Javelin argument

The javelin argument is an ancient logical argument in support of the cosmological idea that space, or the universe, must be infinite:

:As to space, I need but ask you, how can that be bounded? For whatever bounds, it that thing must itself be bounded likewise; and to this bounding thing there must be a bound again, and so on for ever and ever throughout all immensity. Suppose, however, for a moment, all existing space to be bounded, and that a man runs forward to the uttermost borders, and stands upon the last verge of things, and then hurls forward a winged javelin,— suppose you that the dart, when hurled by the vivid force, shall take its way to the point the darter aimed at, or that something will take its stand in the path of its flight, and arrest it? For one or other of these things must happen. There is a dilemma here that you never can escape from. [ [http://books.google.com/books?id=GyQgAAAAMAAJ&pg=PA86 Google Books result] : W. H. Mallock, "Lucretius". John B. Alden:New York, 1883. p. 86]

This argument was used to support the Epicurean thesis about the universe.

However, the argument assumes incorrectly that a finite universe must necessarily have a "limit" or edge. The argument fails in the case that the universe might be shaped like the surface of a hypersphere or torus. (Consider a similar fallacious argument that the Earth's surface must be infinite in area: because otherwise one could go to the Earth's edge and throw a javelin, proving that the Earth's surface continued wherever the javelin hit the ground.)

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