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20 Dec 14
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Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates.[3]
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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.[4] Some philosophers, however, say that Zeno's paradoxes and their variations (see Thomson's lamp) remain relevant metaphysical problems.[5][6][7]
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This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.
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adoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion. An alternative conclusion, proposed by Henri Bergson, is that motion (time and distance) is not actually divisible.
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ed solution is to question one of the assumptions Zeno used in his paradoxes (particularly the Dichotomy), which is that between any two different points in space (or time), there is always another point. Without this assumption there are only a finite number of distances between two points, hence there is no infinite sequence of movements, and the paradox is resolved. The ideas of Planck length and Planck time in modern physics place a limit on the measurement of time and space, if not on time and space themselves. According to Hermann Weyl, the assumption that space is made of finite and discrete units is subject to a further problem, given by the "tile argument" or "distance function problem".[31][32] According to this, the length of the hypotenuse of a right angled triangle in discretized space is always equal to the length of one of the two sides, in contradiction to geometry. Jean Paul Van Bendegem has argued that the Tile Argument can be resolved, and that discretization can therefore remove the parado
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ans Reichenbach[edit]
Hans Reichenbach has proposed that the paradox may arise from considering space and time as separate entities. In a theory like general relativity, which presumes a single space-time continuum, the paradox may be blocked.[34]
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at Corvini offers a solution to the paradox of Achilles and the tortoise by first distinguishing the physical world from the abstract mathematics used to describe it.[40] She claims
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the paradox arises from a subtle but fatal switch between the physical and abstract. Ze
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ns; C: therefore, Achilles can never surpass the tortoise. Corvini shows that P1 is a mathematical abstraction which cannot be applied directly to P2 which is a statement regarding the physical world. The physical world requires a resolution amount used to distinguish distance while mathematics can use any resolution.
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06 Oct 14
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27 Jul 14
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Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates.
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11 Feb 14
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20 May 13
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04 Mar 13
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12 Jan 13
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07 Oct 12
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10 Sep 12
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09 Aug 12
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09 Jul 12
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That which is in locomotion must arrive at the half-way stage before it arrives at the goal.
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19 Sep 11
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02 Jul 11
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01 May 11
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Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise
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Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there.
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for motion to occur, an object must change the position which it occupies
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in any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not
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If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible
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26 Sep 08
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18 Apr 08
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Proposed mathematical solutions both to Achilles and the tortoise, and to the dichotomy
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03 Sep 07
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27 Apr 07
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20 Apr 07
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