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Topic: Zeno of Elea

	Zeno of Elea - Wikipedia, the free encyclopedia
		Zeno of Elea should not be confused with Zeno of Citium.
		Zeno's arguments are perhaps the first examples of a method of proof called Reductio ad absurdum, also known as proof by contradiction.
		Zeno of Elea Gregory Vlastos in The Encyclopedia of Philosophy (Paul Edwards, ed.), (New York, 1967).
	en.wikipedia.org /wiki/Zeno_of_Elea (898 words)

	ZENO OF ELEA - LoveToKnow Article on ZENO OF ELEA (Site not responding. Last check: 2007-10-07)
		He is said to have been concerned in a plot against a tyrant, and on its detection to have borne with exemplary constancy the tortures to which he was subjected; but authorities differ both as to the name and the residence of the tyrant and as to the circumstances and the issue of the enterprise.
		In reply to those who thought that Parmenidess theory of the existence of the One involved inconsistencies and absurdities, Zeno tried to show that the assumption of the existence of the Many, that is to say, a plurality of things in time and space, carried with it inconsistencies and absurdities grosser and more numerous.
		Of the paradoxes used by Zeno to discredit the belief in plurality and motion, eight survive in the writings of Aristotle and Simplicius.
	64.1911encyclopedia.org /Z/ZE/ZENO_OF_ELEA.htm (1870 words)

	Zeno of Elea [Internet Encyclopedia of Philosophy]
		Zeno was an Eleatic philosopher, a native of Elea (Velia) in Italy, son of Teleutagoras, and the favorite disciple of Parmenides.
		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.
		Zeno showed that the common sense notion of reality leads to consequences at least as paradoxical as his master's.
	www.iep.utm.edu /z/zenoelea.htm (2118 words)

	Zeno of Elea (Site not responding. Last check: 2007-10-07)
		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.
		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.
	cs.wwc.edu /~aabyan/Math/Book/book/node32.html (296 words)

	Encyclopedia Uselessia -- Zeno of Elea's Paradoxes
		Zeno of Elea is famous for his paradoxes.
		Zeno's paradoxes are a set of paradoxes devised to support Parmenides' doctrine that "all is one" and that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.
		Zeno's paradox however implies that if Zeno's method is followed to its logical extent, concepts such as velocity lose all meaning and there is no causal agent that is not similarly affected by the paradox that could enable the arrow to progress.
	www.greatplay.net /uselessia/articles/zeno%20paradoxes.html (805 words)

	Math Forum: Zeno's Paradox
		The great Greek philosopher Zeno of Elea (born sometime between 495 and 480 B.C.) proposed four paradoxes in an effort to challenge the accepted notions of space and time that he encountered in various philosophical circles.
		Zeno's paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics.
		Zeno's first paradox attacks the notion held by many philosophers of his day that space was infinitely divisible, and that motion was therefore continuous.
	mathforum.org /isaac/problems/zeno1.html (272 words)

	Zeno of Elea (495?-435? B.C.)
		Zeno was born in the Greek colony of Elea in southern Italy around 495 B.C. Very little is known about him.
		Zeno was a philosopher and logician, not a mathematician.
		Zeno's paradoxes attempted to show that holding the opposite position, that reality was many, was contradictory and absurd.
	www.phy.hr /~matko/zenon/zeno.html (793 words)

	Zeno's Paradoxes
		Second, from this Zeno argues that it follows that they do not exist at all; since the result of joining (or removing) a sizeless object to anything is no change at all, he concludes that the thing added (or removed) is literally nothing.
		Thus we answer Zeno as follows: the argument assumed that the size of the body was a sum of the sizes of the point parts, but that is not the case; according to modern mathematics, a line is an uncountable infinity of points plus a distance function.
		Zeno abolishes motion, saying "What is in motion moves neither in the place it is nor in one in which it is not".
	plato.stanford.edu /entries/paradox-zeno (10026 words)

	Zeno of Elea
		Zeno devoted all his energies to explain and develop the philosophical system of Parmenides.
		Zeno argued that Achilles can never catch up with the tortoise no matter how fast he runs and no matter how long the race goes on.
		All the arguments which Zeno uses against multiplicity and motion are in reality merely variations of one argument, which applies equally to space or time.
	personal.ecu.edu /mccartyr/ancient/athens/ZenoElea.htm (947 words)

