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Zeno's Paradoxes and the Tile Argument

Published online by Cambridge University Press:  01 April 2022

Jean Paul van Bendegem
Jean Paul van Bendegem*
Affiliation:
Rijksuniversiteit Gent, Belgium, National Science Foundation of Belgium
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Abstract

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.

Type
Discussion
Information
Philosophy of Science , Volume 54 , Issue 2 , June 1987 , pp. 295 - 302
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

This paper has been written during a four-month stay at the Center for Philosophy of Science, University of Pittsburgh. I want to express my special thanks to Nicholas Rescher for this unique opportunity and the Commission for Educational Exchange between Belgium, Luxembourg and the United States for a Fulbright-Hays grant. Thanks also to Michael Redhead, Wesley Salmon, John Norton and Aristides Baltas for helpful discussions, and the referee of this journal for his or her invaluable comments.

References

REFERENCES

Rogers, B. (1968), “On Discrete Spaces”, American Philosophical Quarterly 5: 117–123.Google Scholar
Salmon, W. C. (1980), Space, Time and Motion: A Philosophical Introduction. Minneapolis: University of Minnesota Press.Google Scholar
Weyl, H. (1949), Philosophy of Mathematics and Natural Sciences. Princeton: Princeton University Press.CrossRefGoogle Scholar