Zeno's paradoxes - Wikipedia Zeno asks us to imagine that Achilles, the Greek hero, is in a race with a tortoise. You need to step outside the frame to spot the problem. Can we prove Zeno's paradox wrong? - Quora To fully solve any of the paradoxes, however, one needs to show what is wrong with the argument, not just the conclusions. light - Is Olbers' Paradox Nonsense? - Astronomy Stack ... Loosely paraphrased, the Arrow paradox talks about how taking an analog, continuous motion (the arrow flying towards the target, and in this case a man falling out of a tree) becomes impossible if you break down . I show that this ob-jection is exactly what it takes for Zeno to be right. First published Tue Apr 30, 2002; substantive revision Fri Oct 15, 2010. Paradox of the Grain of Millet Aristotle's refutation: Zeno is wrong in saying that there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. I want to give a big thanks to Mr. Schorpen! His velocity is much faster than the turtle. Yet, we can easily move from point A to B - we do it everyday. The Paradoxes of Zeno of Elea | Daily Philosophy You need to step outside the frame to spot the problem. What is mathematical paradox? Before that it has to travel half of half of that distance and so on. . It has inspired many writers and thinkers through the ages, notably Lewis Carroll (see Carroll's Paradox) and Douglas Hofstadter . It even casually acknowledges that Zeno's paradox has been resolved, but then talks about how, because he feels like it, it applies anyway. Bruce Charlton's Notions: Explaining Zeno's paradoxes The ancient paradox. (PDF) Why Mathematical Solutions of Zeno's Paradoxes Miss ... It's a paradox. Commentator after commentator have struggled to find some reading of paradox that is worthy of the acumen of Zeno. Zeno's Paradox - Science Government and Space Theories Saying that calculus can't be used because space is discontinuous is ludicrous, because the problem is abstract, not physical (it would be like saying that an area of a circle can't be exactly pi*r^2 because space is discontinuous). Zenos paradox seems valid but is obviously wrong Aristotles account of the paradox, is the first sustained thinking on this paradox that has come down to us and still bears thinking on, even today. In fact, the interval of time between successive steps is continuously decreased in the Zeno's paradox so that your timeline ends up being bounded. The concept of . The Greek philosopher Zeno wrote a book of paradoxes nearly 2,500 years ago. And hence, Zeno states, motion is impossible: Zeno's paradox. The Tortoise has a head start on Achilles—let's say a head start of distance 1. Zeno's Paradox. The statement of the "paradox" works by invoking the idea of "motion" while only ever considering instants of time, and thus not considering motion as a concept that applies with respect to change over time. It might seem counterintuitive, but pure mathematics alone cannot provide a satisfactory solution to the paradox. Are there any mathematical solutions to Zeno's paradoxes? Zeno of Elea, 5th c. B.C.E. Here is the short description of the paradox from Wikipedia (image source): > In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. If you follow Zeno's argument, you will prove Zeno's argument. It would be good to make a list. wrong according to Zangari. The Greek philosopher Zeno wrote a book of paradoxes nearly 2500 years ago. 5th century BC Greek philosopher, Zeno of Elea, knew that all along. He was a supporter of Parmenides's theory of one. Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. Reductionism is wrong and I tend to agree with McGilChrist, but Zeno's paradoxes are not the best example to prove that. does indeed converge to 1, so that you wind up covering the entire needed distance if you add an infinite number of terms. That is, it will never exceed some given number (some given limit). The classical response to Zeno's paradoxes goes like this: 'Motion cannot properly be defined within an instant. Consider a moving arrow as it would appear at an instant in time, and consider an arrow that is standing still as it would appear at that instant. This suggestion goes back at least to Minkowski's famous lecture of "staircase wit" (see Section 1.7). The level of wrongness here is pretty astounding. Man, if he got paid for this I want his job. There a lot of experiments that suggest that reductionism is wrong, but materialist scientist want to hide under the rug. Here we'll take just one of Zeno's paradoxes, the famous paradox of Achilles and the tortoise. Zeno is famous for his paradoxes that debunked Pythagoras's pluralism. With an infinite number of steps required to get there, clearly she can never complete the journey. We all know Achilles can overtake the tortoise. Zeno's argument rests on the presumption that Achilles must first reach the point where the tortoise started, by which time the tortoise will have moved ahead, even if but a small distance, to another point; by the time Achilles traverses the distance to this latter point, the tortoise will have moved ahead to another, It is usually assumed, based on Plato's Parmenides (128a . Zeno does not use velocity in this situation. Why I'm wrong, or 2. if I'm not wrong, why the paradox hasn't been examined more carefully. The reason is simple: the paradox isn't simply about dividing a finite thing up into an infinite number of parts, but rather about the inherently physical concept of a rate. It is possible to iterate this to infinity. Then, Why Zeno's paradox is wrong? The key word in the previous assertions is "never". Nov 2001 The paradoxes of the philosopher Zeno, born approximately 490 BC in southern Italy, have puzzled mathematicians, scientists and philosophers for millennia. There we learn that Zeno was nearly 40 years old when Socrates was a young man, say 20. Some mathematicians and historians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution. Fletcher's paradox (aka Zeno's Arrow paradox). Zeno's paradox is called a paradox exactly because there is a mismatch between a seemingly logical argument that concludes that motion is impossible, and our experience in dealing with reality, which says that there is motion. This is just wrong. Never implies time and the problem must be considered in the context of space and time. Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides.
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