	Zeno (Site not responding. Last check: 2007-10-07)
		Zeno of Elea, born approximately 490-485 BC, was a follower of Parmenides, said to be his favorite.
		Zeno is most well-known for his four paradoxes of motion, which argue against the possibility of motion as we see it.
		Each of Zeno's paradoxes can be explained in some way by more modern concepts of thought and motion, and they have been further explained and analysed from Aristotle's time to the modern day.
	www.perseus.tufts.edu /GreekScience/Students/Kristen/Zeno1.html (560 words)

	TMTh:: ZENO OF ELEA
		Zeno was born in Elea, in Magna Graecia (south Italy).
		Zeno taught that there is no movement, and he proved it by 4 arguments, which are quoted by Aristotle in his "Physics".
		Zeno overturned the whole structure of mathematics, for in his view, all human knowledge was based on an unprovable hypothesis, and the same applied to the science of mathematics.
	www.tmth.edu.gr /en/aet/1/99.html (321 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		Zeno's paradoxes have been a source of inspiration and bewilderment for almost two and a half thousand years.
		Of all Zeno's paradoxes, the most renown, or at least the most familiar, are his paradoxes of motion.
		According to Plato, Zeno confesses, in response to the dogged questioning of the latter's young Socrates, to have composed in his collection of paradoxes of plurality simply in defense of Parmenides, who had been coming under heavy ridicule for his position regarding the one.
	cs.wwc.edu /~aabyan/CII/TEMP/Zeno2.html (4021 words)

	Zeno's race course, part 1
		Zeno argues that it is impossible for a runner to traverse a race course.
		Since Zeno was generalizing about all motion, his conclusion was either (a) that no motion could be completed or (b) that no motion could be begun.
		Aristotle assumed that (b) was what Zeno intended (and he based his refutation on that assumption).
	faculty.washington.edu /smcohen/320/zeno1.htm (943 words)

	SparkNotes: Presocratics: The Eleatics: Zeno of Elea and Melissus of Samos
		The movement he founded is called the school of Elea, and its members are referred to as the Eleatics.
		Zeno of Elea was Parmenides' most eminent student and was also probably his lover.
		Zeno did not view these arguments as paradoxes, since he believed that the premises he was trying to undermine (for instance, the existence of motion) were false.
	www.sparknotes.com /philosophy/presocratics/section7.rhtml (462 words)

	The paradox ideas of Zeno of Elea, is motion an illusion or even impossible?
		The Paradoxa of Zeno of Elea are an example of ancient Greek abstract reasoning that is even in contradiction to observation.
		Zeno bases both the dichotomy paradox and the attack on simple pluralism on the fact that once a thing is divisible, then it is infinitely divisible.
		Zeno thinks that we cannot have different results that depend on the observer and thus any movement is an illusion.
	www.mlahanas.de /Greeks/Paradoxa.htm (2867 words)

	Zeno
		Zeno's problem demands some consideration; if all being is in some place, evidently there must be a place of this place, and so on indefinitely.
		Zeno presents four arguments concerning motion which involve puzzles to be solved, and the first of these shows that motion does not exist because the moving body must go half the distance before it goes the whole distance; of this we have spoken before (Phys.
		Zeno the Eleatic, a dialectician equal to the other Zeno, says that the earth does not move, and that no space is void of content.
	history.hanover.edu /texts/presoc/zeno.htm (1738 words)

	Zeno's Paradoxes
		Zeno of Elea was an ancient Greek (born around 490 B.C.) who lived in what is now southern Italy.
		Zeno's writings have not survived, so his paradoxes are known to us chiefly through Aristotle's criticisms of them.
		Zeno also argued against the notion that there is a plurality of objects, for the common sense world of spatially extended objects is supposedly an illusion.
	members.aol.com /kiekeben/zeno.html (1709 words)

	Zeno of Elea (Site not responding. Last check: 2007-10-07)
		Zeno: Well Drew, I was born in the Greek Colony of Elea which is situated in southern Italy.
		Zeno: Well even up to today people are trying to figure out ways to counter my paradoxes.
		Zeno: I didn't say it made sense but if you do the problem logically then you come to a conclusion that tells us we cannot move.
	www.3villagecsd.k12.ny.us /wmhs/Departments/Math/OBrien/zeno2.html (490 words)

