store, Encyclopædia Britannica, zeno of elea Encyclopædia Britannica Article. MLA style zeno of elea. Encyclopædia Britannica. 2004. http://www.britannica.com/eb/article?eu=80423&tocid=0&query=zeno of elea

18. Plato.evansville.edu/public/burnet/ch8a.htm TMTh zeno of eleaMATHEMATICIAN. zeno of elea (fl. 490 430 BC) Life Zeno was born in Elea, in Magna Graecia (south Italy). He was a disciple of http://plato.evansville.edu/public/burnet/ch8a.htm

19. Philosophical Dictionary: Xenocrates-Zombie thinkers. Parmenides and Zeno studied with Xenophanes in Sicily before establishing their own school at Elea. zeno of elea (c. 450 BCE). Follower http://www.philosophypages.com/dy/x.htm

Philosophy Pages F A Q Dictionary ... Locke Xenocrates 396-314 BCE Greek philosopher who defended the philosophy of Plato against the criticism of Aristotle . As head of the Academy in the fourth century, Xenocrates held forth the quasi- Pythagorean view that the Platonic Forms , including even the individual human soul , are all numbers. Also see SEP ColE BIO ,and ELC Xenophanes of Colophon 570-475 BCE Presocratic philosopher. He criticized the militarism and anthropomorphism of traditional Greek morality and religion, arguing that fundamental truth about the world is difficult to achieve. His opposition to conventional notions earned him the respect of later, more completely skeptical thinkers. Parmenides and Zeno studied with Xenophanes in Sicily before establishing their own school at Elea. Recommended Reading: Xenophanes of Colophon: Fragments at Amazon.com Also see SEP IEP ColE BIO , and ELC Xenophon 430-350 B.C.E. Greek historian. Xenophon's dialogues, especially the Apologhma Apology ) and Memorabilia , offer an account of the philosophical career of Socrates through more practical, worldly eyes than do the dialogues of

20. 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

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