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	Zeno's Paradoxes (Stanford Encyclopedia of Philosophy)
		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 (0 words)

	Zeno's Paradox, Aporia: Achilles, Tortoise
		Zeno Of Elea's Aporia: Achilles Can't Outrun The Tortoise (?)
		Zeno Of Elea's Paradox: Achilles Can't Outrun The Tortoise(?)
		: : Paradoxes of Zeno The Eleatic: Aporia of Achilles And The Tortoise.
	www.saliu.com /aporia.html (3104 words)

	NationMaster - Encyclopedia: Paradox (Site not responding. Last check: )
		Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context or language to lose their paradoxical quality.
		Zenos paradoxes are a set of paradoxes devised by Zeno of Elea 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.
		Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context or language to lose their paradox quality.
	www.nationmaster.com /encyclopedia/Paradox (2281 words)

	Essay: Describe and analyse Zeno's four paradoxes against motion - What do you think he is trying to do with them?
		Zeno's four paradoxes against motion are amongst his few surviving works and even these only survive via the writings of Aristotle and his Physics.
		Each of these paradoxes shall be in turn, described and analysed with strengths and weaknesses of the paradox explored.
		Following this, the paradoxes will then be brought together, to help us see what Zeno was trying to achieve overall-if he was trying to achieve anything at all.
	www.coursework.info /GCSE/Physics/Describe_and_analyse_Zenos_four_paradoxes_against_motion_L35896.html (261 words)

	Zeno's paradoxes - InfoSearchPoint.com (Site not responding. Last check: )
		Zeno's paradoxes are a set of paradoxes conceived by Zeno of Elea to support Parmenides's doctrine that all evidence of the senses is misleading, and particularly that there is no motion.
		Zeno's paradoxes may seem trivial today, but they were a major problem for ancient and medieval philosophers, who found no satisfactory solution until the 17th century, with the mathematical results on infinite sequences and calculus.
		This paradox is resolved by calculus as follows: in the limit, as the length of a moment approaches zero, the instantaneous rate of change or velocity (which is the quotient of distance over length of the moment) does not have to approach zero.
	www.infosearchpoint.com /display/Zenos_paradoxes (643 words)

	Zenos paradoxes (Site not responding. Last check: )
		Zeno's paradoxes are a set of paradoxes conceived by Zeno of Elea to support Parmenides 's doctrine that all evidence of the senses is misleading, and particularly that there is no motion.
		This paradox is resolved by calculus as follows: in the limit, as the length of a moment approaches zero, the instantaneous rate of change or velocity (whichis the quotient of distance over length of the moment) does not have to approach zero.
		Zeno's paradox however implies that if Zeno's method is followed toits logical extent, concepts such as velocity lose all meaning and there is no causal agent that is not similarly affected by theparadox that could enable the arrow to progress.
	www.therfcc.org /zenos-paradoxes-52379.html (1184 words)

	Zeno Of Elea \| Zeno was the son of a certain Teleutagoras and the pupil and friend of Parmenides. (Site not responding. Last check: )
		Zeno was the son of a certain Teleutagoras and the pupil and friend of Parmenides.
		Zeno of Elea was a Greek philosopher famous for posing so-called paradoxes which challenged mathematicians' view of the...
		Zeno was an Eleatic philosopher, a native of Elea (Velia) in Italy, son of Teleutagoras, and the favorite disciple of Parmenides.
	www.theflirtzone.com /Zeno/Zeno-of-elea.html (987 words)

	Hampden-Sydney College \| Philosophy (Site not responding. Last check: )
		Zeno of Elea was a disciple of Parmenides who sought to support with more potent arguments his mentor's unusual claim that there is no change.
		The most famous of these arguments are called "Zeno's Paradoxes." According to the paradox of the race, for example, a runner will never finish a race.
		Zeno concludes that the runner only appears to move and cross the finish line and that there really is no motion.
	www2.hsc.edu /academics/philosophy/zeno.html (150 words)

	Devlin's Angle: Soft Mathematics
		By the time they graduate, most mathematics students have heard of Zeno, he of the paradoxes of motion: Achilles and the tortoise, the arrow paradox, and so forth.
		The better known Zeno, of Zeno's paradoxes, was Zeno of Elea, in Magna Graecia, who lived about 450 B.C. That Zeno was a student of Parmenides, the founder of the Eleatic school of philosophy.
		Clearly, it's high time the other Zeno was given proper credit for his role in the development of modern logic.
	www.maa.org /devlin/devlin_june.html (1189 words)

	Zeno’s Paradox Deconstructed - Zen’s Paradox, Ze’s Paradox, and Z’s Paradox » Alpha Gecko
		Zeno’s paradox: motion is impossible, because to go from one place to another, you have to first go half way.
		Ze’s paradox: area is impossible because before you can add the last line segment to the far edge of a two dimensional shape, you have to add the line segment that’s half way there, and so on, so you can never get to the edge.
		Jumping straight from Z to Zeno, just as lines have something in their nature (length) that is not derived from the points on the line, space-time, or the four-dimensional space in which motion occurs, isn’t made up of a bunch of instants–an instant is just a description of a “position” in space-time.
	antone.geckotribe.com /mentalarc/2005/08/zenos-paradox-deconstructed-zens.php (851 words)

