Atomism and Mathematics

Atomism and Mathematics - Atomism and Mathematics Its...

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Atomism and Mathematics It’s possible that Democritus thought not just of matter, but also of space in an atomistic way. That is, the size of an atom would be an atomic space . In such a system, the ultimate unit of measurement would be the size of an atom. Within that framework, the very notion of half of an atomic space would be unintelligible. So, Democritus would be able to say, coherently, that an atom has size even though it is theoretically indivisible. a. The Weyl Tile Argument : But if Democritus “atomized” space in this way (as he very likely did), he runs into another problem. For Euclidean geometry (in particular, the Pythagorean theorem) requires that space be continuously divisible. Hence, if atomism denies the continuity of space, it will fail to get mathematics right. Why is this? There is a famous argument by the mathematician Hermann Weyl (the “Weyl tile” argument) that clearly shows what is problematical about atomistic geometry: Consider any geometrical figure (e.g., squares, triangles, etc.) with straight lines as sides.
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This note was uploaded on 11/14/2011 for the course PHI PHI2010 taught by Professor Jorgerigol during the Fall '09 term at Broward College.

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