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Zeno's Paradoxes and the Tile Argument
Jean Paul Van Bendegem
Philosophy of Science
Vol. 54, No. 2 (Jun., 1987), pp. 295-302
Stable URL: http://www.jstor.org/stable/187807
Page Count: 8
You can always find the topics here!Topics: Squares, Paradoxes, Tiles, Geometry, Parallel lines, Discrete spaces, Pythagorean theorem, Geometric lines, Euclidean geometry, Chalkboards
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A solution of the Zeno paradoxes in terms of a discrete space is usually rejected on the basis of an argument formulated by Hermann Weyl, the so-called tile argument. This note shows that, given a set of reasonable assumptions for a discrete geometry, the Weyl argument does not apply. The crucial step is to stress the importance of the nonzero width of a line. The Pythagorean theorem is shown to hold for arbitrary right triangles.
Philosophy of Science © 1987 The University of Chicago Press