	Zeno Potpourri (Site not responding. Last check: 2007-10-07)
		It is known that Zeno lived in the fifth century B.C., and that he was a devoted disciple of Parmenides.
		Zeno proposed a series of paradoxes designed to show the absurdity of the views of those who made fun of Parmenides.
		Zeno's paradoxes have been the object of extensive historical research, especially in the last hundred years.
	www.cs.cornell.edu /Info/Projects/zeno/Potpourri/Welcome.html (227 words)

	MSN Encarta - Search Results - Zeno of Elea
		Zeno of Elea (fl., 5th century bc), Greek mathematician and philosopher of the Eleatic school, known for his philosophical paradoxes.
		Zeno of Elea, a disciple of Parmenides, tried to prove the unity of being by arguing that the belief in the reality of change, diversity, and motion...
		In a famous example from Zeno of Elea, the warrior...
	uk.encarta.msn.com /Zeno_of_Elea.html (112 words)

	Zeno of Elea - Greek Philosopher - Crystalinks (Site not responding. Last check: 2007-10-07)
		Zeno of Elea - Greek Philosopher - Crystalinks
		Although written nearly a century after Zeno's death, the primary source of biographical information of Zeno is the dialogue of Plato called the Parmenides.
		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".
	www.crystalinks.com /zenoelea.html (317 words)

	Zeno of Cittium: founder of Stoicism.
		The school was founded by Zeno of Cittium in Cyprus, one of antiquity's boldest yet least known thinkers.
		He is not to be confused with Zeno of Elea, who earned far greater fame from a handful of paradoxes, designed to prove true by logic what everyone, from experience, knows to be false: that motion and change are impossible.
		Zeno seems to have been quite old when he himself began teaching to small groups, in a painted colonnade on the Athenian agora known as the Stoa Poikile.
	members.aol.com /Heraklit1/zeno.htm (1251 words)

	Zeno of Elea on Encyclopedia.com (Site not responding. Last check: 2007-10-07)
		ZENO OF ELEA [Zeno of Elea], c.490-c.430 BC, Greek philosopher of the Eleatic school.
		He undertook to support in his only known work, fragments of which are extant, the doctrine of Parmenides by demonstrating that motion and multiplicity are logically impossible.
		Why mathematical solutions of Zeno's paradoxes miss the point: Zeno's one and many relation and Parmenides' prohibition.
	www.encyclopedia.com /html/z/zenoe1lea.asp (433 words)

	Zeno... (Site not responding. Last check: 2007-10-07)
		Zeno of Elea was a Greek philosopher (c.
		The Zeno critical fluid experiment requires such a stepwise approach to a point in thermodynamic space so that the sample gets closer and closer to the critical temperature T subscript C without ever reaching it or going below it.
		The goal of the Zeno experiment is to measure the decay rates of density fluctuations in xenon 100 times closer to the critical point than is possible on Earth.
	home.earthlink.net /~fjlawson/why_zeno.htm (643 words)

	Zeno of Elea [Internet Encyclopedia of Philosophy]
		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.
		Both groups of Zeno's arguments, those against multiplicity and those against motion, are variations of one argument that applies equally to space or time.
		The concepts of space, time, and motion have to be radically changed, and so do the mathematical concepts of line, number, measure, and sum of a series.
	www.phy.hr /~matko/zenon/zenoelea.html (2077 words)

	Zeno Of Elea -- Encyclopædia Britannica
		He is especially known for his paradoxes that contributed to the development of logical and mathematical rigour and that were insoluble until the development of precise concepts of continuity and infinity.
		The position of the other great pupil of Parmenides, Zeno of Elea, was clearly stated in the first part of Plato's dialogue Parmenides.
		There Zeno himself accepted the definition of Socrates, according to which he did not really propose a philosophy different from that of Parmenides but only tried to support it by the demonstration that the difficulties resulting from the...
	www.britannica.com /eb/article-9078321 (745 words)

	Biography of Zeno
		Zeno was born in Elea, a Greek colony in southwestern Italy, around 495
		Zeno taught in Athens for several years before returning to Elea and joining a conspiracy to overthrow the city's tyrant, Nearchus.
		Zeno wrote only one known work called Epicheiremata, where he attacks the opponents of his teacher, Parmenides.
	www.andrews.edu /~calkins/math/biograph/biozeno.htm (692 words)

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