	Eric Gunnerson's C# Compendium : Zeno (Site not responding. Last check: )
		Annoyingly, I did remember that zeno had significant maritime interests - he had his home on the sea and had built significant moorings for his ocean-going vessel, and he also had a second residence on a nearby lake, also with a personal boat moored there.
		This was rare, rare enough that Zeno was known for his maritime holdings rather than his philosophical contributions.
		Zenos paradoxes are actually great examples of reasoning that leads you to deem something to be impossible.
	blogs.gotdotnet.com /ericgu/archive/2006/12/05/zeno.aspx (278 words)

	Zeno's Paradoxes: Interesting Thing of the Day
		Zeno, who lived from roughly 490 B.C. to 430 B.C., was a student of Parmenides, founder of a group of thinkers known as the Eleatics.
		Zeno’s Paradox of the Tortoise and Achilles at Platonic Realms
		Zeno and the Paradox of Motion in Reflections on Relativity
	itotd.com /articles/529/zenos-paradoxes (0 words)

	Modernity of Zeno’s Paradoxes :: Strange Paths
		The paradoxes thus appear at a deeper level, from the comparison between the phenomenon of movement and its disappearance implied by a thorough analysis of its model - either it being continuous (dichotomy paradox) or discontinuous (arrow paradox) -.
		In a discrete model (arrow paradox), Zeno’s argument is even stronger, and we can find a similar formulation of the argument in loop quantum gravity on the basis that time, being a pure gauge variable, is fundamentally nonexistent.
		Based on the Zeno Paradox alone would show that it is not and this is how we are able to move.
	strangepaths.com /modernity-of-zenos-paradoxes/2007/01/16/en (1684 words)

	Zeno’s Arrow Paradox « The truth makes me fret.
		In this paradox, Zeno argues that an arrow in flight is always at rest.
		Zeno’s reasoning, however, is fallacious, when he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
		I can’t imagine how Zeno could salvage his paradox once it is allowed that time is infinitely divisible (of course, this itself he thinks is paradoxical, as he tries to show in his other paradoxes).
	aeolist.wordpress.com /2007/01/13/zenos-arrow-paradox (1138 words)

	Alanyzer: The Kalam Argument, Zeno's Paradoxes, and Omniscience
		A second response to Zeno's paradoxes, and the one I favor, is the one proposed by Aristotle.
		Although it wasn't specifically addressed in your post, one thing that perplexes me about people using Zeno's paradox to argue for the possibility of traversing an infinite, besides the fact that it begs the question, is that Zeno himself didn't argue that way.
		Zeno basically argued: There is an infinite amount of points between any two points; it is not possible to traverse an infinite; therefore, motion is illusory.
	www.alanrhoda.net /blog/2006/04/kalam-argument-zenos-paradoxes-and.html (2131 words)

	The Unending History of the Infinite
		Paradoxes of the infinite have plagued thinkers from ancient times to the present.
		Zenos of Elea made great fun of the atomists by pointing out paradoxes that took several millennia to resolve.
		The paradoxes that were once on the fringe of mathematics now sit squarely the middle.
	descmath.com /diag/history.html (1142 words)

	myriaden: Solution to Zeno's Second Paradox
		Zeno’s Second Paradox purports to show that in a chase, the chaser can never catch the person or object being chased.
		In Zeno’s footrace on the other hand, Achilles and the tortoise make smaller and smaller strides, so that near the 2 km mark they are making infinitessimally small strides.
		The upshot of comparing these two descriptions of the race is that for Zeno’s Second Paradox to be true, both the pursuer and the pursued must be able to reduce their ‘stride length’ an infinite number of times.
	myriaden.blogspot.com /2006/03/solution-to-zenos-second-paradox.html (902 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 and the Paradox of Motion
		The greatest of the Eleatic philosophers was Parmenides (born c.
		Of the 40 arguments attributed to Zeno by later writers, the four most famous are on the subject of motion:
		This brings us to the last of Zeno's four main arguments on motion, "The Stadium", which has always been the most controversial, partly because the literal translation of its statement is somewhat uncertain. In this argument Zeno appears to be attacking the only remaining alternative to the unintelligible G
	www.mathpages.com /rr/s3-07/3-07.htm (263 words)

