Logical Paradoxes
A paradox is an argument that derives or appears to derive an absurd conclusion by rigorous deduction from obviously true premises. Perhaps the most famous is Zeno's paradox of the runner, who, before she can reach her destination, first has to reach the point halfway there, and who, before reaching the halfway point, has to reach the quarter point, before which she must reach the point one-eighth of the way to the destination, and so on. The conclusion is that no runner ever reaches her goal, or even gets started.
To contemporary ears the argument does not sound so irresistible, since we can attribute its appeal either to an ambiguity in the use of "never" ("at no point in time" versus "at no point in the sequence") or to a dubious hidden premise that it is impossible to perform infinitely many tasks in a finite time, perhaps because there is a positive minimum to the length of time each task requires. To the ancients, however, the paradox was deeply disturbing. The most influential response was that of Aristotle, who concluded that it was not possible to partition the runner's path into infinitely many parts. Any segment of the runner's course can be divided in two, so that there is no finite bound on how many pieces the path contains, but the process of partitioning the path never concludes in a path with infinitely many parts.
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