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A ncient G reek philosophy, logic Also called the stadium or racetrack paradox, one of Zeno of Elea 's arguments to show that motion is impossible. If somebody wants to move from A to B, he must first reach the halfway point between A and B; but before reaching the halfway point, he must reach the halfway point between A and that halfway point, and so ad infinitum . Thus to move any distance at all, one must cover an infinite number of halfway points, which is impossible in any finite time. Therefore, it is logically impossible for someone to move from A to B. Aristotle 's first diagnosis of this paradox was that a finite time is also infinitely divisible and that will be sufficient for someone to move an infinitely divisible distance. He later decided that that response was not adequate, and claimed instead that the infinite number of halves is only a potential, rather than an actual, infinity. Contemporary philosophers and mathematicians are still inquiring whether it is really impossible to complete an infinite series of tasks; if it is impossible, whether the impossibility is a logical one or merely a physical one and what the impossibility really consists in. Many answers have been proposed, but none is generally accepted. “For we have many arguments contrary to accepted opinion, such as Zeno's that motion is impossible and that you cannot traverse the stadium.” Aristotle, ... log in or subscribe to read full text