	Ephilosopher :: Puzzles and Paradoxes :: Zeno's Paradox Solved? (Site not responding. Last check: )
		Lynds says that the paradoxes arose because people assumed wrongly that objects in motion had determined positions at any instant in time, thus freezing the bodies motion static at that instant and enabling the impossible situation of the paradoxes to be derived.
		The paradox is quite natural when you imagine the possibility of examining the state of a system as it exists at a single instant, but Einstein showed us long ago that simultaneity was relative to the velocities of the bodies involved in the system.
		The only way Zeno's paradox could really be a problem is if people thought that the progression from one instant to the next was really the nature of time.
	www.ephilosopher.com /phpBB_14-action-viewtopic-topic-329-forum-14-start-0.html (3918 words)

	PhilSci Archive - Zeno's Paradoxes: A Timely Solution
		Zeno of Elea's motion and infinity paradoxes, excluding the Stadium, are stated (1), commented on (2), and their historical proposed solutions then discussed (3).
		Their correct solution, based on recent conclusions in physics associated with time and classical and quantum mechanics, and in particular, of there being a necessary trade off of all precisely determined physical values at a time (including relative position), for their continuity through time, is then explained (4).
		Jones, C, V. Zeno's paradoxes and the first foundations of mathematics (Spanish), Mathesis 3 (1), (1987).
	philsci-archive.pitt.edu /archive/00001197 (0 words)

	Quantonic/quantum examination of Zeno of Elea's four paradoxes.
		In Quantonics, we choose to view Zeno's first paradox as his own derision of classicists' assumptions of both analytic motion stoppability and analytic temporal stoppability in a single context.
		An implication of our quantum-enhanced version of Zeno's view, assuming we are correct, is that he intuited macroscopic quantum uncertainty of any moving entity's position and momentum.
		Ponder how this paradox's assumptions outright deny quantum reality's probability distributions of 'place' and 'motion.' You may be able to QTM relate this putative as akin Aristotle's excluded-middle.
	www.quantonics.com /Zenos_Paradice.html (1926 words)

	Dropzone.com Skydive Forums: Community: The Bonfire: Math problem: Zeno's paradox
		Zeno was a famous mathematician from Elea, a Greek city on the Italian coast.
		Zeno was well known for posing puzzling paradoxes that seemed impossible to resolve.
		Zeno argued that in such a situation, it would take Achilles an infinite amount of time to catch the tortoise.
	www.dropzone.com /forum/Community_C7/The_Bonfire_F1/Math_problem:_Zenos_paradox_P845655 (1302 words)

	Zeno’s paradoxes
		A series of paradoxes posed by the philosopher Zeno of Elea (c.490-c.425 B.C.).
		None of his writings survive but he is known to have written a book, which Proclus says contained 40 paradoxes.
		Although they have often been dismissed as logical nonsense, many attempts have also been made to dispose of them by means of mathematical theorems, such as the theory of convergent series or the theory of sets.
	www.daviddarling.info /encyclopedia/Z/Zenos_paradoxes.html (323 words)

	Eric Gunnerson's C# Compendium : Zeno (Site not responding. Last check: )
		Annoyingly, I did remember that zeno had significant maritime interests - he had his home on the sea and had built significant moorings for his ocean-going vessel, and he also had a second residence on a nearby lake, also with a personal boat moored there.
		This was rare, rare enough that Zeno was known for his maritime holdings rather than his philosophical contributions.
		Zenos paradoxes are actually great examples of reasoning that leads you to deem something to be impossible.
	blogs.msdn.com /ericgu/archive/2006/12/05/zeno.aspx (278 words)

	Ephilosopher :: Puzzles and Paradoxes :: Zeno's Paradox Solved? (Site not responding. Last check: )
		To resolve Zeno's paradoxes by claiming that the measurement of space and time is a meaningless act is indeed to a use a sledge hammer to crack a nut but in the process you destroy the table, chairs and all the crockery in the room.
		As this relates to Zeno's Paradox is the question of what can truly be meant by measurement of distance and divisibility between two points of reference in space.
		Zeno's body making progress across empty space therefore cannot be made infinite, as a body cannot be infinitely divided.
	www.ephilosopher.com /phpBB_14-action-viewtopic-topic-329-start-15.html (2385 words)

	Hopes Only: Second Zeno's Paradox (Site not responding. Last check: )
		Due to this second paradox, he will never be able to catch the bus.
		This paradox is similar to the first one, but in this case hommer is moving and the bus is stopped.
		Effectively, when hommer has walked the half of the way since him to the bus, then he is to walk a new half of the way.
	troublehouston.blogspot.com /2007/03/second-zenos-paradox.html (387 words)

	The NSTP Theoretical Resolution of Zeno's Paradoxes Computers Pageranklist.net (Site not responding. Last check: )
		Zeno of Elea's (b.490 BC) arguments against motion precipitated a crisis in Greek thought.
		Zeno's paradoxes, except the last two, are not a matter of language or symbolic theories (e.g.
		The first two of Zeno's paradoxes are out of the misbelief that space exists in the ontological sense, i.e.
	www.pageranklist.net /searchengine_news/The_NSTP_Theoretical_Resolution_of_Zenos_Paradoxe.html (768 words)

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