For example, McLaughlin claims that Thomson's lamp is inconsistent if it is analyzed with internal set theory, a variant of real analysis. Philosophers who reject their possibility tend not to reject them on grounds such as Thomson's but because they have qualms with the notion of infinity itself. Most of the modern literature comes from the descendants of Benacerraf, those who tacitly accept the possibility of supertasks. However he disagrees with Thomson that he can derive a contradiction from this, since the state of the lamp at t = 1 cannot be logically determined by the preceding states. Benacerraf agrees with Thomson insofar as that the experiment he outlined does not determine the state of the lamp at t = 1. Paul Benacerraf believes that supertasks are at least logically possible despite Thomson's apparent contradiction. He concludes that supertasks are impossible. He reasons that it cannot be on because there was never a time when it was not subsequently turned off, and vice versa, and reaches a contradiction. Thomson asks what is the state at t = 1, when the switch has been flipped infinitely many times. At time t = 0 the lamp is off, and the switch is flipped on at t = 1/2 after that, the switch is flipped after waiting for half the time as before. He considered a lamp that may either be on or off. Thomson believed that motion was not a supertask, and he emphatically denied that supertasks are possible. Much commentary has been made on this particular paradox many assert that it finds a loophole in common sense. While these distances will grow very small, they will remain finite, while Achilles' chasing of the tortoise will become an unending supertask. This continues, and every time Achilles reaches the mark where the tortoise was, the tortoise will have reached a new point that Achilles will have to catch up with while it begins with 0.9 metres, it becomes an additional 0.09 metres, then 0.009 metres, and so on, infinitely. He instead suggests that Achilles must inevitably come up to the point where the tortoise has started from, but by the time he has accomplished this, the tortoise will already have moved on to another point. Common sense seems to decree that Achilles will catch up with the tortoise after exactly 1 second, but Zeno argues that this is not the case. However, the tortoise starts 0.9 metres ahead. Achilles chases a tortoise, an animal renowned for being slow, that moves at 0.1 m/s. Suppose that Achilles is the fastest runner, and moves at a speed of 1 m/s. Zeno himself also discusses the notion of what he calls " Achilles and the tortoise". They accept the possibility of motion and apply modus tollens ( contrapositive) to Zeno's argument to reach the conclusion that either motion is not a supertask or not all supertasks are impossible. Instead, they reverse the argument and take it as a proof by contradiction where the possibility of motion is taken for granted. Most subsequent philosophers reject Zeno's bold conclusion in favor of common sense. Motion is a supertask, because the completion of motion over any set distance involves an infinite number of steps.Zeno's argument takes the following form: Zeno further argues that supertasks are not possible (how can this sequence be completed if for each traversing there is another one to come?). Thus it follows, according to Zeno, that motion (travelling a non-zero distance in finite time) is a supertask. However many times he performs one of these "traversing" tasks, there is another one left for him to do before he arrives at B. To get from the midpoint of AB to B, Achilles must traverse half this distance, and so on and so forth. To achieve this he must traverse half the distance from A to B. He argued as follows: suppose our burgeoning "mover", Achilles say, wishes to move from A to B. The origin of the interest in supertasks is normally attributed to Zeno of Elea.
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