Extension and Measurement: A Constructivist Program from Leibniz to Grassmann

Studies in History and Philosophy of Science Part A 44 (1):20-31 (2013)
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Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

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Erik C. Banks
Wright State University


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